A bicycle odometer (which measures distance travelppoi to11uy4o-7wrv5 ed) is attached near the wheel hub and is designed for 27-inch wheels. What happens if yowro41yp7 to vp-o51uiu use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular6uyvi/nd .7 hu velocity. 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 a.hun/yd 6i7uv cceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid bod9h y(-f(,zb1/ pfpn9z f ovbedy be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert g1o8,a8c;amd6d 2wubf 4ng sda greater torque than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up d f+t ua9+vd*swith your hands behind your head than when your arms are stretched out in front of you? A diagram may heluda9 +vfd*s +tp you to answer this.

A 21-speed bicycle has seven sprock.5eprf qsiboei2 15l2 ets at the rear wheel and three at the pedal cranks. In which gear is it harder to per p.if152sqebo 52i eldal, 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 ; :ue1d qej1ndrun fast have slender lower legs with flesh and muscle concentrated high:qed 11e;j und, 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, narro;p:v- ub ta dh*,i i(vwq5g9vfly.4flw beam?

If the net force on a system is zero, is the net torlq hy22p6a2uls+uvd vb ly/79que also zero? If the net torque on a system is zero, is 9y ul+2lq2dsp vl6b 7yh2ua /vthe net force zero?

Two inclines have the same height but make different angle4 6qst6v26iis*uxeai s with the horizontal. The same steel ball is rolled dow6 eitxss q4i v6aui2*6n each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously syi.h*4cy:jx8rl u zul9j8,z: en+ o sitart rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Whic u su8zyiez*8x:,9+. ljcyjor:n i4hlh has the greater total kinetic energy at the bottom?

A sphere and a cylinder hb,*wlsmpwh4v o/ s.3fave 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 energy at the bottwhlf/ws.o,p s mv4b*3om? Which has the greater rotational KE?

We claim that momentum and angular 27b 4+eulatfkmomentum are conserved. Yet most moving or rotating objects e e2lkub4a t7+fventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equ ds13e r,on yhr,vy)1w8+ljx np-h bj-h jda37ator, how would this affect the length of tw8 h)h+n7 p,r3-sx1 je13bdnryjo dhyla,j -vhe day?

Can the diver of Fig. 8–29 do a somersault withourlr, 68f -kjkaqd1o9vt having any initial rotation when she leaves the bvq d f1 al,rr8kk96-jooard?

The moment of inertia of a rotating solae; + azvr+9;)e6t*so*k ibmgo y uxh6id disk about an axis through its center of massage o9kuyz;i *to +r6h*6vbms+;aex) is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding fj76co/g wcld60a 9gla 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular veloc lg c0a96cl/fodj67wgity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is o4u)/ata 8ze+j9: nq v h7kunlhollow and the other is solid. Descrjk z avtl a/94q7neuuh:n)8+oibe an experiment to determine which is which.

The angular velocity of a wheel rotating oevy-md(:u2seg/t:lo iy) rct2h5qmm j*h-/sn 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 angular speed increasing or decreaso5im -: :yjd*hv r2ecms/q-)t ge2t(/sulymhing?

Suppose you are standing on the edge of a large freely rotating turntable. What(s0i 2d 4ddelb happens if you walk toward the cens40 b ldied(d2ter?

A shortstop may leap into the air to catch a ball and ths 0 /r;lwmavblzr7/j6pr 7-b h,qzl,hrow it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rota-zz,,7bq;r/l l r/ 6ahjrpsmwhb7 vl0te in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a y h3dbz t*oyo(9r* ksc3d-y c7helicopter must ys r y(9zt7-docobc*y*3kh3dhave more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radia ywef3 m.emr/sv- 64bans: (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 s,9(*gkoqut 7 hlstc-dv)/r x (ahmo.because of an amazing coincidence. Calculate, using the information in*t)7gsu(h k9hsx t la ,-omqdc.o(/vr side 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 beam diverges ds1o*dlp6rfu/f(ayuh4 3 q l;at an anglu 6p;d 1o* f 4q/yhfur3als(dle $\theta$ (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 a3; z6-wuy4rn:x ugie at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to r;rgwyn 6i-a :4e uzux3est in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a lev gv47a3;ld) p)0hnnk,ek rl:rshrko 3el floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diameter? lv):p 0 43);khg3eandhlr,ns7ro kkr    m

  A bicycle with tires 68 c9gl g1b6v5 uqj68 zgiim in diameter travels 8.0 km. How many revolutions do the wheels66qvz5ui9 ggig1bjl8 make?    $rev$

  (a) A grinding wheel 0.35w ni522sog0pb)td9 ieb kxn *; m in diameter rotates at 2500 rpm. Calculate its angular 02be2on5dbk g* w ni)t; x9ipsvelocity 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-rounds bty 3v8qh6zy )cf;)a makes one complete revolution in 4.0 s (Fig. 8–38). (ayf83y)s cqh;tbv)z6 a) What is the linear 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 Earth (a) in its orbwv156 zz;o nq( m7tymtit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of lpwqlq5ui6ydhgyjz,,7- lo -r n:6(ta 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 cm from the axis e//wr q, w;cfu+2vxx hof rotation is to experienqx /u;ew,vw +hx2c/rf ce an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter whee2 son)eaf3i0o) n j)dwl accelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determiea3jdo n)2) i0)fsow nne
(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 u6k, fc amdm69 py0x/ oleosebn( (3)f$R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft s)httqd s n11z*qd3 k,put themselves into a slow rotation to distribute the Sun’s energy evenly. At the stsd1qhdk q t s*,3znt1)art of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 q,e-f++5qlhkayz9yk i3 g, yn rpm in 220 s. Through how many revolutions did it turn in tq, 5lkyyh+3i+-fk , qya9eg znhis time?    $rev$

  An automobile engine slows down :i(q1g n:4 gaw lw h2sut(dxy3from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a ejf;j 6 c oy.w,t*p jtpp/bvm.5m98ap whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutiop;t8 p j9m ,po .5jb/pajwvtmyc*e6.f ns 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 acceleraha;sz ; b2j+l9udlf;ptes uniformly from 240 rpm to 360 rpm in 6.5 s. Ho29bf;l+d ps hl;a u;zjw far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revol8 :chu4lvxcv*utions v u h8c*vl:xc4before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the carfifmu8e 31 qd1 o,i m0yq,aj9m reduces its speed uniformly from 95km/h to 45km/h The tires have a diamdia, 39muqoe8m ,fi1q1m0jfy eter 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 ca2d9 8hrlc lh5nr reduces its speed uniformly from 95km/h to n982l cd hh5rl45km/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

  A 55-kg person riding a bike puts all her weight on each p27 ,p/xb5ah ox krqg9ledal when climbing a hill. The pedals rotate in a circle of radiuslxxohrkpg2bq/, a 759 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 jh2u zqnamatr8 i163fhi b, /;of 55 N on the end of a door 74 cm wide. What is the magnitude of the to; har nai12i/h,tmubf 3z6jq8rque if 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 the wheel shown in Fig. 8–39uhh0x . s7) ntx.vdwrw9 kp.q;. Assume that a friction torquunx9h7 d0kq)pshv; r t.xw..we of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a mass-in6gorzmje3o bb)91 nb *7un less rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the jzr nbno9obe6-7ui *) 3gm 1bnmagnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine rhna - 7wf6p3xhequire tightening to a torque of 38 a37-6hwhxfnp$m \cdot N$ 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 108 xtw(z,/jf(jc8 pnrwwq. l-h+msq9 ) audu,z .8-kg sphere of radius 0.648 m when the axis of rotation is thro,jr-cz )w.hmuf+d xjup(88z (t/nwaq,q lw s9ugh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle d;3xtcr ,y3mx*k+k krwheel 66.7 cm in diameter. The rim and 3,krxyd k3k c;*xrtm+tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated judf6-*p9j--w f - 5m1tpbwr3hwkut lin a horizontal circle of radius 1.2p3jl twuf9tf-wd1p6- w*k-r- jh5 mbu m. 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 scvfb:+ fx bonrkg6;54peed (Fig. 8–42). The fr6vb +cf rgn;x4:kobf 5iction 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 thlj 5mb,*r dshf*wu; .axatc/,uk+k 8ze array of point objects shown in Fig. 8–43 k.cab5 sr,ufxl*dk/+t*8uahwj ;mz , 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 oxygen atoms whose totalgars:w7q.a a9cje pki( / )(may.jra/ 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 satell8(i9c s hgick2pe*c4e qr, +xgite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to ck2psc,h8eg(x ri9 *+qe c gi4reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a unifod x qbr9uw 47l f0*u(j5ef2zqmrm cylinder with a radius of 8.50 cm and a mass of 0.580 kg. C (u0 92w7*ld 5xbzjqu4qeffmr alculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest tor:og+qv19f b d 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 and is 416oexb32(bt gadlj iqc +ln3able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume6goe4i 313axn t c+ (qb2jlldb 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 rpm is shut off and is eventually e 1cro(z-)pb3e 6zn gmbrought uniformly to rest by a frictional torque of 1ze pzn1 c)rmgo(b3- 6e.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 ak 9a,q(y ikiu u.,7 ekga1tt.t 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 -mh m: s(89z nyoyn9feforearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. Thehofn8-mmz ey : 99(sny 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 in Fig. 8–4v9 q 6ux/v(ubt6.6uvxbt vq9( /u
(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 mawdo)u0n :lxi) sses, $m_1$ 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 iix/(ixc c6 o/4njeum.4wet3 full turns (revolu46 4xnj/cx cwt.emio e/i(u3itions) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a mome0vuzk -8gs 0pba1fq. pnt 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 of 28t v/oqnqg, mf6/o/ mjc00,avj0 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg at:*sb0xcjv fm28 0 h6zb+spd und radius 9.0 cm rolls without slipping down a lane at 3.3pj8sd 2xbzs t fv6:0m*c bu+h0 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun a o3wv/8r/ grg i,q v,b3euqt+bs the sum of two tegv g,ew3v rq3o/qu/bri b+ ,t8rms,
(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 (y68byt1 0przeufz: xand a radius of 7.50 m. How much net work is requireyepx6 :t 8buzfyr 10z(d 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 sv)k9mi)btm,+g4d ut g tarts from rest and rolls without slipping du 9md )tgg v,i4)mbt+kown 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. Ito( oanq o0k6j h7gn9a4 starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: U gajoan ho076kqo n9(4se conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a lfw2 r+z:o 7ysthin string in a circle of radius 1.10 m at an angular spee7s +rwz fyo2:ld of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momenv d7yh2rd;n,8z 5x i-b4kghe7fyty w6tum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 2d8;th,vkew4 zh67yr y 7x-5ngbfidycm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating a p iee1/qwd,l2:k1wr h(qy hg:t a rate of 1.3rev/s If he raises his armeh dhkr:wp,l :q(yew i1q1 2/gs 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 sh bz:m4 pe9yq4iown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight: 9m 4p4ebqyiz 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 incre je377tbcg)iiwy9q) n ase her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate ofeji )gi c9w37b7qtyn) 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 througekw, ,rs0rbo4gbh+f48qpi6 nh 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 clay, approximately shaped as a flat disk of radius 8.0 c8s w4nkb + r,higrbq,4pfo 0e6m, 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 spinning at 3.:yfx v b551iefzpu7(y5 $rev/s$ 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 momentumgf +pcmnpap07l95 hs*- 6fvrl 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 cylindrn;lh/chpc 6r9m(r-o gical disk of moment of inertia I is dropped onto an identical disk rotating ato9/h mgrr l;pc6-n( ch angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2l-y 8 yahs)ry- 2cgps0.4 $rev/s$ 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 s b mp61+rpd7q(q;n trplatform of radiqpn6rr+ p ;7bmt1 q(sdus 3.0 m and 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 with an angular veloc3 l- 3d.iieircity of 0..i3 lcerid- i38 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about haldojp6uvye3j9slvi7n066 c1kc 9 vsz8 f its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the80uj6in6z pjvscv3 ly9d76c9 k1s evo 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((g9,lqwzq/rs w (htw winds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass ncnkjg5+q feut-ew4 v009sq2$ 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, tha,tmp5 3 lp9bwgt can rotate freely without friction. The moment of inel pmp9t,w 5b3grtia 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 6.5-m q4q ctli193lf2p vg4s diameter merry-go-round turfl342sqcq l4giv t9 p1ntable that is mounted 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 of the rope lying,5 ,o)i rica+z.bzohq 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 +a b,cohz .i oqi5zr),from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Ea7z+ufnfyj -c6vq j: s64p pp3f vh8.hdrth such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particlejpy 8fp6cs.df:j + hnfv7 v-h p4u36qz orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at akh a9p(kd :/l0tfo*b d 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 cylinder of radius 0.20 m awjw6h6,v ayt-cquires a rotational rate of fr-v wwh ta6jy6,om 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 8t i87o6xzv-ye. (lbs u1x djwsolid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg8i1.l 8 7tb-juxs6e dwx(vzoy 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 s f):htzzxyfjnf,c7 bw- bhsqx8 507/gpeed 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 wi7; l-h jszo- d5bv2t8foswu+ r3uu ef4th 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 thar +-2fou ol;hzesj385b7u 4duts- vwf t the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use enerj*1 c g ew(;y7ilt suvmu0pin;-b/z 8lgy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50i um jlwc/ 0izv e 7b-np*t(u;1s8y;lg 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 illustratesxe;/ dcg evyr6-- zu-gkmi+y93 tv+ma an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surf/u2f:smpw 6y 0l gbiah p5t*h9ace 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 pivo a6 e6s+xg9 nbi:nmeo)t 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 bnoe+nsi6me9x )6g a: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 whvdl 8mzdp2f xg:.r5gm*m(0 s ant to exert a horizontal force F at its axle so that iv.ld :2 *gsm8f5d0m(hm pgrx zt 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 road ilr kj8x/ h4i/k 4uaej6s making a turn with a radius The forces acting on the cycli8/uj 4hka ex46/ ikjlrst 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 into a sling of length 1.5 m andc s1n*l9n tah0 begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0clnsth9 0*n1 a 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+q 1nxk0:f uy88ozj)91vhzet q0yz kv solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the yvoe zqy+80n 0ut: 9j11 8khxqz) zfvkangular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consisz:m 0yk2kz0ugvvj;:d9e xiw.ts of two cylindrical plates, of vjx.k :e;yizkgvm0u 9:w 0z2dmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 h)arrcns81t ,r : -*nrb3blcy z3ecz4track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop ifcly*n:834bsr, 3 c-az tn rrb eczh1r) 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 vyrif6x*b)d d; hj s+jm,8/ ltdo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutidg4u ,z eg*a vit(27pm yr0nw.ons as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of w.r( ,uz p4vinm*7 at2gydg0eeach 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