A bicycle odometer (which measures distance traveled) is attached near the whee14+z ma1 hiytcjw 4c9o /7twexl hub and is designed for 27-w4iw t4 7myo1ez ct/ca+hjx91inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates n 6/u hb dc poh-)gr5:j urfq(xylk5:.at constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would 5.-u (pxj5 q:rduhl/) 6k:fhyro gbcnthe magnitude of either component of linear acceleration change?

Could a nonrigid body be described5cw+,v5p) j4 m z2t/ ardfrrkq by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Exp+ekl6dw- sht,q9(fz ylain.

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 difficult to do a sit-up (g1dh le7km,twith your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to ans m1k,dglthe 7(wer this.

A 21-speed bicycle has seven sprockets at the re:fx4 -psh8ge+k +iiv xar wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprock: ix sfex8-v4pik +hg+et or a large front sprocket? Why?

Mammals that depend on beink +lq)02cnie hg able to run fast have slender lower legs with flesh l)q0 c hk+2nieand muscle concentrated high, 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) carry a long, narrob5,p8a* vnrj.cv- 3dmnxr z vv)9vr o*j.b0 onw beam?

If the net force on a system is zero, i a*8 rub/d8c( .+zj jyboav5nco6p0k is the net torque also zero? If the net torque on a 5vnk p ba0dj 8+r(b.oocia *u 8jy/c6zsystem is zero, is the net force zero?

Two inclines have the same height but make different angles with the hor r4dvhmd i0,:hizontal. The same steel ball is rolled down each incline. On whichr 4vi, 0mhdhd: incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rollingr 5,xv wi0kep0 (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reachesp0e v,wkr05ix the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start f lzg:j6bia79s a-zyp;r .y0ybrom rest at the top 9yzrjal; -s 7 z:.yb a0byg6ipof an incline. Which reaches 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. Yed u:g( zukit- 0mz*i88 jm,wyct most moving or rotating objects eventually slow down an* uu,z 8tm zj :c0ygi(kdwmi8-d stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wou, m7opc,en p7z2qhuv7v0f. 7 u7gmxdhqquw*7ld this affect the ln7c 7exp mzqogqu7q*v2du77fm uw70,hpv . h,ength of the day?

Can the diver of Fig. 8–29 do a somersault withoux8;(p6 h 8n/h hgmmyixt having any initial rotation when she leaves thm/6in8;g8 xp x(yhmhhe board?

The moment of inertia 0+vo ovf fj+eid8qt0-of a rotating solid disk about an axis through its center of m+8i ve0 f0+jtqf- oovdass 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 sitting on a rotating stool holding a 2-kg (6ksqp8hb6 cv mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or sb(hq p8kc 6v6stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hol zed0(e un;3twlow and the other is solid. Describe an 03en;deu(z tw experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In w;chp a u5oxy)9hat direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decxaohc; 5)pyu9 reasing?

Suppose you are standing on the edge of a +ig-opw(uq9u large freely rotating turntable. What happui(+ up owqg9-ens if you walk toward the center?

A shortstop may leap into the air to catch a ball and 0:kz ftiwa3qn ev 3u8s to9*-9ri zzi,throw it quickly. As he throws the aw-,uz 9sikz3 9v3 0ezfq8nt i:it*ro 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. 8–36). Explain.

On the basis of the law *whe6 dohrit+c 74l.zof conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propelle7wr* itd.o hl6z+4hce r can operate to keep the helicopter stable.

  Express the following angles in radians: (a4gxewgv:c.o; (2 uapd ) 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 Earthl-4 te (b,8zihbdzmi ( because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians db4i ilz(8ez-(b,t mh) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from b;jp 4xf otc30Earth. The beam diverges at an angle 3b0pjt;4cfox$\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotavzu::j:be1+ r9ss 3t3 zww pdlte at a rate of 6500 rpm. When the motor is turned off dud z 9:1:w+rv:bjzws3 3tu peslring operation, the 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. If the 2nye6rk eag1fpah: e 6/oxzju 8458cjball makes 15.0 revolutions, what ia8z1e:h eyc ufr62/ke4pj g8o6jx5a n s its diameter?    m

  A bicycle with tires 68 cm in diamz /7nhwd.p l 6nts(d1leter travels 8.0 km. How many revolutions do the wheels make? .d6l/l1swnt( d7zh np   $rev$

  (a) A grinding wheel 0.35 m in diameor 0*e:on*qaswa8o/bter rotates at 2500 rpm. Calculate its angular ooe0o/n*a*8 r sq w:bavelocity 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 complawq mk*01pa.y-)w ha pete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 mywa-k01)qp hwma p.*a 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) in its orbit around the0;omyzc z 0dep95m,t 0sw hg(d Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spehdbq;ik.v73 d ed of a 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 rotate if a particle 7.0vy-9.tgte zs;dy (c.k cm from the axis of rotation is to ty yg .ck;sedvzt-9.( experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 13j )u twhd2z y62rc7i*.dl*h yo0 rpm to 280 rpm in 4.0 s.**6d ly7 2zcd2wruhj)y i.hto Determine
(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 radiustrvg :0.biz 94n s ,:hfcfpf*v $R_1$ 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 themselvese2mb x q,1 3fprx:feshy /5*ej into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thouxh /r:f3 pjmy,2*5e1 sbfx qeeght 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 uniformly fromf2j/ 41 u fj6b typxi,8p g+u6eqtwwi4 rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this timejq/gf1wtix6p82 6u4u+f ,4tepwbjyi?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm iniy 6cpx:krrj3 /fn9epj3e+j- gte e4 smq)9.l 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 e sc)z9 otjeft5 q.x32jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete fj tcos .3e)qt9ez52 xrevolutions 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 uniforg1sydiui2/4d .d w)sy mly from 240 rpm to 360 rpm in 6.5 s. How far will a poi1 sy/d4g .i)w2dyd siunt on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1509iljm g38v)temlre6t d6l *.l0 revolutions before it comes to aje rml3 ltge6l6d *l)i. 9m8vt 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 its spee3c jm8.8h gvnx0 fhai+d uniformly from 95km/h to 45km/h The tires havgh ni8jhmc8f+x03. a ve 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 iti0 *.6nli5gx;h inri is speed uniformly from 95km/h to*inhxi 0. in i6;5ligr 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

  A 55-kg person riding a bike puts all her weight on each pedal when climbing6a 1t29m u 4qv zx3uh4mv8awutw; w(bs a hill. The pedals rotate in a circle of radib2uua4 4s v8x wm wwmtt3 1q6zhv(;9uaus 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 th9vxjkya6ldl 3*d) t9v e magnitude of the torque if the 6 t)xv3y j9ldlvkda9*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 axle rb--s koxmn1-of the wheel shown in Fig. 8–39. Assume that a fric-o -rx -ksm1bntion torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, a7 hul2y/0naq4n) -*efainwj vre attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of 7ny )* jwevluna402- f n/qhiathe net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a t( 3nnpkdj t)2iorque of 38 2j)d3tnink p( $m \cdot N$ 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 when the gj:/roh3s9 fz axis of:frz 9o gj/s3h rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycl4 q*vaactz1vgzyo6s(bew3m b(* 8a0l e wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub ct(q1 zvg 6*c 3a4ose lba0a(ym*wz8 bvan be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a hori2st-9 02 y3rqjybrtqec9z) nlzontal circle of rtc-eytlz3 js9r2 0 rq9q2 ny)badius 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 poso8x,ka j2 ,b9d(jc6ms nep(ngo)3dytter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N to, )k 8b9p( xs6c ejsmd32,daongnyo(j tal.
(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-4+ a wh9heldw8 j5wzp objects shown in Fig. 8–43 abo8al z dje9h-w+4w hwp5ut
(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 atoms whos ttsv4pgi2 0y0e 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 tf865 b3jl y1lkfzx h:nhe correct rate, engineers fire four tangential rockets as shown in Fig. 8–446y5zl1fh kj nfb8 x3:l. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the 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 vl, /uy: r(snmbufcm*z,((abuniform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Cal( bl a,z*u:y sr vu(/cm,f(nbmculate
(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, acceleratin p-mwcwfd(+4yer*rp+ g 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 small hand-drive dpphuh7 oqm2 x/q+42qn 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 unifor q2m/+ u2hdq7opqxp4h m 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 frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor row,y*mv wt u-o/zf+ep q rs2;q)tating at 10,300 rpm is shut off and is eventually brought uniforw wqp usym,)vetfo 2-*+z;r/qmly to rest by a frictional torque of 1.2 $m \cdot N$ 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-kg ball abwo ikw c4,a+:t 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 the action of tfs9rg/ 26mdtkhe forearm, which rotates about the elbow joint under the action of the tr/k g9t2rs fm6diceps muscle, Fig. 8–45. The ball is accelerated 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 long thin rf7to;y( 6gr diod, as shown in Fig. 8–467( 6ryfodgi;t.
(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 consis;,l2von5yc:b9wrd cp2z1m b,p dv -umts 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 accelerates the hammer from rest within fu.jir8c qlb uu2td1nq.4xydclb. /7( our full turns (revolutions) and rjqq xu.u.(t 4i/clbyu.ld8nbrc17 d2 eleases 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 of inertia oh c pcb3:w:y e7ol*pi 79ay2saf $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops anw;;jb5z)m gj *c nz+l 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 ikhzv(-zoew+ j 31c0sradius 9.0 cm rolls without slipping down a laic0 jhz z(kos+v3-w1e ne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the3w k zp c z 0lr4jf2ev:y)iyv/ir*yh.3 Earth with respect to the Sun as the sum of two tereiv yij zlf r ck2zhv r3*3yw4:0y/)p.ms,
(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 oj6u 8)ic wq sxr;p6)lhf 1640 kg and a radius of 7.50 m. How much net work is requ6scux i)6w;pr8 hlj )qired to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts f+na u(v)td7yuxr 8fp0- + a cnluy2y:brom rest and rolls without sli-80xy:2r v npu7a( b )a+uytyd+ufcnl pping down a 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 is balanced vertically on its tip. It starts to fall and its pu tbtm7u13/v lower end does not slip. What wi/upmb37 t 1vtull be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating w,pd/cjn.r g- x 1xfy/g (yvn.5: vnv23kyvlbon the end of a thin string in a x,v5: pnyjg vk/ngvl3b/vdy.cf (n-.y21wxr circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-k 4r;; 0zp(k/i yem,vlvb5qs-nb-ecdxg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm? 4d -;,i/kn5 qye0-vr (xmlszbp vcb;e   $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a8gfh94 blb:)n sxu 9nu platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the sp gnn89shx)9 f u:u4lbbeed 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 sriv 0-ubj 0 cdlv2qf,x6 px34qhown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight6i4 rv up xd3ql0v,0-qfjc2xb 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 rotec*zyk; qa;a( ation rate from an initial rate of 1.0 rev every 2.0 s to a finceq *;ak ayz;(al 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 around a vertical axis through its.makqvc.u3z1hunx r ; 52 wan2 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 shaped as a flat disk of radius 8.0 cm, onto the center of t2;x aw .zu1n hqa c53.nu2rmvkhe rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a *ge-gnje: n,dk ts(;3ay sfs+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 angularn b a 6*;a42s +ed,;csfqezrkv momentum 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 v:4sfi1mq43czvxb h5 of moment of inertia I is dropped onto an identical diskqz 341xif4 cbhv5 :vms rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ai0-. *mn nutrr ju9y e/ivp+jjl*k*t; t 2.4 $rev/s$ 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 stands 0xa7u)e ; lw 5lea*6yq6 vxquo,b)wyy at the center of a rotating merry-go-round platform of radius 3.0 m and mo uwo vu6b l,06q);way) 7a* ly5qxyeexment of 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 rotating freely with an angular gbfo at 5 c(tq)tm1x(2velocity of 0.)2o(ct gtbf5 mq1atx(8 $rad/s$ 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 eventually collapses into a white dwarf, losing about half its myx c-42e739oq+qworn hjst k *ass in the proces4 qwyt+e9nrxhk q23 cosj7o *-s, and winding up with a radius 1.0% of its existing radius. Assuming the lost 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 4 pjj.m4rqy/vwinds in 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 sf+pib ;loo; -a qfieoo3b.o8 7apc-,$ 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, that c pfirdqbhxbl( a+m6ggk)ap 9,8e+.c -an rotate freely without friction. The moment of inertia of the person beg+ d6xia 8r9-kfq +mhp).agl(,bcp plus the 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 stanscr *w9;fg g;3ed)kr n9sqy6cds at the edge of a 6.5-m diameter merry-go-round turntable that is mounted ons c3d g w96;;sgn9frrk)ce *qy 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.b1:r n*tam kk rolls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the persnb:trk1a *.m kon 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 same side always faces t*: 5 nsbxdwve)he Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital *s xdnwb5) e:vangular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rh( xm,,.shh+lpy*vjt n4,gb p nem3m6ate 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 uniforvya;.by8d , gc+ kh6dym cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular ,bhaygydv ; ck6+y.8dacceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of tw((pi m8eq(x1 es6 s /-letakhlo solid cylindrical disks, each 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. Use8tee ( (/q-lmpe16ikh x(sals conservation of energy to calculate the linear speed of the yo-yo when it reaches 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 speevja90t r- 5kbnd of the rear 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 wit)1yv:9b js kx0n+a4 uzs drsd4h mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo j14snsb d:0x)94szau ykvrd +gravitational collapse to a neutron 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-v,n c371 *u3u7pnbcuxxqjx 9upollution 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 cylindrical flywheel of diameter 1.50 m and mabncq 71pj,c u*7xu3vux3un9 x ss 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 illustrates awe6(ku l4ofbv(swr ljj1 /6.j n $H_2O$ 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 horizontxqoz6g 91 *jiwfg4jebx. 89yg al surface at speed 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 freely (i.e., we ignore ff,z3.fp v *svdp 4rx0oriction) 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, determine (a) the angf0pf4*z,o3.rxp d v vsular 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 d3i,) 0a,sfpbxva +riR. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step againi,,x0pi)db 3sfa ra v+st which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn witdafoa*rnec0tx2y( kf -v+2 e 4h a radius The forces nd -2ercf2t f(k y ave+xo*0a4acting 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 r0 lfa ltg.k8wtai ( y)whq4,/3wekhf; ock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque rekg(h ie /w,a. y0a;tlwq)hltw4k3ff8 quired 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 rods, oi xei*9- :7stama,to+k 8 hpmmaking reasonable estimates for the dim+ea i:-9oos t7*hxpkt m8,a imensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical platesv z fo 4q6o5 8.rcwvjo0x.64vthi u:df, of.xq:i 58vc0vou 6 .z6 orh 44djvfwtof mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 Fig. 8–58.;f5lr5+d8uumwk-rjc c -p6hfn i*c7 d What is the minimum value of the vertical height h thpcr-6 id+w* ukc- 5jc;nm f5f8rlh7duat the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but+rvoto 0ij: zro5 q;(b do not assume $r\ll R$ h =    (R-r)

  The tires of a car makesyyyk,sc :w 4: rb86ma 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.906,sw yc8kbyayr:4s : m m. (a) What was the 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