A bicycle odometer (which measuresi bjhkan ), 50n81*t 1gcjh co.hqojq9 distance traveled) is attached near the wheel hub and is dest0c)b8nig5h qahjnckoq oj1 j1*,h9.igned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velon/79xdd0:z j ui *hpn c3imo3fi /gq-wcity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component/if0 gqx/ui- mn9j: nwi3c*d7hz3dpo of linear acceleration change?

Could a nonrigid body be described by+ g /c nbb c/f1f.t5c1yf47ztorc+dnh a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger f z+j/fccg3q;g orce? 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 z,jmkgci+7i 4i m1mdk: fl( z sg*1a2fwith your hands behind your head than when your arms are stretched out in front of you? A diagram mayma +fzm1 idm :zfi k2 4(gicgj17sl*k, help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and thr3(;a; qpxk*azvj--id 0p qzvcee at the pedal crax*j0 aqizqpp;-c azv -d3vk; (nks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to runx1o3t. oa9siry m)y./ t1xi(2luisxe 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 distrib1xex9 taytrms(/)io ii .ulso312. xyution of mass is advantageous.

Why do tightrope walkers (Fig. y3- u 0dioi1k kxsn(xki v6+ga 2mn(a28–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torquetnd-ac(wa-0hn(v y5v also zero? If the net torque on a system is zero, is the net fon(5a-w - h0vvdcn (yatrce zero?

Two inclines have the same height but make differen w8a om9g+mq7 .rx i+ex3sh,lpt angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Exple+lix ox ap9h. + s,m83q7mrwgain.

Two solid spheres simultaneously start rtyehc1 4epl eng.-s1z )y(j:)vt ju3 holling (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 s.e c g -ujp1z:lyh4vtty) hjene)13(the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder hvtfo x m1b 4f+eh6 w+2u iim txwps3;mz2:ke8*ave the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic+ti phx6s3;b t:+e8f*vmo422zwm xfim1e wuk energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet mo-wm c34*g3vlmt wv7cm eqs3x,st moving or rotating objects eventually slow dwmcgm 3v* 4xs7e,- ml3qwv3tcown and stop. Explain.

If there were a great migration of people tod3s2fe4i q/evward the Earth’s equator, how would this afie4 3s/2fdqev fect the length of the day?

Can the diver of Fig. 8–29 do a some38lfx2)en 0nmpo gb )trsault without having any initial rotation when she leaves xe)0mn3b tfp2lg no8)the board?

The moment of inertia of a rotating solid disk about an axisk/) 7-/yhilr q)bay4*ab knry through its center ofyqi al7y b *nka4rb)y-kh //r) 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 os m(nkn-)s1m fy;h0ul n a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Exssh )m-mnlnfyk(u0 ; 1plain.

Two spheres look identical and have the same mass. Hock8tkohw.y:d5 a ;ktdp1y18 twever, one is hollow and the other is solid. Describe an experiment to determine which tto1kd8 p.5w yycht; d1k:a8kis which.

The angular velocity of a wh wd17pz* *-k pk s.p,zm ap*yxgy(pgi,eel rotating on a horizontal axle points west. In what direction is the linear velocixppp*zd . ,kgwp1y(ak7gi *,z- y*s pmty 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 w-pz 3hj5g.cz 3ki7onthe edge of a large freely rotating turntable. What happens if you walk toward th7 w-g3j . hoziz3kc5npe center?

A shortstop may leap into the air to catch a ball and throw it quickly. A mr3 jlf2wlq4)s he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rofr4lml)3 2wq jtate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentu1 nlqb:)4bwxq g2is;2m u6pst 7xohw(m, discuss why a helicopter must have more th( is)pq1w qgwmo7tu26n b;2sb:l4 xxhan one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians,bj*a56 lz0k q bfl+vz: (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 b eff67k:ay gz*23isch ecause of an amazing coincidence. Calculate, using the 6i :f2zce h*y3sg7 kafinformation 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 dire7m nlnqx7 o+s5cted at the Moon, 380,000 km from Earth. The beam diverges at n+ lxo5m 7qs7nan 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 blendef ws u767yzrukr kfz,*k750xgr rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow g0z* kfwurrf, skz7 5x 7y6ku7down?    $rad/s^2$

  A child rolls a ball on a level fe.rho( 8cky ( qdf0 kmy/2s0xsloor 3.5 m to another child. If the ball makes 15.0 revolutions, what is iy0sse.(yor 2 /q f 0khdmk(xc8ts diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revol5fedj3t4o o0f g s-r8sutions do ths8jof3o gf s-450redte wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 6 szjj m7ba7fh1f89 pbrpm. Calculate its angular vems76 bb9af8z 71 hjfpjlocity 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. 8hgow3nu 51 y5mttaq75 –38). (a) What is the a755w3huo51nt g qmytlinear speed of a child seated 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 7i ag)/x5 czagEarth (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 poin p ej 8(p,l*qgn:- vmdzgmra.*t
(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 ce:p eniwi 5h0l3ntrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 1w5ie 0ipln: 3h00,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformn23e)0x )td ajr7zbjip 1t( jkly about its center from 130 rpm to 280 rpm in3dz7p 2ekaijr1j t()jt bn 0x) 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 ew 0jq6ksu8:dfw aiy 871mo l3$R_1$ 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, astrq1;xapa :twk zm-5 c.rzk*tv7onauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip,5z a17z; tq-pma vt:.kxcrk*w 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 rest to 15,000 rpm in 220 s. Through 7jdp 1-a )lml pwjvq)8how many revolutions did it turn in this tim8jlmvwd-p) l1)a7 qjpe?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rzj f4h f6 0betv0eob0(pm 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 of84-:faqtz cpakf:k 7q flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final sp84a kk :qa-fpft7z: cqeed.
(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 acceleratesmul amd87:,q f uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the w uf7:la 8q,dmmheel have traveled in this time?    m

  A cooling fan is turned off when it is running at kp* kq f:2vm a6 ite(5c7j.poz850rev/min It turns 1500 revolutions before it comes to a stop.pct2:ep f a.6z(k iqjv57omk*
(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 tht4agv,a) tb2 pe car reduces its speed uniformly from 95km/h to 45km/h The tires have a diame 4 p,vtag)a2tbter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its s b6,g bbophrf;qz )3d1vbf.-mpeed uniformly from 95km/h to 45km/h The tires have a diameter o.vfo hbg6brm,pbz -d;q1f) b3f 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 weight9,:e d +uafdr3.y bfmb on each pedal when climbing a hill3df, y9a f.bd+m:urbe . 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 forwn7d5rx1bnb :ce of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the :1xb5dr 7n bnwforce 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 abi q04at8u6ivepgw 5e9out the axle of the wheel shown in Fig. 8–39. Assume that a 6 ea utigi qv84e059pwfriction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of massnwu3a *z( r..7qud;poc tp(gg m, are attached to the ends of a massless rod which pivots as shown in Figw(gu7n3az g *d.(pt;pourq .c. 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 engxk -+cfwlhdj sh+v,43ine require tightening to a torque of 38ld4fhws3cxvjk+h+, - $m \cdot N$ 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 tc;z mw8hn 0q.bhe a0bh;8 n .mqczwxis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicywfq tp+mi,9t8duwom, i6z e.. cle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be igntdmqw+if,ue68zmt op .,9.wi ored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod ide 5a+, tkl /yvfu-gf(s rotated in a horizontal circle of radius 1.2 m. Cat+ yg(fk5l v uf/,-eadlculate
(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 potteruv0)6/ aje o6uivsj j)’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and o )uvjesa j0v6/uji6 )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 point objects shownvx8a l8, qu.dsgj6qr6*tozb6 in Fig. 8–43 abouusaj oq d6b8.,v68gtl r6z*xq t
(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 o(sa) yh5si1 mrf (t/ p -wrc0qg(4ywfrt,9gow xygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, engi 6 mq x)e)cf5ni7wpw**u:jlui neers fire f)p6xi:lu w *miuqjn*7 w)5fceour tangential rockets 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 uniformmw;xk 5zm hznpw6.d 23 cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calp5m3kn;xm2d.wh zzw 6culate
(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 v.mx 2q1z;hila bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-d5a9y)0 /ehusyw- 0 mn qi(upivriven 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 of5(ih0 qeyyi v9u) 0uswmanp-/ 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and i9tz 0gkzfah3 nxw;*:ds eventually brought uniformly to rest by a frictixt9;zw zdnh*0a fk3g:onal 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 r 4qgpo fr5lu ;qo--,sball 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 throwni y8 jeg262 xgpmx+u z0;iyh+g solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. j0ph+mxi+2 uigzx; g y28 yge6The 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 con0 p5zegn ypvj,kb w07c.4ys6asidered a long thin rod, as shown in Fig. 8–4s jn0 0y7az5bevy6 .k4w,cpgp6.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consis zr (0+.f7y*ubexthbp 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 fb imy9ptstmbner)lyu x ;;4 -4m,,j ,jeuqy)5ull turns (revolutions) and releases it at a speeuq9xi 45 tn,ye-m)) je;sjbtyr,p y4u,b;mmld 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 mome(o :axilrpy v. x zj(7epm2w64nt 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 devel2ahs k0tl )tb+j(9,zl vc m7hvops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 c/;*qcpkcq :ejm rolls without slipping down a lane at 3.3 cqq :kc *ep;j/$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of tih5-hx ( o;py,sh1tvd he Earth with respect to the Sun as the sum of two terms,(h oi,h- d5py;txs hv1
(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 much net woriey-e 9 u a2au*3qh-ef80bk7qdbfm o( k is requir bu-eafm* 7yd0 -q aikhu(28e93ofqb eed 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 ur0dz,:by (de cm and mass 1.80 kg starts from rest and rolls without slippi u:ebyrd(,0z dng 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 vertica4m d.r6q yqsby13ws9 xlly on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just befo4q 3xsby.md91s 6wy rqre it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ballje -2:djh 4a6n:vnwiz tac 04a rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 1ve0-nnd 4aia 2w4hjc: :j6zt a0.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical ghip sp9u,,p*zj +sn2yrinding wheel of radius 18 cm when rotating at 159p+yj,hp s is,z upn*200 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 hiew** z05kqxo bs side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizonta* 5kx0oz*be qwl 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 momen yf+evto :,*oh m0eqq2t of inertia by a factor of about 3.5 when changingveq 0 h*yo2,fetm: o+q 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 rotatimg3mw(f4e 8v (p du8iotir .x8c0pzs/on rate from an initial rate of 1.0 rev every 2.0 s to m(me8(uptvxr8o d 83/.ic40z ipwfsg 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 vertical axis througc 71kvu*d-uilh 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 clau*u1-kvcl7 diy, 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 spinning3 vjuim)vy.n8+rg i6d 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 angulam3*mkkhh hk/-wgo 82r r momentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is hvt rh+ld9z19dropped onto an identical disk zvt +dhr1h99l rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 0 as kbgf)o) 0i+knfiqz -0wn($rev/s$ 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 c lvy31 6iw vpimnqqr91d2ucmy0 *c)2 at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia 920muvrq*i mw10l)3qnd 9 yyip 2v612ccc $kg \cdot m^2$ 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 gu b2m 48vfrbi1:d ug,with an angular velocity of 0.8 rbm:4vb iduuf,g1 8 g2$rad/s$ 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 2 3q0b/p+az* :anql(mhajqdw e4hen7dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(roun de* a qj nb740mah:+qal(wp zh3q/ne2d 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 ofjoncgr0zgnf p (+457r 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 e gfl sy2g6w ow7v6;s6$ 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 rst,rogrep8 (+.a:ivz est, that can rotate freely without friction. T( e.izt,v: apsr ogr+8he 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 edge of a pj6a 9fvqxgum-v9+n 86.5-m diameter merry-go-round turntable that is mounted on frictionless bearings anu 9a-jx+6 8v 9mvpqfgnd 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 of the rope lying on the fsl1sw- f:mx: 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? How far does the spool’ss1 :xwsff- ml: center of mass move?

  The Moon orbits the Earth such that the same sideuh o( qxt3a;5w evv 4ps-23fem always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (abevu5 -x;sv3tmh3wqe42f oa p(out its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates f*dyy31 gt*z derom rest at a rate 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 cylinderbyylr/-ry5p y)o zj23 of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval aolyy/ y)23brr -zy 5pjt constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylind 1uqbv1s:y li1rical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrica1q1 :v1lisby ul hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-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 rea ,gfsz(.q o *iyb hh(yi( zwmtxqct m,*5.ky/4r 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 wi15vvzfmqo s863 pr2e ivty, .ath mass 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 in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost masss2z.65ivv,m8qf ve at3r1ypo carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution0 qo4i fu3d :s27gpomg 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 an gi0pdfos 42:73 muqogd 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 anht :ta8bi:q) ltpk:i ; $H_2O$ 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 horrbg)sw e4t3 cir0.c:j izontal 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 yziqm8g+ 1m;z,f8 7)bfr nijmpivot 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 center of mass of the rod, as shfbm7m z;)rm, 1g8qf+zijy8n i own. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floog p7+in xvg48ukjk7emhrbc ij1 8 *9+vr, and we want to exert a horize+kgj741m njipu98ir v h +c*8 kgb7xvontal 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 speed v=4.2m/s on a flat v cvzp)l ,g2o9uw86mw1 l/wf eroad is making a turn with a rav8fwzom16w)p 9 2, ll wgcu/vedius The 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 rock int7ta6vapky/o(1t lufz*g:s. a o 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 sga1/z t*suv lypt 7.f(ao6k :a. 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,r* xzv7*;ld x.ftlp8o making .dtrl*fx* lvpxo8z;7reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical pu ue6zn 8wu+f(+c bdl)lates, of mass8nc + u(ef6+dbuuwz )l $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 l jw6:vt30w)i 3ftgf qb2tgs( ;x6v ekfooped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the markf6 ( vwxw2;gffet)ji3t v q0g3:bs6tble 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 do9jqcnt m+d8dk*05v zo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions9 qsp.m)v lib* as the car reduces its speed uniformly from 90km/h to 60km/h The tires m.p* 9il) qsvbhave 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