A bicycle odometer (which measures distance travthh ys j:q7.,xxm 2w;deled) is attached near the wheel hub and is designed for 2mxdhs x:,2. ;wt h7jyq7-inch wheels. What happens 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 h:l )mmivf1a -have radial and/or tangential acceleration? If the diskmavli :fm-h) 1’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 body be described by a single value o,,5 cl . 3ldnndktt)ggf the angular velocity $\omega$ Explain.

Can a small force ever ev4a43 ta3 mblr5oux)pxert 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 248:dxi e -dyhgd qs8esit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help48e: qxe h8idys 2d-dg you to answer this.

A 21-speed bicycle has seven sprockets at the rear w0kb6h: n;opzi5 /jpwaheel and three at the pedal cranks. In whio/;jp: bn0wka5 zh6i pch gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs 9nf5 vwg/uyq+x/;pohw4 lp:l with flesh and muscle concentrated high, close to the body (Fig. 8–3w ppv+9 lgy5 uo fw/n:/hlxq;44). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers nj,hij+0wqr78 *nxma(Fig. 8–35) carry a long, narrow beam?

If the net force on a systea dq0.an*n oglu:v: dg8s4(i n)q)qwgm is zero, is the net torque also zero? If the net torque4 qgn8a)vndq :dwla*(nqgisg .o)u0: on a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizont2k5bh cvh ied:xv74 7nal. The s4h2:bke nc7 hvi5 vd7xame steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an7n;xi i4 wyf4b+nnhi( incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the inclinen 4x; 4w(nniiyhi7f b+ 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 massvm4fkz*fy3 xc;ocx;ea .z1 j. . They start from rest at the top of an incline. Which reaches the bottom first? Which has the greatejy ez;m.x1zo3 ;f. ak*4fxcvc r speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and ap8): iwnh5(rk khsgb*ngular momentum are conserved. Yet most moving or rotating objects eventu5h(w* s: pb h8)kkingrally slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how would r4ms t92c( q(oi8qnwfthis affect the le94qmr8wq 2(tcosn(if ngth of the day?

Can the diver of Fig. 8–29 do a somersault without having any initijw e,g qkmparc36q; 5b:z7( swal rotation whem5q,z6b (pq :w jg7 wcaers;k3n she leaves the board?

The moment of inertia of a rotating solid disk about an axis through its cedo0bzj w0q v ):mj/ ;k*zrmvmnp1 7nh:nter of mass is nz 7v0* 0bpj: n; 1mm)zhwvomrqj dk/:$\frac{1}{2}WR^2$ (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 holk-7 ui.j kon*nvff1x2ding a 2-kg mass in each outstretched v uj-.*kn7kxn2if of1 hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, onehf,4evo;xqy, m.zt l / is hollow and the other is solid. Describe an experiment to determine which is whicqo; tf,hl4xmv. /yze,h.

The angular velocity of a wheel rotating on a horizontal axle points west. ej/p+ 08yffctj(;mu* xa (2+ z)5afziyhjctoIn what dir(+i pf;caujxy8fh z2c mat0( ftjyeo*zj/)5+ection is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating tu(g fr*d/i;pi .e3ug 04uxnup vrntable. What happenu34(upxgipn.r;f0 diu*/e gvs if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quicklyny,d ,mkgpx2 3n7mk,j. As he throws the ball, the upper part of his body rotates. If you look quickly you will notkm2m7p ,n3,jkg xy d,nice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentumqt wea cl-7/0b)mdvf k1 j70 u9nvih*l, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the slhul-a nc i917 t0d/mjq)*f e0vv7kwb econd propeller can operate to keep the helicopter stable.

  Express the following rg6mev b18n3 -k2tqpy7spej vm *3cx1angles 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 because of an amazing coincidence. Calculate, using th b;kaup z3v4kiflxr)7h+9i; fe inform lpz i9;7h)4vrif b+aku3;kfxation 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, 38c/ +7j txg8q1vdzyelx0zwi a: s55 jg80,000 km from Earth. The beam diverges at8:x l e55/71zzc dj+vws 8i0gxjygat q 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 blender rotate at a rate of 6500 rpm. When the motor is turned rt9oz-p*wpvsfcw7-q ;x2 :c x z, 1nts7zt5qcoff during operation, the blades slow to rest in 3.0 s. What is the angula t*w-vtf oz9p5s7qcntxz:1 ; zsx,7qc-2cwr pr acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a ley*fq-c2t:hiur0us q 2z ; zks5vel floor 3.5 m to another child. If the ball makes 15.0 revolutions, what irk 2u ;sch:uyzqsq-t*0 if z25s its diameter?    m

  A bicycle with tires 68 cmw)l,b(8kh zxt in diameter travels 8.0 km. How many revolutions do the whe8z h(klx),t wbels make?    $rev$

  (a) A grinding wheel 0.35 m gy*i*ozhu ;aj2 lcsa+kl)ar ;,.kh c 3in diameter rotates at 2500 rpm. Calculate its angular velocity l h;csk;c2 .g+)l3r yzj*ak,ah o au*iin $rad/s$ $\omega$ =    $rad/sec$
(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 revtf rt-n k/x+iwo( 56ssolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child (stsw o+i/k t 6-5nrxfseated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit aroundpqf 9oa kg5m;h8kp.5(p/t iba the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed m3gopn9 )tlk ktd4r/3rh9,lyt7 2xj o of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 c o9ygq5,qq )vp1ahc(bm from the axis of rotation is to experience an accey5q oqb1(pa ),hqc9vg leration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerate-4t ikyh- t3cw tv:nlw6 b/-grs uniformly about its center from 130 rpm to 280 rpm in h n4:3cyktt /v-igwwt-6br-l 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 b4l54 *mtg cpb$R_1$ 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 Apox (dt(qida -j)llo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they acce ajidq d(-()txlerated 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 rest to 15,000 rp0f;xaoob uh8 0m in 220 s. Through how many revolutions did it tuh obu8a;ox0 0frn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s.aldntp2(4g :(irc k-r 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 highsp47b a((ap q+hk k)x(bkjhaf 9peed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete ()kpk7+9 4b( hhqp( aafa jkxbrevolutions 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 diameterrl6jrxih 57+aq h )q-h:+zk z4n1 jlhz accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel havnlq6x+z ih1) rk7jhz5-r:ajlh+zhq4 e traveled in this time?    m

  A cooling fan is turqi/:a0/m /leej s7n..:zp7m opxfdzr ned off when it is running at 850rev/min It turns 1500 revolutions before it eo:pp.n/iae.dmf:7/m 7 lrz jq/ x0zscomes 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 makd qv0)su *q 4.tmg5fa8tk2q zve 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a z )0 mvq2dqtsf5 4av8.* utkqgdiameter 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 maz5 md5k2 j*gzrke 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tire* rjzd5z 5km2gs 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 *7zs2 p;4nhxhgx sw,yall her weight on each pedal when climbing a hill. The pe s7x,2*4hnp ;sghzxwydals 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 o zoqu*u)e jgrsl q,c24ep.p (:f a door 74 cm wide. What is the magnitude of the torque if4euzp*2,pq:gc)jq.lo r (esu the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of therg t ogoss3 8d: )bc b+g8jy/xr2ijn(1 wheel shown in Fig. 8–39. Assume that a fricn+ri3tdcg8oj 2ory b( jg1 gxbss:8/)tion torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of ma o;j451 /v t9nntapjvwss m, are attached to the ends of a massless rod which pivots as shown;15wpj/v 9tat4njvo n 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 heakxcu +vl +j x7:.tn,gts q5f5cd of an engine require tightening to a torque of 38j.l7,ncf+xg5xk+ u5 c: vttsq $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m when(tnbnb i g6j90 the axis ofn6(0 ni 9gbbtj rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of-z)u.4 o kdunc a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can ko4u)z uc-.dnbe ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a hogg pu 8:al3a o*egk4x/rizontal circle of radius 1.2 m. x *akg4le3au /o:g8gpCalculate
(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 conaelt ou,zf2w)g 8. x l-rxz90wstant angular speed (Fig. 8–42)..zt e 8fzlxw0xur2 9a l,owg)- The friction 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 array of pv1ja c mdsaa+c6a256d oint objects shown in Fig. 8–43a v a566ajd1dm2sca +c about
(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 oxygene+ aznquwv.6, 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 thj l+6fqpn*rx 4e correct rate, engineers fire four tangential roc+4n6qrxl j f*pkets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a massg k9 qk4,cn+p8va xq6) yqg,eb of 0.6b q4 kqek,x ay8g+ gvnp,q)c9580 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest tp -6xd a3 bdmf,e;c0hpo 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-driven merry-go-round anduo,dg50vp +nb3o k13csf5c)n fq6wqo is able to accelerate it from r5c k ofc qbn36o)ng50df1u qs,w3vp+o est to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotv nfzu1(ghk op *r1*q 8ism;(pating at 10,300 rpm is shut off and is eventually brought unifo*1 8smz vp(krof;gh*qu p i(n1rmly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ida:;t gzky;bapq51),4lk w(s .qkvw 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 ballohu: 2ls*sgs( )fpd 4x6;bqwz is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the shq6)u :wxdzs2lg ( f;*spob4triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a *cty /e .9yulelong thin rod, as shown in Fig. 8–4./9tc*yeulye 6.
(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 two masghy 31ot.9frg ses, $m_1$ 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 fr1(rspi 9m; ykqom rest within four full turns (revolutions) and releases it at a speeyq(ms kpi;r9 1d 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 hx pf4j0u z3u9pas 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 torque dlhcq r6+j hs27hr))q9 l-fn5 )emjsxof 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 withyo+(uiaq,e (a- d3hs xout slipping down a lane si(ae 3y,dx-oh( +qu aat 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic ene8ru; .;(l vrgoa86zge; cfgvorgy of the Earth with respect to the Sun as the sum of two terms, uc6; gogr.fg;ovl8rv 8;e a (z
(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 mw+ i 9*,sn7 pdah -pd:unbo,zh. How much net work is required to accele bp+npu*d-,hw in:a97so , zdhrate 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 tqhkro mnq ;.64kk3 e8starts from rest and rolls without slippingeqtk. 8rh mqko3k;46 n down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall and cvs* woij 4y3mtm(a5 yg07*mvd-3 emn its lower end does not slip. What will be the speed of the upper end of the p0g-cdnmevi ma3mt y75vo43 (*w mj*s yole 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 the2z(y fha/k0 ,)agto* mgp9dbt end of a thin string in a circle of radius 1.1/amhtyaf2tpdg g0 k,b)* 9z(o 0 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentj1(bpa8q c /zvum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm whenqvpb1(jac z8/ 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 platfoz.p//jb ke. gu.d gf1srm that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–4.fz/g.bd / .1 skpguej8, 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 ej f/*9jw sky(+xgb1r moment of inertia by a factor of about 3.9jw1 gj/xy + fk*sb(re5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin roti:* )h be0rvyuation rate from an initial rate of 1.0 rev every 2.0 s to a fin0evi*r) yu: bhal 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 verp9 iz p sg 71txu*/gbcwpwo:05tical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of bx/sugcpzpgpwt*51 7 9iw o0: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 spinni ljr4 bv+jig1e314tp/qqqc(j ng 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 mgxy**fz+wut iq j4 osg2k 0.;jomentum 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 an identi zod 2h-;uqx,lcal disk rotating atohz;,dul qx -2 angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2ybyg+n; h9)xz un wag: )0bor).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 rotatingy,a0/n) thw of 4grthcx(jta,*, up+n merry-go-round platform of radius 3.0 m and moment of inertia 920, tr(*pxga fact4/ u0n ,) wjtnho,h+y $kg \cdot m^2$ 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-goxat 0l wap4mym67l) f+-round is rotating freely with an angular velocity of 0.8 pmlay+064 axt)mfl w7$rad/s$ 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 collaps bri.xo x.jbsl;1l: 7yes 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 .:sboil7yxl rb .1;jx lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of8(fuf qkius/ ; 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 mx+4slcwd / l:hi5nple8g3 -i$ 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 ren ip o88fz0 .fwox,-fotate freely without friction. The moment of inertia of the person plus the platform i.iz ffe0,o ow8xfn8- ps $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-rouno3rqq.zy /e) zd turntable that is mounted on frictionless bearings and has a moment qz)3eor ./qzyof inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope :hg4xqp-g9zuxfcx g/ 1p(l1n 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. What length of rope unwinds from the spool? Hn9p1uzp4xlfgq1g/h (-cgxx : ow far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the :v2xu5qm t a 41,zgtjwEarth. Determine the ratio of the Moon’s spiq45t,mv :z1t 2guxajwn angular momentum (about 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 ratekys7mpi3xota ;8j. +k of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radijwv7998lhrf ius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the tor79l i8 rfwvh9jque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindr76:kv,cp/s 1vo .m jn;db +hnd06eqrtz flvr8ical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the lt7b p+v61 :v;dnjr,0 /k8foqcrsze 6dv mh. nlinear 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 f0 s*qbhemve.8(wxc 36jq d3xspeed 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.e2*bpaw7b 6;md2+)l c+g ayded. cjlk 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 in the process, what would its rotat6dl . abc;)kdeg2ceda b2y p*lw+j+7mion 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 u+/-xp wumvl 8n dtqt75se energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cyl7t/ l-quwv8x+npmdt5indrical 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 * nmn 59f;twcf$H_2O$ 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 rollingh,75 3v+ fb2 zcfqlahqb2r- ;)vptbos 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 pivot freely (i.e., we ignore fe-w5evbp2p j i+q;m +wriction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. jq iew+p-2 evw+bp;5mAt 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 risgyttb +w rvb+*wvm5j m.1:7 adius R. It is standing vertically on the floor, and we want to:+mbtyr+5.7s*b mv i v tjwg1w 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 h

  A bicyclist traveling with spee0hf)yr: b(ss cd v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the norma csh)0ryb:(fsl 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 roihi5mk/ ; :jcaya-n;bck into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to aci ;h:/yakj5bmin;- ac hieve 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, is1i kw jxwbtl++c)x71;t5dx making reasonable estimates for the dimensions. Then calculate the ratio ofw)j s51 bxid7w;cxxl+itk1t+ the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical platev8x0r2ks1 sbs s, of mass vxss 1 2bs80kr$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 tr6ew)jnz qya+kt/ ly /e bz44uadwh4.+ ack of Fig. 8–58. What is the minimum value of the vertical) uyy4l /ahkqdb ja 4+zze+wnewt.6/4 height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not qdao rhlz:; uv;2) ip ,v i)z(o.4iqcqassume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its sp +il /rj:0-t-esvbklq ou6d3ceed uniformly from 90km/h to 60km/h Thcel03dkjsr6 v-: liu-+ q/tboe 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