A bicycle odometer (which measures distance traveled) is attached near the 1af fe xj48vs(wheel hub and is designed for 27-inch wheels. What happens if you e( ffvx4 s8a1juse it on a bicycle with 24-inch wheels?

Suppose a disk rotates at covdd:ro) cj;a 79fnsh4qal4o/e;g .n hnstant 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 havejenh4 :/ ;ga;cl vdraq)9.7 sfhdon4o radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described bykm2 c5)3nn fm x),xauh4mp(s 3vxwt7c a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a 3q5 na)fmd 1xiv c7cye bdl4vfe:e 2/4larger 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 sjtx3, vx(4 usdo a sit-up with your hands behind your head than whe,tj(xuvsxs4 3 n your arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has s0grs,:f0o spt pinh76f, 1f/kfkcak1even sprockets 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 it harder to pedal, a small kkst6f r0o0p1pg1,h , iafknfsc7/f:front sprocket or a large front sprocket? Why?

Mammals that depend myu *d(r2aeb 82(mfmoon being able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this diedmm2fuamr*8 oy ( b(2stribution of mass is advantageous.

Why do tightrope walkers (Fig. 8g)ta7f0wkmi i3ppeu mflp /a;gz )w42xr);(q–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? Ifchank,tj.xv2-u 5.. br2rsj,r /sre g the net torque onk,rrh t sjr.e2n-2.u5b, .cxsav/ rgj a system is zero, is the net force zero?

Two inclines have the same height buwl2c kt+xxa 09un)zy-t make different angles with the horizontal. The same steel ball is rolled down each incline. Ona+x yznu9lt0kwxc -)2 which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously staf)) aq*2p(wfkeq m *7hya 6rotrt 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 therey(p eaoqf r*am 6*wf7q)) 2thk? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. Thehsf6s;iw ; 5ky1gsr -el7 1bzby start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the botto1hs6yb;z1gfw i 5;kls s7b-r em? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or r 2,l jkf,jxy.lotating,xy.l,l 2fjk j objects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equ9z6scb 6z6bc*+2sypiyijiw +d 6a1y vator, how would this affect the le6z2* 6s +vizcjw1 dya s+i6y9cbip6ybngth of the day?

Can the diver of Fig. 8–29 do a somersault without havingfe8hk, f; xcd9j92 rwrr: i1hp any initial rotation when she leave x,wdfhfe c89 2 jr91rirhk;:ps the board?

The moment of inertia of a rotating solid disk about an axis throug3 r9hmxq zg.;n cox1h5h its center ofz;x r531qg9h m xc.noh 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 rotating stool holding a 2-kg mass in each out u(snn/ dkm1e3(dqk:y stretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? yk (su n1ekd(:mn q/3dExplain.

Two spheres look identical and t2n ; dyf9j:uy1y3t9l zw (qzghave the same mass. However, one is hollow and the other is solid. Describe an experiment to determinyt(;2n9 3guywj1:yzf lz9tdqe which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In wklbku;5-y ex 6hat direction is the linear velocity of a point on the top of the wheel?xb; -5ek 6lkyu 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 decreasing?

Suppose you are standing on the edge oyhlju9 2g5 ir4f a large freely rotating turntable. What happens if you wal 2jyl5ir ug94hk toward the center?

A shortstop may leap into tb 8cxd+)5hc oh5co c8dhe air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will not+ocd8h5 5bchc x) dco8ice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angu,3tl5h sz m:gndvq3 5blar momentum, discuss why a helicopter must have more than one rotor (or pro g5s3l, bq 35tvzd:mnhpeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following m:ccp - )orqd7 ig11:amoz flk9d9 d4nangles in 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 because6 y2qtt1m0fv2v /gct1,ohz qj of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Mov20 gt1m qqfh 1o v,2tjz6/cyton, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 i rhu1vi ; e,*0u6qb+*sid9mrcsw a-akm from Earth. The beam diverges at an+ ;rvwqra,- d*1sc eb69uh*s amiu i0i 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 blender rotate at a rate ou8 q(y-gg9h pu p7n.zkf 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. Whaknqg 8ph uypu.-97z(gt is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m toz0/ jw ynt2r*vcf,2qo1j vmk , another child. If the ball makes 15.0 revolutions, what is its mw kn , 1fq/vzto2r0y,jv2c*jdiameter?    m

  A bicycle with tires 68 cm in diameqjy 6k/,pncb)vc/ f(u ter travels 8.0 km. How many revolutions do the wheels make?c/fq6/p jvby, k()nuc    $rev$

  (a) A grinding wheel 0.35 m in d ktn*ex detj345;g r)piameter rotates at 2500 rpm. Calculate its angular velodg j p*xke)et n4t5r;3city 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 4.0 s (Fig. 8–38)l(xiue0 e+h h).shk3xblq+5n . (a) What is the linear speed of a child seated 1.2 m from thk x+h+x)bl.e5h h0enluq 3(i se 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 the Stk2bqq nkkj:t/ a bnf r::j5.,un    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poin576m tlsib l,+h )ergqt
(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 centrif 4- 3e,neyns(-umpxz puge rotate if a particle 7.0 cm from the axis of rotation is to experience pp-nn my zeus-4(x3e ,an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel ai c-9tnz)y yo,ccelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Deter9c ,ion)zt y-ymine
(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 5 0rdrt fit+dq2 +dxx7$R_1$ 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 Mo1* aw2m s5bfyvon, astronauts aboard the Apollo spacecraft put themselves into 2smvfwy1a* b5 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 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 from o +.tx0z g6fbjrest to 15,000 rpm in 220 s. Through how many rev6 f+.xobz0tjgolutions did it turn in this time?    $rev$

  An automobile engine slows down4i(/j sssbb,ppss. 9n, fwz2 v 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 whirlrf c9(ugz l.)fing “human centrifuge,” which takes 1.0 min to turn through 20 complete rcz9f l.)guf (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 frrkp+y/1 lhvp/ om 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheelp lkv yph//+1r have traveled in this time?    m

  A cooling fan is turned off when it is run2 b(ed,:hd0-ld6nl yed vx1 nining at 850rev/min It turns 1500 revol(l n0d e1xyi6e -b2dhldv,:ndutions before 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 revolutionsm8qbr-yj )cqp zxp3wfs286p :ej,2ux as the car reduces its speed uniformly from 95km/h to 45km/h, ye jwz)r8pqb2xupm6fqxj:82cs -3p 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 revolul.xc+ 5cp vxvcw829ogtions as the car reduces its speed uniformly from 95km/h to 45km/h The l5xcpcv8owx.9 2vc +gtires 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 oneaj adrd16p n-v /e-3n each pedal when climbing a hill. -3 nren6/dapv1d-eja 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 b2,q 3dj l4naua door 74 cm wide. What is the magnitude of the torque if the force isljq2bd , uan34 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 of the wheb o.,f4h/-d , b(2yplzc wvobael shown in Fig. 8–39. Assume that ad4 f,-cbobbly o hvwaz./ 2p,( friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless ro:pvef40ccn1gjc25 fh d which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then releahg0cc: ec2n fv5pj f14sed. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of c7f savr n 1ai( wvub--1o 8x;*q/qlijan engine require tightening to a torque of 38q sf7j/ cr;*8xonu(- 1a bwi v1l-qavi $m \cdot N$ 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 ineg6bjz8o e0jx-rtia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through itgx0bo6 ze j-j8s center.    $kg \cdot m^2$

  Calculate the moment of inertia of a e (3pc d5 pt:mhyyfz81bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub ccyep 13 yhp8z:5 m(fdtan be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball egq 63ca2gg) pon the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Cggac 26g 3pq)ealculate
(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 wheel rotating at cgvwi60n o3gp )ug0e8c5irr n*onstant angular speed (Fig. 8–42). The frictiug8 v n5)0*3onerwir p6gc0gion force between 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 ax0xz;. g.4cx7ntl1c9q gt bz lrray of point objects shown in Fig. 8–43 7.nz0 .zt9g;cbc lxx q1 4lxtgabout
(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 whose total maikkpa6q- n c7j.rf b p7e yi*./:hhok)ss 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 satellio; xu,os bw:n)cld5l) te spinning at the correct 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)l,:n)5l wx o;cduob s 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 tmn38jcma v zhgcsq f3.jl,1 :-.cvh; cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Cz. hh nf:l-sm, cvqj c8vt1jcmg33 a.;alculate
(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 rest to txrc e3s6c:jx9ra0*g 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 tangeni2d ;7g.ccei ztially on a small 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 o c7 c2;igizde.ther 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 rotatine 9gmeqby,b0tb)y2 : bpk5if( g at 10,300 rpm is shut off and is eventually brought uniformly to rest by p, b t2gbf:)9i qykbembye 05(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 acceleratesf 5alfg2 5xjnb,(8kre a 3.6-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 sp*+ jj9b;yvozolely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 1zb +y9vj;j*o p0 $m/s$ 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 r 80wz 4n7ecokcy96avg( q;kww od, as shown in Fig. 8–46. cnackveg8;w47kwz 6 0q9w(oy
(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 consishso2-r5h;ueb 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 accelerates the hammer from rest within four full turns (revg 72ssu.ot1n q9vj u(rolutionuorgs uq2n.ts1 j(9v 7s) and releases 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 ofy y k.*l6xmil,eyjg.j6 zon;8 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 9vhkz */ ck uppa)0n+zzud8+f55 ww sxtorque 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 rolls without slxexu8f+ 26h)xjs .rk:dmvp ;cipping down a lane atkh;6+rs:x) dmxu . c pvj2fe8x 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the p) w+etm3azw0b,x b8e Earth with respect to the Sun as the sum of two exb,p)ebma + 0t8zww3 terms,
(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 oe;qo3 x.6+0 o gggftkt*axsw3f 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 pergt6wxg+o0 .gq3s; 3 exaf kto* 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest anecbwwt9/m0+ md rolls without sl w9 /c+mmbe0twipping 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 ona- a;p-fk(n31n 41fqkhk r tgk its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper 1(;khf k-k3aa-nfrt q1n4 gk pend 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 on the zb4s lt,1e4un end of a thin string in a circle of radius4sn14zu lte,b 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-kg uniform cylindricih v8vm t (983smsyvmn0v7; xyal grinding wheel of r8i0h;3yv9vv( ms 7ymtm 8xsvnadius 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 a v foxb2:eec-,t a rate of 1.3vco,x b2ee f-:rev/s If he raises his arms to a horizontal 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 sbb k vq7bb0gdsg4fnwv (, hmy;3cq 2-;hown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck gk-n7bwbq3hd40s;c m;y g b2v(vfq b, position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can incr i+0hw7yj69 pnok; tpfease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate j7+w6ypohi; pt09 nfkof 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 cend3lv cfx ie7)7ter at a frequency of 1.5rev/s 7) xidfcel7 3vThe 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 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 1r(u tn8ob24sda d.doj9, itufigure 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 mb5aihihml7 /+f1wd (gi 38wyjomentum 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 mome ,jgare1 06nuklm8da8nt of inertia I is dropped onto an identical disk r8rl16 ,au j gkm8ean0dotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at gj e*rlb. 2i.f-ngh -gs bg0l-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 ovs h j 64vpmf;zx/7y/center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia vy/hszop f x6/47;vjm920 $kg \cdot m^2$ 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 bnupp o h*,9h4an angular velocity of 0.ph obnhp,*4u9 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, losi cuwjmq22z* jg)2wt (5tz -mehng 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 integerqgwut tz 2j-)c zjh (mm*52ew2)$\approx$    $rad/s$ (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 esnmu 5u1 )/;4g nfskawinds 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 4v d+mhj on6, 2yyv7z9mgpkl+ $ 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 c3uwoef5i pnk9;il6u . an rotate freely without frictio f39 le5iku.uin6opw;n. The moment of inertia of the person 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 the edg5,:h uerk;kk v4m q1 ehpoo74pe of a 6.5-m diameter merry-go-round turntable that is mounted k5kqhue1;7epp 4 mko4 vr:oh,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 with9hr vjzm616fkek50 4xmagn:y 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 person without slipping. m15f 9gkjx6k 0y nher6mz:v4aWhat 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 a377(jfotp n3ioqacw p0:m1xea2ex h 3 lways 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 Eart: 2tfhjx n xw7p p3ce03(7aaeoom1qi 3h.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate dz5 8e ait0) 97*zpbbwpwi,ipof 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 cylinder6mrx5ad/)vq nqy2q d x v00jp8 of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque deli yqn dp0qa 5/) vj8qdvxr02m6xvered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg aub8rto1m;0 k f;ug+ krnd 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 e1kmb;; ro08+ ugu fktrnergy 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 angulak/we,)i heaj/8 * bn0 bbs6tk,gvx.ta r 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 9gtzdnh2*6oer u6n og 8duj,3mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass ido2 zj6r8 tego ,u 3g9ud6hn*nn 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 n(5u g1 00kca3 pcfucta low-pollution 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 mass 24c c5 k u0f1ctp(3ga0nu0 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 a3-eq 9n4yg zfcn $H_2O$ 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 a7 qbhel)(h :no5lz 9zn vqm8i5t 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 hc -lirjxj.: m.i. i2oand length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as2ho ml.i.c .ji-j: ixr 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 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 standing vertically on the floor, an0i1t6zqxn9 h d: jtm0r.d ,aved we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where iqhx1,vr n.0emad: t9tjdz60 h

  A bicyclist traveling with speed v=4.2m/s on a f cs3y rnx :m(4du*a j+e+krtmgv+b)n3lat road is making a turn with a radius The forces acting4vrcnxj e s+t3:a n(* +g my)bum3+krd 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 rq:lc8pf fbw )7ock 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 sf ql:bwcp)8f7 . 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 cylindu d2pxd.,kp:o er 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 outs,.2:pkudxdo p tretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical pla9h4wyqbcn. uyw j* 20ytes, of nq9.0yyuy2* whjb4w cmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 lk0n 1hjs6.kknooped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marblnn.j6k ks01hke 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 do n 6jwcng9bkh)hjkxb 339 2oc8uot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reducfe 7eg ybr5n;0es its speed uniformly from 90km/h to 60km/h The tires gyen;b07 5ref 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