A bicycle odometer (which measures distance traveled) is attached near t0p/ g:lwyj:cvv,pm)c he wheel hub and is designed for 27-cp)cl:,ygjvp: vm0/w inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant )v- fh3(issza angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases (vf hz-i)s sa3uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular velomy fn40o/,j s-hv+c 5up.pdrt4noedp 7bh/n+city $\omega$ Explain.

Can a small force ever exert a greater torque than a larger for;pmtx /*gq; 8q tikhpj8(f6g d5tijs/ ce? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficul drsd7z*ly+ hd1m qpv)l41x/ lt to do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram * x1 hsdr)7m/z+d4y1lqllvpdmay help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and thrh.2 l5duisi2zoa ink0 (ao 1;vee at the pedal cranks. In which gear is it harder to pedal, a small rear spd i0n. ;vi5(kliz uha2aos o12rocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on beip2/yld:2ji 4 r oj6kkwiitx-9ng able to run fast have slender lower legs with flesh and muscle concentrated hiy224itp9/kxlki jw :do6i j-rgh, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carr4ccer8u ggy23r0 u35+l zpckhy a long, narrow beam?

If the net force on a system is zero, is the net torque1ifan 0cyme x 0n7 el5hln824a also zero? If the net torque on a system is zero, is the net8l0ln ni7hm5ex ca0 e4 21fyan force zero?

Two inclines have th1m16 al4cd;/s f;ujdxfwu 3i ie same height but make different angles with the horizontal. The same steel ball is rolled down eafm w/li6 cfsa d; ;411uxdj3iuch incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down z )vtd -wl7l/man incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic enlz7-m dw)lt /vergy at the bottom?

A sphere and a cylin1f4rlnugbl 1je/t e0kj v( m++der have the same radius and the same mass. They start from rest at the top of an incline. Which reelg114b +j0mf /rkvn(ejut +laches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moz8 clse) 6lt2xving or rotating objects tl)e26cxl zs8 eventually slow down and stop. Explain.

If there were a great migrah-) ) qfchnuf)tion of people toward the Earth’s equator, how would this affect the length of the da )fu)h)-f hnqcy?

Can the diver of Fig. 8–29 do a somersaul t4c.qg.dj9 -t pe 9sadj;igu;t without having any initial rotation when she leajap-9;d.4.; 9gutjgsce it qd ves the board?

The moment of inertia of a r6e9* (dolq:: tnsip6d5wp k dkotating solid disk about an axis through its center *5 tdwsl(qp6ki6kp::o dd 9neof mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitt jt*uqb6 gp lbi(re1 rm-1+f*ting on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explainlt 1perb ** 1r+i-bu6 fjgmt(q.

Two spheres look identical and have the same mass. However, one is hollow ankxum i4l 6g95hd the other is solid. Describe an experiment to determine 9ih6xlkgmu4 5which is which.

The angular velocity87 ca:5te0p2)x xqond(8 u2riz cxwgg of a wheel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If t5:o2gdu(cx2q )xc0peg ix zr 78n8awthe angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the+ x 6 vum dlmzs5p)q:xn/:x *nyj7new* edge of a large freely rotating turntable. What happenxl qmwxxv: 5j*pz:mu7)*+s/n y6ndn es if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly.n6)a.t3bhxl+/n(fq tb h6dn p kqq9k; As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8p(n dx;.qkhbn) n69 tfqql t/+k h63ba–36). Explain.

On the basis of the law of conservation of tvc5 :*heh z: ioee(0sangular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicoptetee: h*5cv:o0 hez(sir stable.

  Express the following angles in radians: ( :w2g7u7;lxsp9pe vv ya) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. C b/dctq6j65ahzv44w galculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen4z6v 46gbqc jwd h5ta/ on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at theg6eq6mr zi*)q h1kd)*)bz sz d Moon, 380,000 km from Earth. The beam diverges at an ang61 i 6)r)mddbeqzsq)kh *gz*zle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender x tmjb)v7.25fjs ;zpa rotate at a rate of 6500 rpm. When the motor is turned off during operation, thbs;v5. mt2)x zp7 jfaje blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. /wz; woejwe *d 99gn*nIf the ball makes 9 *w9;zw j*od wn/eneg15.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km.w lw swcp3pzsap*h0( 8)pf 6n5 How many revolutions do the wheels mhw0( s8 )ln* zfwppwpc36ps5aake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate crse) /y*ygx.d gs( w:its angular veloc*:rcw yesxy .d s(g/)gity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.06o6a8+lx nl 6i9o.0g g;symzc 3 hgu *vishst4 s (Fig. 8–38). (a) What is the3loguog6s*gl0 a+m9ivyz c xs4h t.s6;h8 i n6 linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) ibdrq/os4 aj7yab*c1to 0v6 2w n its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a4osztit .sg5:m 6;u ra point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotat fw 73(cfm2vz.k+jxu ze if a particle 7.0 cm from the axis of rotation is to experience an acmk 32vuj7f.xw ( +cfzzceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accel w7 dspi6k6;xxerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determinep67k xx6iw;ds
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiug39tkcyt .ts3+)h cwj s $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put ths b+g h8)arech87 2ab 9wv:ghpemselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rota pcsahrw+8eb8g)g2h9a :hbv 7tion to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformy7kto(kj6tf;qr8.j hp 7cc x 9szz6f6 ly from rest to 15,000 rpm in 220 s. Through how many revolutions didjotx9fjsf6h kzrc c7k t;( .786 6ypqz it turn in this time?    $rev$

  An automobile engine slows down from 4500 i+b/ml,-ee ubkh9wy) rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirli1qfmzl ) ouqw ho1 ;tjaw3t09kd7 ;4dyng “human centrifuge,” which takes 1.0 min to t o) 3uwh1t1 q7;m0fao 9dy4z tlkj;qdwurn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6.g +ncanwwav9br3y; +l0 yk,e+5 s. How far will a point on the edge of the wheel have traveled in tw ck9;l n+ ea3agybv+yr0+ nw,his time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 150)9f3smfzc;mwqykwy4 l/8nd 242 fh bw0 revolutions before it comeskm42fsq lw 2;w3mc9y8n /zb f)yhd4f w to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces itsl2bf 9 cm5.rqn speed uniformly from 95km/h tolfc5m rb 2.qn9 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly fr0+cub 5j1ey9y xy+tqgty e,i+ om 95km/h to 45km/h The tires have ueg b +t+5e1yyy,+y0cq 9 tijxa diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike p a0bpsrtrpbksim(1a- ;j, r7;uts all her weight on each pedal when climbing a hill. The pedals roakja0s , tp1b;spb(; -rrmri7tate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is p mnh7n86;thn f 9b2yrthe magnitude of the torque ihm2p9h; y8 6 nnf7brtnf the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axmuht6q /p* q0lle of the wheel shown in Fig. 8–39. Assume that a friction torque of plum/60t h*qq0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a ma7.jzkvu9vi *uk l .4:n bhmh7*ls) ynassless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate thevn9*u:zl*47kksh v b l ih.aj).unm7y magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tig1n(h;+tkr /y.rh lbpd v0:f gehtening to a torque of 38 ( kr0e.dvph/h1ntf:+ ybgl; r$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m wce- uh v*t8z0rm6jm *dhen the axis of rotation is through cvm-h * *rj0tum d86zeits center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. T+9g u f0jlch+khe rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (flghu0+ ckj9+ why?).    $kg \cdot m^2$

  A small 650-gram ball onert4zs5c6a 7 j the end of a thin, light rod is rotated in a horizontal circle7j t rc6sza45e of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a psu mtt(, 2qs(lrfv x8/otter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between/xmlf(,vru(8s2s tt q her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown 3b:dq;9iot) fgba2p p-k3fhlin Fig. 8–43 aboof ;ab -l3kb9h qi)t2fp3dg:put
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen a,i f ;k:(hyjobs e38mutoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correcwi ia/.od+6 x/al 0a;9xvb yuat rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is 6i a.9i d/0av; b/yxa wxal+uothe required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cyquf2trgmv nu d;3w.*6fki6r 5linder with a radius of 8.50 cm and a mass of 0.580 kgtm*g 5n r;fqv6r6k3u2fudi.w. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, bhmzs f.ldhrfs+(/y mt6ni3 5;-l3sk accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a smb) phjrb(:;3xqtg9n1i fl;m y all hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictioi t 1plmgy hxj9bfb ;;(3:)qnrnal torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotatingny(92e lv +sqb at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.2yq9+ lve(ns2b $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6 lg*x7lx cd;m y:i6r2p-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by tht0 k ybt j)aap-+zltvh(074gde action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is a-py0)7 kat4b lahztd vt0+jg(ccelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a lonmln7arto d0eniii06y5 y1 5f-g thin rod, as shown in Fig. 8–46mir i7ile0a-n56ny oy d t0f15.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consis1 vg4wn + cqkpqpqm*i9d0i:yo03e8tp ts of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower acce71l5f.hxn1 v4ko;2g s sidnd-4 k*tz vmuhto3lerates the hammer from rest within four full turns (revolutions) and relfli -. zn 4k 7o53;v1d xg hsm2vunhsttdo*14keases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment op.:1swd9rrsk5 fcla+u/uin :f inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develophenmc 9puj7dp.+8citc7 )1 pxs a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rollsg2 jj0kn)co3ve 0v at5 without slipping down a lang2 ej0nt oj)53kva 0vce at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the S. dcq4om(*:, ss thu k4h8axipun as the sum of two terms,c(4,ki xhhomq8tup4.sad * s:
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m.5zd:u5 c q) bdd7rl86lx*hyxb2u 2d dj How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution 2u86q 5 7ddldd bhclu:z 5xx*2ydjrb)per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm andbq. 76gzsyp(i1j h y9s mass 1.80 kg starts from rest and rolls without slipping down a7zgsys. 1 ih(6q 9ybpj 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole i :wh+jzj1gqpi)a z 5 :oxvfk54m. 2jils balanced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use consjq j2)k5i+p:4 wzlm ih:azvx1go 5.jfervation of energy.]    $m/s$

  What is the angular momentum of a 0.210-vyj :oj, 1ruw4(4h9mpfuvf gm5ktq 1 dr 1*jx4kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 1*rwvxp m41 1yj1 rf ,oj4um fqj5 vtg4(d:huk90.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular m0 ke/0a j9inkrw(po7 lomentum of a 2.8-kg uniform cylindrical grinding wheel of raap0(r 7iw/k le 0ojn9kdius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a rate on+a1zmtz8tb e t2kuf(x6 *dbs-.sm5mzk h(3 s f 1.3rev/s If he raises his arms to a horizontal pos((k -ts1ze.m +bsank*fmbu5tdxmz3 8 2h6tszition, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown ye2( t9-e, ozorxn+ :+qsha9eta wm g1in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the strhex z 2+y-n1astw9m+oo:(e9er qtg,a aight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initialp wz2t0jz :jt) rate of 1.0 rev every 2.0 s tozz0t2wp :)tjj a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating aro7b.3 pw -huroiund a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaperwbp37uo-.ih d as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentuj6ihq/ml;wgf tnd(p1+* (x qgm of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular mome-vonyqtl4y42w0 t8c rv+xh:e3ovj d6ntum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropif0 cw /sgvm:)ped onto an identical disk rotating at angulv):ms0w f/cg iar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2d+*equ9l8vu.1 ljeos .4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg 4e0xtl scz9o ,stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment lx0e94,zto s cof inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating82 faow.ms :s vsuw*y0 freely with an angular velocity of 0.8 mfvu:wsy20wa8.s* s o $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventualldqpy+s kunw5;o s8e )6y collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the 6+s8p dy ow)k; uneqs5lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds ih1ba ;)z3cx/p a*dkean excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass 0,0 lw(uex o) lwvkkq9$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, tha pnl 1ig1.t11oc jgqr+t can rotate freely without friction. The moment of inertia of the person plus thl 11cinr g1j1tq.go+pe platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-round td igj+gu2 gur2 +4p ;q62yylzfurntabley2;g gr24+2 iy uu p+flgqdj6z that is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of them7 v:zr0-cmmy y/j.rb rope lying on the top edge of the spool. A person grabs the end of thevr7ry0.z/ byj-:mm mc rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the sam,tsg-f-cfe: 8s 0qonje side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.) s-e-f 0s8c nqo jf,tg:   $\times10^{ -6}$

  A cyclist accelerates f: d*uoq zam4 mt4qcg.;rom rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acqui) wmy,:egvge2 q3qzxu2vd,0 ires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by thz,0vdi)2 wvqem3q,:uxygg 2 ee motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, 8 zs c(kg,kreqc)32-/quc jh 4maj8x qeach of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it r js2e zc g q-mqq u3k/jxcah,84)8rk(ceaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the refkp7c.rc*s weq7uv3p 0p-w e6 ar wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.e8w )j- vgb ;e ih/*kclha(0uh0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a ne;h ebl v/caiw 0he*()k8ug- jhutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollutd0(zi vce 7b92 p/isq-k,dsjrion automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform-s 92d,zrjcq(v7k 0 i/si pdbe cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustratesax 96ln (o g:u0 uq.ddj:qa/1l1vuhjp an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at tww*e9ocl60hyjm y/ovf 70 *tspeed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot idzpz l 80fcnn+; by(3 7jw)zmzlb0jl/ g2 it1freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, 7znz8 y+bwt 31dnpjll f/c0) lj z(0g ;mb2izidetermine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is stanbjy b djt* 82(zms 3.owofuv4c(o/k4jding vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it re*3ojz(ofbj4d/u42(w8mjy.s c kt bvo sts (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with spy p- leh,1op/: n)mkyj ef,(qjeed v=4.2m/s on a flat road is making a turn with a radius The fohf :jn/ o)1y ,-emqpekj(pl y,rces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock int(,hewn u 6p3hvo a sling of length 1.5 m and begins whirling the rock in a nearly honv, h eu63pw(hrizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rouhiy o9w1iii2+ i bm:5ds, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly oymiwi 59hui+ bi:i21 against her body.   

  You are designing a clutch assembly which consists of two cylindrical xv3 )7odn/55actma:ho3 zjre1vhvd 1 plates, of ma)3 mtj e:o v3n 1va7a1 d/5cz5ohhrxvdss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fg3.nz(pm soql1l d4u s)3c jb6ig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without lea o(.spqlcug nj4l)63sd3zb 1mving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not asj8j g q bajkfdx (o52aycci il1,/0:z8sume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revoluth*kv2gq p5d h/ions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the h/h5pk*gvq2 d angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s