A bicycle odometer (which measures distance t.lugfnorif)c1a8 n:8 raveled) is attached near the wheel hub and is designed for 27-inch wheels. What hal )o.g fucri 88n1anf:ppens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim f)y*aov h+):g/:vgf 0jrx if7hm.svn have radial and/or tangential acceleratihm7o*. 0 yxf+)r) vgif sfvjn:gha :v/on? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid bod *tk je:vt.xp)y be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger fa hl/z 99-lfhm: 8bomvorce? 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 hanew)t+we dlvqm 00;:fk ds behind your head than when your arms are stretched out in front of you? A diagram may help you to ans w+ldw0e: f;v) em0tqkwer this.

A 21-speed bicycle has seven sprockets1ax+d3 vr;gafio;.d q bml* 2d 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 g 1badxd*qai2r mv.;lf o3;+d it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to o7-al0zbtw6u) uzp h l6a75mzrun fast have slender lower legs with flesh and muscle concentrat6- zzuzal7w0)at6bpmhu7 5loed 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, naor .33u eyn( nq1qk;l w6jeb1irrow beam?

If the net force on a system is zero, is the net torque also zero? If thyb2 v qj29x6t:gr0v;4a san8r j8xyroi r5xx:e net torque on a system is zero, rarn gxv:j9 :a8qvjsxt ;x4i2xy68b5r y2r 0ois the net force zero?

Two inclines have the same height but make different angles withlf0x(*b : 7 ll1ekuzlz the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be :llzz(f*l lk1u b0 7xegreater? Explain.

Two solid spheres simultaneously zpdfsu 8e, o1lw/:;q)/wekveeiz)i0 start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of z0e/vo8;e )iw,l iz /:)edw1peqsufkthe other. Which reaches 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 maswrfy52vg- i.ma )8wzr ab;kn 0s. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed ;if-5zn.w2rg0a wyr8kavb m) 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 momentuxf7jn4p2 ux1e m are conserved. Yet most moving or rotating objects eventually slow down and stn7xux jf2p4 e1op. Explain.

If there were a great migration of people toward the Earth’qa 4mijxp:/3 k;*70qj j zlhfms equator, how would this affect the i3 jpmqk; alzfjj 47:m*/ 0xhqlength of the day?

Can the diver of Fig. 8–29 do a somersault withocdz )c*77 864;g t,nkx hkizxfrlcuo:ut having any initial rotation when she leaves the ufzk7,)6 *l8 xtid4occkg z7;xr:chnboard?

The moment of inertia of a rotating solid disk about an axis through its centerlfv l7q2.ot uyk;2 blv 294sxx of mass is7lfl9q x u22vs 2yoktl4.x;bv $\frac{1}{2}WR^2$ (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 iny 6wtvac1ht986 utdq9f kg+,z each outstretched hand. If you suddenly drop the masses, will your angular veloci9ag wt,v9t6ycd8z6qk + t uh1fty increase, decrease, or stay the same? Explain.

Two spheres look identical and hacp,bk80 g*srw ru1btb5 p 8 mkvl/d,d7ve the same mass. However, one is hollow and the otk8wdk8 g,pl0 t/mrd*rv sb5u1 b7,cbpher is solid. Describe an experiment to determine which is which.

The angular velocity of a w(eooboz. he5 ;heel rotating 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 point at the top of the wheel. Is the ango .(o5;heeob zular speed increasing or decreasing?

Suppose you are standing on /f* z fcb5si 26g(yv,uh6d4t alsz,kothe edge of a large freely rotating turntable. What happens if you walk toward the /z 5ufk *aod6ls gyz,fvith6 bcs 2,4(center?

A shortstop may leap into the air to catch a ball and throw i bd f-4p7d+v*s3zojwyxbt ,nw,. 1qhl t quickly. As he throws ,l,qwy h3-1tv*b dn zwx.+7fpod4j sbthe 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 of conservation of angular (x qq9b0puyq(i2f(d nmomentum, discuss why a helicopter must b(x inp20((q qy9ufqd have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the followin4ox5,jlfnstt*y 0f- j g angles 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 dk aq/b9vwnw:p2ome( 0sd2l9because of an amazing coincidence. Calculate, using the information9sp nma:w vd2 0e/wbq old9k2( inside the Front 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 Earth. The be q ;p1rf )i;t8anvu,csu72yz0eo-4;lrl dwbuam diverges at ;w2r4bry7 c;t vsp qo1ain0u;,-8u) z fdelluan 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 of 6500 rpm. When the motor is tu3 z r ;zi)t+b9xkw:xxcrned ofkb rctx: wz)3x;x9iz+f during 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 anotheb )5 b+uh+immumq(;z/ q wky3j rdg.m:r child. If the ball makes 15.0 revolutions, what isjm /zmq)ub wd+u3(. ; qg r+:ky5bimmh its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How mad h64/ezqwk/k4u6 fx zny revolutions do tx64zwzk4/k/ dq ueh6fhe wheels make?    $rev$

  (a) A grinding wheel ( iexfl c);en/p:; qcyr (n9ao0.35 m in diameter rotates at 2500 rpm. Calculate its angular velocity in) (cryxplq( 9f; eio nea;/:nc $rad/s$ $\omega$ =    $rad/sec$
(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. irvr.qvs.n. u/ iv9;q8–38). (a) What is the linear speed of a child seated 1.2 m fr;iv siq9/ uvr.vn ..qrom the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity 9d;oa me,ao3; hv 5dqeof 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 poinar 76kc: glkp7t
(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 aama-5t+dok n ( particle 7.0 cm from the axis of rotation is to experience an acceleration o-m (doanat5k+ f 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly aboutlmjlnij9ou +::-ip 2bc5f*z +yqy3 lg its center from 130 rpm to 280 rpm in 4.0 s. Detez ny+u-yf lg: 2:cj+omlpbqjl59*i i3 rmine
(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 radiu2+*tms z q )y5h++qfzs4kurpk c3vsq-b hep02s $R_1$ 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, astron:rj+vljh3 4r6rsp vvk(o j u4(auts aboard the Apollo spacecraft put 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 revolu vrsl hvurjor((kj44: 6+jpv3tion 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 1 d(r nzwv-9jsfrom rest to 15,000 rpm in 220 s. Through how man j rd-(zv19snwy revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpcfp02k ew/p s2a*fk, fm 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 vhx3 w*yzgf u,h/2wfgi-rx 14for the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 compw xy,g 43f*u- i1hrz2x/hvg wflete 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 accebd3g oj4 9(qq7qvm; o -zyrn5klerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheeo7dvj-qbzy;5nk 93gm4r ( oqql have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 rg+)d +u4f nlqoevolutions before it c )q+l+ufg dno4omes 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 cars rxt7vxnjhq(*i, 4d;dt2/ zz reduces its speed uniformly from 95km/h to 45k2xnt q d trzx/v4i;(h,z *sj7dm/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as th. .-c vyu:pjgsmvfwh z-2dt;*e car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.8tf*s w:.v ;dv-uhz2.gj-mcyp0 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 cl +hocz xi0cr; /xv5oy(imbing a hill. The pedals rotate in a ; 0c+o5ox(xcz vr/h iycircle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. ln(w *njwl3oc 298 sjpWhat is the magnitude of the torque if t2wj83(nlwj onc pl*9 she 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 ax;pe 3j r(c2iikle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0j2 i krc(p;i3e.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are iuzv6se2 qc k0c5csq5l7ge z ;+0+kzv attached to the ends of a massless rod which pivots as shok;+vgz2l e qe0zz5s 0u+sk6c5ic q7vcwn in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an en.oe.n pw mc8cqv39pl7gine require tightening to a torque of 38vq3c ep 7cn9 .8lpo.wm $m \cdot N$ 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 sphe p2iytt(4 woq5 )wz/vmre of radius 0.648 m when the axis vq wt/i5 p)tw2z(4m oyof rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle whe g kq9oj(hxe r(;bi-htfoh m9))- ze3yel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hu)m r- 9(hohgiox9q) ebkj(ft -3hy;z eb can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of 6 3xd ivtftf26w( yf6lkuea;l r/rq*4a thin, light rod is rotated in a horizontal circle of radius 1.2 *v3 ulfr;irq (/x af6646ewk 2fd ttylm. 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 wheel rotating at constant angular ;tfg.c hf,y3wklfxa8: xor8: speed (Fig. 8–42). The friction force betwegor:l,a:3x. x8w ycf8khf f;t en 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 thf+r1nlvnk ud76(k6 jue array of point objects shown in Fig. 8–43 about kju +66f 1d(uknlrn7v
(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 atop adnq4zx6 ;fas-g4a mg9.g+6f hyh w6m9 s8xvms 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 correct c887 zs7fpj mh36 5lt g;uxfworate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite wmptc83fogz 7f;x6h j5 slu78has 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 uniform cylnjyw:cbs7tq61p ;j nn1 6zq2winder with a radius of 8.50 cm and a mass of 0.580 kg. Calc6j w 1b6wjcn2sq1y:z t;7nnpqulate
(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 3cztsp 75:8 uvw $rev/s$ 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-driven m,;yblw7: a+*o qurgbuerry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.:lb+* uorybq ;w u,g7a0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm74u-e8 cc k.fizi92renaj v(z is shut off and is eventually brought uniformly to rest by a frictional -i2e8ej zr(ncf79uzvcka4i .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 accelerat )dc mp8*y5f4 phrkcl0es 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 solely by the action of the fore-eydkaruvtgx1bnkc77283t ip 9 j0/ varm, which rotates about the elbow joint under the action of the triceps v/- tc 3ir27vpxu djak18e9gt0n 7kybmuscle, 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 rod, as shown ini0xgn5z sa-;w Fig. 8–46.- ;g0aswxzn5i
(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 tworme e4(4e0gh u 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 byn. r -v1dg.i8u )oumthe hammer from rest within four full turns (revolutions) and releases it at a spe.b)ud vmyriu-8on 1g.ed 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 inertiw/ ,syka;dwg (kuid 14a 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 torqueb9gpg/ 3 (odta 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 slipping down a la,bol46hs q02ajb/ef )gad b u2ne at d2 h u0lf6) gbqa/abo,2 esbj43.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum o57j )xi fxv)wxf two terms 7iw5x)f)xxjv,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How mu(2gyie;lnh3h p, jkf6z oui 04ndr1f* ch net work is required0ez* i(ph62y4d,uf i3rgk; hn1 oj fln 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 from rest and rolls without sfsdfe7 dx5j k3)m2v4kr 8 kmp:lipping down2pvs m5:4d)k3rf d 8kfx7jekm 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 a elcm.f8x7eea. ljx/( a4x* cw,fjv.lnd its lower end does nljxcel.fv/4c.x,7wax*.8ae lj ( mefot slip. 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 on the end of a thin s5m u.r.1vx+xh1gvq mgtring in a circle of radius 1.10 m at an angular speed of 10.q+1uxrx1 m .mvg5v.hg 4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momenh i;f(mki+ u pjm5;:nqtum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm whenf+k5iuq( ; njmhp:m i; 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 platform0 myg6z5dj9my pq.1it that is rotating at a rate of 1.3rev/s If he raises hismm 0i9jydgtyz p .1q65 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 shown in Fig. 8–29) can reduce her moment o.* scngd 7;ig * 2qr xe*gz1:.daetjuof inertia by a factor of about 3.5 when changing from the straight position tg crd o 1.qza2.xeen* ;gsju7:g**dito 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 h:u4 4 pf: s2b bx23a3hmoetfcder spin rotation rate from an initial rate of 1.0 rev evcs x 2uo :eh2m:f 3tb344fabdpery 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a veri )s2+nmfefk(iw0 2 oatical axis through its center at a frequency of 1.5rev/s The wheef(o+wa2mfn )0 ikise2 l 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 skate(;0d4 ijzptz9 jyqezm z;2wf.zr+ wf+r 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 momentum x i41scu4*ffe of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto aen+ w)j6rgn1vib * --udf7 cb(t il cax30ok4gn identical disk w1uogc04-kgf)xietj a*nv(l 3cibb r67 d-+n rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsmom,.cfbq *i,d:rz85onww u4dth 3z9 at 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 center of a rotating merry-go-round platforu+s- zt8jybsa y.kayo:v53 )am of radius 3.0 m ansjyk+vbs8- ou:a3azt.a5y) y d moment 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 wkqtsmz.s6e;uq39 v )q ith an angular velocity of 0. qq)vt9 u;zmqek6s3.s8 $rad/s$ 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 ic.1 1ivdg2ss bnto 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 thec ss.21gvbd 1i Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in ex da dywfkq/)up)p2k; (cess 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 0qdc9 d/ewnkp 49oy7h $ 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,n,5x*ns ee 4br that can rotate freely without friction. The moment of inertia of ,exners5 4nb *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 t6y/gqbk7,i g 0.tn lzjhe edge of a 6.5-m diameter merry-go-round turntable that is mounted .bzt,qgijl /7k0ngy6 on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end ottuytx q89 s1yx;. p1lf 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 pey.txtx s89qp; u1tl1 yrson 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 facx /28a w(bpp;rzff8h ces 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 orbitiacwx p8rf8b;p2(f/ zhng the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 b a(utd:2dt6m 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 uni,qoad 9zub-10wxakse+ c2 ci, form cylinder of radius 0.20 m acquires kwic2u+cd 1a-q a,o0 ,9bsxeza rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cym);alol77,suwcex)we wy y;a,.p*+u ge u ds .lindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050eex;*; cd),7 agmul..s wuy+)y uw7plse, owa 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-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wheel ( hn1qs1,: ty uu: (mfzlgqr;)w$\omega_R$) 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 o8h4(adsv e(6b yrawi*f our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo g r (avy(*bhd8s e6wi4aravitational 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-pollution automobile is for it to use ener(: lmzoif ajrxk9 fa+nvj3d v;-5sb) 1gy stored in a heavy rotating flywheel. Suppose such a car has a total masrk3nfmb1: f-)v +lvs 5;d9oi (z xaajjs of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an bm i,6htu3hr gcx82 5.x+ qqsy: xp1uj$H_2O$ 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 onticss4s-t8rd (p2- o z 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 l jvgkas2a4)n /ength L can pivot 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 linear acceleration of the tip of the rod. Assume that the force of gravity acts at the v )2gsa/anj4kcenter 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, and we lp90.d1esqfovfzw(-o,t(k f want to exert a horizontal force F at its axle so that it will climbo ( sle,1(tp9 f v.zqff-odk0w a step against 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 ma*xebsrzy 9 8eg (i;4ep r v87vxv7j) grrq1s3jking a turn with a radius T1e *x 48g7z ) 3(jyg8 rr9s;pvie qrxvsr7vebjhe forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rw j 56hhkrlni0p82pr0ock into a sling of length 1.5 m and begins whirling the rock in a nearly horizon5p06 rprnhikj0lw 2h8tal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, mal.0g8*(kyng; x jpbv gbed0j -king reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly againsg08 k-vp ;yelxb( jgdgn. 0*jbt her body.   

  You are designing a clutch assembly which consists of two, cd(fbk++7kk cd ak*n cylindrical plates, of massc7 ad+bcfk, knk *d+k( $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ro, qwm-rud97 bblls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the tra7b -mbrq,uwd9 ck? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not a2ds 5 otg*kbz c5ec2z5ssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car rebzyejlq0ns v6w t. hm0eb 6x-r) z2)j,duces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angul.srx)0nj zztv0-l ,h eym2)q 6beb6wjar 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