A bicycle odometer (which measures distance trav*y1i)lnm:w8/5 z/jme pnns j eeled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch mm nney */) ziwsl/nj85e j:p1wheels?

Suppose a disk rotates at constant angular veled) -sx9 h:kc yl/kz7(ux(lgcocity. 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 woul lk ecdxy/)(:9l h(kzgx-cu7sd the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single valuf6zd:d8af psxea l(dhf 5f)twu2(e *9.k +ya se of the angular velocity $\omega$ Explain.

Can a small force ever ed0f8epve ie 36ut.(paxert a greater torque than a larger force? 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 difficult to do a sit-up with your hands behind your head than wh x nlg*vs6 bj:,szr63zen your arms are stretched out in front of you? A diagram may help you to ansrx s*6, 6lbv 3jgz:nzswer this.

A 21-speed bicycle has seven sprockets7+el7/6uvvpvks(m sh w7drvb ri*z42iq 8k8h at the rear 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 it7 (d*r74 sm vp8h urlezv67/qi8is bw2vv+hkk harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run ftx -xl5od j)i.uj( nr2 y2zg.dast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–3in .oz dlyjrj 2t(x.g)-5u2dx4). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beaaaby 886dqu s(nmc r5 aj1 n4q;k.btu*m?

If the net force on a scjw0p ih8,ka, ec py19ystem is zero, is the net torque also zero? If the net torque on a system is zero, is the ny18,pepw cc k,j9a0hiet force zero?

Two inclines have the same height but make differy/rk5cjp/rc 6ent angles with the horizontal. The same steel ball is rolled down each incline.krc/yp 6cr/j 5 On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneousdg+4r5qksbe(fn tfo*4hpte),ib 9b knd9 +e- ly start rolling (from rest) down an 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 n*pe4btio +gt 9 ,5)fr kdqb+-shn ed4f9bk(etotal kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the * (afig-wgi5wsyn6 r* same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has th*gw sfw(56iaygi -* nre greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yethhti(c6y*l+sb )*7ghc i lcv; most moving or rotating objects eventualhly7cbih*c) his6l +*tg(;vc ly slow down and stop. Explain.

If there were a great migrationjw;hp9.efw z 5 -fn)tz of people toward the Earth’s equator, how would this affect the le t 9.enjfw5;hpz) zwf-ngth of the day?

Can the diver of Fig. 8–29 do a somersault without having ax2 n 0/xrb.fefny initial rotation when she leaves the board?f b 2xr/0nf.xe

The moment of inertia of a rotating solid disk about an axis through itgen(z5m-rd 9gp26n ums center o -m96g 2zrum5gp(nednf 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 sitting on a rotatin khx/0sd8idv 6g stool holding a 2-kg mass in each outstretched hand. dksid80xh6/v If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the +jdl34z k xq:msame mass. However, one is hollow and the other is so 3zx ld+j4qk:mlid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotatcokm* k3o1k:uing on a horizontal axle points west. In what 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 p*oo kc 1m3kk:uoint at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing 8m+- pksxe6ycq e8.qfon the edge of a large freely rotating turntable. What happens if you-ex6p ekmqy+. sqcf8 8 walk toward the center?

A shortstop may leap into the air to catch a ball aig 6r;mdq/7o: egc/ pknd throw it quickly. 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 r;qgem/c67gip:/d ko opposite direction (Fig. 8–36). Explain.

On the basis of the law of conser+q e b/l-gk4blvation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the seco/elg4l -qbkb+nd propeller can operate to keep the helicopter stable.

  Express the following angles ii7+fe+w6q z upn radians: (a) 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. Calculate, using theba2,r:p j:spy p87gp v information inside the Frontj:p7vra:bp y,8 g2spp Cover, the angular diameters (in radians) 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 Eartojr8r1 . oy(zkh. The beam diverges at .koo8jy r1 zr(an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blendewe--i7g m h hky5l03:wpu/psdwi59q lr rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades s79w:5 uqpikg-m- i5wlpesh3 l h/0dwylow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another chilit o 17yk:l)kxd. If the ball makes 15.0 revolutions, what is its diameter?yl iotx):k 71k    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions du6o,biudu n45bh0m 74om1l q to the wheelumhliu4bm7 6 ,0o1n5t4u dboq s make?    $rev$

  (a) A grinding wheel 0.35 m in zo ov54 ;th42nm7 wlvvdiameter rotates at 2500 rpm. Calculate its angular 4h; nvv 5zo wml72o4tvvelocity 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 revo7bvy bgi x7k77m8f x0nlution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seatedi87 b x0m7 7knfxyvg7b 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 ve +;webj+t 6*lq p0o* )pexpv ry+ay-dzlocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a p*h:3qkm zu.bl k)ye*1n(y q onoint
(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 .:,c6lpe cb/( uot d:ruqdd v2particle 7.0 cm from the axis of rotation is to experience an acc,cdu u/ dpq:2 d:6.otbcvel (releration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accwe uzhztoux6 4-9ke e*5r56x/w ppq o2elerates uniformly about its center from 130 rpm to 280 rpm inwhq ru5pzu o9 5xxeep/2te4o66- *zw k 4.0 s. 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 radius ct.h,4 rfa :2; fdaqyf4 kkgx3$R_1$ 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 pew1f.v(f9n15 s p cmgwut themselves 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 thought of as a cylinder with a diameter of . 5 nwvsgm9f1wec f1(p8.5 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 from rest to 15,0mo 3yyc-;fj (o00 rpm in 220 s. Through how many revolutions did it tyf( jy;o- m3ocurn in this time?    $rev$

  An automobile engine hw r/s.m*mob* slows down from 4500 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 wh q3 :ph8owb1smmv nn 6n2-a0ie-4 9:xdr wvpayirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachinyn6 1wrp e-2 h:wa xnmspm34vqn9 bi0do:av -8g 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 acceleo a.pndr.u.p)9k-ujqrates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel havrnpq9p-.udo .u) . kaje traveled in this time?    m

  A cooling fan is turned off when it is r v 90pgrd/uogbb4/ e,xunning at 850rev/min It turns 1500 revolutions befo0 pvx49gg,/ubr /eod bre it comes 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 rehgto e4 o+d 4f-gv;w24oyfnz :sq/ej(/i3fj zduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of wjo q3 4nz y/og2 tj:- (4oihg;efefvzs/f4+d0.80 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 revoluti;8tswyftu: d6vr3q y r:c*2nzons as the car reduces its speed uniformly from 95km/h to 45km/h The8*rzy t2c; vws:r:3qtn y 6ufd 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 whena2 p)uth)69.gub jfl d climbing a h )af.j 6uhudbp)l9tg2ill. The pedals rotate 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 wi/q2b,ijds xsz y0swmd8ji0 83 de. What is the magnitude of the torque if the force is exerte dszi2y8dqix0sw /3b8j,mj0sd
(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 of the wheel shown in Fig. 8–39. Aswpg/ rl /b0s*kndrl9 6sume that a friction torque of 0. *k 6l/nrrbwg0 l9/dsp4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attarbn6s 1;jcy:qched 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 the6br; jysc:q n1 magnitude and direction of the net torque on this system.

  The bolts on the cylinder hed mm0:*pa0w 0oupfe+iad of an engine require tightening to a torque of 38+0afm00woi:p u d*me 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 inerk 3(baelb3d3 5grey s(z+3q tctia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is througd q33s czg+3y ( rab5t3bleke(h its center.    $kg \cdot m^2$

  Calculate the moment of inab21 n da +q2 ddj.j()0ly5rrbb b-czhertia of a bicycle wheel 66.7 cm in diameter. The rim and tire hadn0-a (ydj1acdbrh bjbr2.2+zb q5)lve a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the lqpe7*+ n9 dxqend of a thin, light rod is rotated in a horizontal circle of radius 1.2 m.pqdlq*x 7n+ e9 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 potter’s wheelg e3 i;vx*lh(d rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N totalhg ;d* v3lx(ie.
(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 ofps kpqki)ohac /::ji8g:du -6 zbp y-( the array of point objects shown in Fig. 8–43 aboutgia:(8 y zubpqdk:pscoi6 )/--j:hkp
(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 cou a.8nxcd(v0 k9 j v;kvqf3*wn.cp 5gnnsists of two oxygen atoms 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 c,.q jbo eid*.:+ 6uev+wxmqnkorrect rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a ma j+n bwk+*vu. mdio6,x: .qeeqss 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 uniform cylinder with a radius of 8.50 cm and)9lp cmtg.j,nz w,l. / uvj0fo a mass of 0.580 kg. Calculajz glm),9/vn0j lp futcw..o,te
(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, accelerating it from req -kvujte3) 1v//hh k;yodd8b st 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-drivevgd ::r3y6bgc7 pn1xr lr4/h ar2qz5d n 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 childre:3c2g7rq v5d:r6/1a lxyr h br4npzdgn (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 rotating at 10,300 rpm is shut off andrme :8+t/lw.trb g5(chcrv)8k fg)k t is eventually brought uniformly to rest by a frictional torw.8h)tmr5gkrbv8tr g ck +)fl /:(ectque 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 at 73; ..b+v g7onx utwdpx $m/s^2$ 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 epk z6vj0j,0yws y2*sn i;e 1m ihu4w)solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle,6)n,ym4his;* jes z1wu0i0 vpw2je y k 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 consp ki8(6chxju 0idered a long thin rod, as shown in Fig. 8–46.x8 jp (u0ikh6c
(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 consists of tw nzws fd:)kf47dio;7lh y5x:vo 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 four zyn qzyu6 1j5:l 2,0vqhzy1 nbfull turns (revolutions) and releases it at a speedby6y qh z,lzuy0 1 2vz:qn1nj5 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 nwxc laro 3,::a moment of 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 develops a torqu7e8 u dl):b3- wzg7 7pkwenvlpe 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 ra riuw:)34 p::n y8 fr:qx;txqot9zu jadius 9.0 cm rolls without slipping down a lane at 3.3xzuqr8ip n94;a qjur:t :) yx:fw 3:to $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as,rvx5d+e)-ck 7p ox m;2kvytrol)7 iu the sum of two termklr5v -d;upvikmc))rot2o 7yx , 7+ex 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)4 ov ryyrct.8 mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder cy8ov r)4tyr..    J

  A sphere of radius 20.0 cm and6g a8y.6h)qq4gyl c sb mass 1.80 kg starts from rest and rolls without slipping doahyc46.sgl )bq8gq y 6wn 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 auqxu o*)p) am.-ehd j4i58vgj nd its lower end does not slipjem o d*- g5.v))x84upi uhqja. What will 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 oksp0ycu0 ;qo3 n the end of a thin string in a circle of radius 1.10 m at an ancy0u;oqs0 p 3kgular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum oi4hb+y+st p6.v e:nskw.:im .kj 9 tyl:fl ec;f a 2.8-kg uniform cylindrical grinding wheel of radius 18 skv e.il+h cp fi4ynjst+m.kw6el::by9t:;.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 ats-o d3uu4 day- a rate of 1.3rev/s If he raises his arms to a horizonu 4 sy-d3udoa-tal position, 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 in Fig. 8–29) can reduce her moment of inertia+c9kp 2jubxo:9nynx . by a factor of about 3.5 when changing from the straight position to the tuck position. Iby 9 jk:nx9u+xc.po2nf 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 fro1u-m0 7siwiv*t ; iiggm an initial rate of 1.0 rev every 2.0 s to a fi wi*mu ;1gigst0v-7i inal 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 center at a frd4+ mm k c8(iodau(fx.equency of 1.5rev/s The wheeuxk i moa .4(8+ddm(fcl 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 the 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 figure skater spinn/v/d6onel ix, 1) /op5p15jgpcwyu .rckhjx ;ing 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 angulamh,ut6uj:l : u0k as*lr 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 of moment of v i -fpr av:mx445btu-inertia I is dropped onto an identical dis-:4 p4rux -vbimfv5atk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a z4xkar t;y- jdpqz+95t 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 at the cent;t-v-vdu rs .sm2jo-ber of a rotating merry-go-round platform of radius 3.0 m and moment of in -;sjut2.vm-r-bsd ov ertia 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-roue9 de2y*0 vxblnd is rotating freely with an angular velocity of 0.09xe lydv 2eb*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 event k6c.y:yv vo8lt /iom:ually 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 lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integcmky/o:ty :iv v8 o6l.er)$\approx$    $rad/s$ (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 windsaz n.:z3)1ejz q6aph u 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 q51yfxzagr/p +r2/,e p i iw1s$ 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 can rotate freel:7gt3rwy )uiu qw y7t:y without friction. The moment of inertia of the peg:ry)iut3 y7wu w7t :qrson 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 stands at t e)1aw)q2wtbe7b5xzg he edge of a 6.5-m diameter merry-go-round turntable that is mou)w2ga xtz5)1qb 7ebw ented 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 jw mcbo 7 (6g sv4(kt/q/q*gjbthe 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*6tv bk7g m s/jgqq(b4 w(oj/c 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 t5wx( :nvw438 wa ccctg-gyet/hat the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (abcww4 (8y 5c:g aet-vwx gct3n/out its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 t0cj+sj w7 1xwm/$s^2$ 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 unx1prj*5s6a-c r*d7 mzzn8 d gniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular accerndma r657 n-d*8gpxc* zjs1zleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, (kr dnjm: gbf6z p;t.n5;yj/vwa i(v.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. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-gn mw/(rdfjba j ; (k;y:iv.tn6vpz.5m-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 a2mnb/eaps f1)ngular speed 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 with mass 8.0 times asub s7r :gr qn/*c0n9hyw8fcp 3 great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron stw9byc sfu3 rq7r :/8hp*ngn0 car 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-pollution automobile is for it to use energy stored in 6lr egjzl76ttcmd/90 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 mass 240 kg, and should be able to tr/tmj0z d6lt 6ecl 97gravel 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 illustratesn uyf.v vz:0nw.lyk e:hv k7,+ 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 rolli;*zu qjwhc7j2a0g3g*p vjxjy 05 i(z7ri4me z ng on a horizontal 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 pi8x:uk vn g+p6fvot freely (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, determine (a) the angular acceleration of the rod, and (b) the l:k8pn 6g vfux+inear 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 ra6oeno xm(9iinmjmn 7);vmj,cy cuf(2r0 r 01 mdius R. 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 against which it rests (Fig.o;9rjmv n,0n0 6m x2 m ci7fymc)1uoj(m(neri 8–55). The step has height h, where h

  A bicyclist traveling with speed6z 50key( u8nwi2txi w v=4.2m/s on a flat road is making a turn with a radius The forces actk zu6 xwey0( iw5ni2t8ing 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-h j :zp)y.h0 coy,g2+mkv1tbjkg rock 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 the0h y)2py t h1,gbjm+ovcj.:z k 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 c/24uf)-h y j tkwxhm1uylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstret4 hk )yfumh/1 j2utx-wched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consj/ zcx0k80dlxv 5zfhqi1s9v , ists of two cylindrical plates, of z 9zdisfh5vxvq kc0,0 /1lxj8mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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.hqnv,xq4 sm9z,38 nuf What is the minimum value of the vertical height h that the marble must drop if it is to reach the hig9xh8s z4,f3 v,qmnunq hest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assuq7o9xev:ii hw2n ns-5me $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its k6fzkz .ug9pqyf,mrxg 293,cspeed uniformly from z26gzp u q9 .,mk ,krgc9yffx390km/h to 60km/h The tires have a diameter of 0.90 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