A bicycle odometer (which measures distance traveled) is attached near the wh*x-;2l26agqpe b owuleel hub and is designed for w-xqa2 ob lue pgl6*;227-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 th 3q er3bjbb0yo9)b)m3y(ytkj-pkq e 5e rim have radial and/or tangential acceleration? If the disk’s angular3b )eqyy ey(j5kk3p0mqb jbb-ot9) 3r 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 k720r.hlt5;vgbeozrk )o f -g described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exerqds y.dq7, ys/t 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 sit-up with your hands behind y,w fi5 rv(.nn(bfb9 gvour head than when your arms are stretched out in ,(vnvb5gn( . ifrfw9 bfront of you? A diagram may help you to answer this.

A 21-speed bicycle has seh4v6 kb ;l 0,hpoaqvy2ven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket ok04b6qyao;pv vh,2hl r a large front sprocket? Why?

Mammals that depend w2c;jch4h7-m+o taer on being able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advanrjc oema-t; +w2hh7c4tageous.

Why do tightrope walkers (Fig. 8–35) carrvlflu/3s 2ha3vd r-v -y a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the netzvaoy :-* 1i-)vpz -wbxxh:ng torque on a system is zero, is the ne-hx* ipbog--w v:) x v1z:ayznt force zero?

Two inclines have the same height but maga ,n0s5y fmrf2-a ,acke different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will -fa20g rcnyafma,s ,5 the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultane t o5m rh.pg8aih-5xp:ously start 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? Whip5mx ha-tr8 g5ph: io.ch has the greater total kinetic energy at the bottom?

A sphere and a cylinder c n4u ;bno7c4p7bq(.ve ys0a rhave 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 tcyap 4r70.esn 7u(ovbnb 4c;qhe bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving6kznoo3 1sb 5: ww qch*wxeh6+ or roc:hqnw6x5 who3 1bek z6sw*o+tating objects eventually slow down and stop. Explain.

If there were a great migration of people towar,-tgetf tyls; -3ibyny9e h4(d the Earth’s equator, how would this affect the leng4ynte t- 3-bgyf,;(lsyti9 e hth of the day?

Can the diver of Fig. 8–29 do a somersault without havint+ 6nbi;,6 cfco z3feng any initial rotation when sh;n3t , +66ebi nozfcfce leaves the board?

The moment of inertia of a rotating solid disk about an axis thrce y v1e9wehue;4 pd,cn79kr/ough its center of mass,cre17e9 vkcen / 49uh;dewyp 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 holdingo ylm-toh8.hw*4g b4;g wim7 q a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay thohih.tm- wb;m l gog 4*yq48w7e same? Explain.

Two spheres look identicalx3pe btq .qd84h//khx and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine whick3qt8h4b/ dhxx./ q peh is which.

The angular velocity of a wheel rotating ak* 1gpv 2qrj3ygtd d9h (ic;1wqf0j. on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of jrk0 d 3 .djpf1*wy29qavtc qg i;1(ghthe wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a largq;v:kg+t6wv e e freely rotating turntable. What happens +qgtw;v:kv6 e if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it qupq)hnv9nypj z, rc jq9 ( e2tk *ag4)gx7m;c-nickly. As he throws the ball, t* p)n , ap99 -tjn(2gkev)g7hxczm4qy;nrc qjhe upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of c,qhep;pb xhc1iox(76onservation of angular momentum, discuss why a helicopter must have mbqh(pcpx 7oi ;6xhe1 ,ore 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 radians: (+7zwrm plv y 1t6(z,jma) 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 coincid4;te;e *xibh pl+ rh(uence. Calculate, using the information inside the Front Coverb*p;h+(h xtl 4ue rei;, 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, zhmlyfmr18) ))6mgv k380,000 km from Earth. The beam diverges at an an)l)r) hmk61y8gvz mmfgle $\theta$ (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 th8jf o: d5m4,mul/m8cmt; s ra.v-bc que motor is turned off during opesmm;ua d lj:,qcf/4m vbmt.-85ou8rcration, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level f b73kf7mr5fa uloor 3.5 m to another child. If the ball makes 15.0 rm7fbu37k5 fra evolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutioc mrxo5yxi47 o/t* 8sjns do the wheex7 4jymo 58xrto */scils make?    $rev$

  (a) A grinding wheel 0.35 m in diac i7kd ri/+4kvmeter rotates at 2500 rpm. Calculate its angular ve i4dc7krv +k/ilocity 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. bq f8:lt1lzj :8–38). (a) What is the li1:bzl ft8lq: jnear 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 o nrz f*q)h)3wthe Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sp /92 .nyfprgio 4 ju)adg7uxc1eed 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 cm iev ;w5,sfuy .gj4 9hpfrom the axis of rotation is to experiensu9g jf ew,;pi.h5v4y ce an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uni5.m v,u6p,owjdf fv)yformly about its center from 130 rpm to 280 rpm in 4.0 s. Detej. 6v ovmfp,y5fu) w,drmine
(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 radiu ohdivm((fs5ev0 cte (:gn.g9s $R_1$ 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, astrok, vry0it au.vd,ujouq5 1f92nauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minu2j v.,1ofvi d 5taruyu9k0,q ute 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 acceleratwibqlr(3( f ;ses uniformly from rest to 15,000 rpm in 220 s. Through how many revolutis(3wb i ;rlfq(ons did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Ca9hc r p( u+es.kz u,sg.rrr /b:7mwof2lculate
(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 whirlip)f - (fjflu 5,avcia3ng “huma 5aufla(cp fvi3fj),- n centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter r a*vg66am:bvd .c -xfaccelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point oaxvdg6 *c .vf:6-barmn the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is (*vf j h2eh(n,o2:sa5 ai io1afdj.xx running at 850rev/min It turns 1500 revolutions beforhsofd nj5,xe(21*o. 2xjiv(a ai a:fhe 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 rcw (n g)ln2k/95bokxievolutions as the car reduces its speed uniformly from 95km/h to 45km/h The x9cb2wk/n(ngk o i)5ltires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces itsi t: jfxu*lo-d39v )mi speed uniformly from 95km/h to 45km/h The tires have am3:ixjt fu )9vl*i- od 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 pedal wh1xj+wom (xqug/yf55l en climbing a hill. The pedals rotate oug+q5( yx/ l1jmfwx5in 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 rqgjs)4h u9s;55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exer s9q;gjhus4)rted
(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;7f9mfkdqx bhq9m ,x. axle of the wheel shown in Fig. 8–39. Assume thx.k; bdxf 9mf7 mq,9hqat a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod whic4 dmkz8;5(y+hpvvm rl h pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the n(kmz4r ;vhm8v dy5l +pet torque on this system.

  The bolts on the cylinder ,f(txp a5kkrz ;+z6vohead of an engine require tightening to a torque of 38o,;xkzvfp5t( r+k z a6 $m \cdot N$ 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 inerx eq-i8z--1:e1kl( qmdr)g t vk)dxbztia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is thk-qdv qe1 bx:izzdx1)-kmt )e-(8 lgrrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a 4jd6dt2(ae wqw2xu+e bicycle wheel 66.7 cm in diameter. The rim and tire have a combinedejatuw +xw(qe 4dd 622 mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball x 6z0; svt;pj xq010hlotfn0 kon the end of a thin, light rod is rotated in a horizontal circle of rqkvptlfhz o1;00; x0 xjts6n 0adius 1.2 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 wf)jy * -xdj/:v c29bdc sx(e(aq9kgc/bc3imbowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force betwee/xb(ca(vx9ekc 3cqgdi jd9ym c b-2)*sw/fj :n 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 3.rqktm vxwb7 1r5k u:of the array of point objects shown in Fig. 8–43 ab17k5mvrbkwqx.:3r tu out
(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 at m hjhqq:fw9b.-y0w9 qoms 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 spil33: +adpbwyc7n taq5nning 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 requiret37+3: nycldwqpa a5bd 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.g fh9 r6x/cpjr .9o5h )kiv3qy50 cm and a mass of 0.580 56fqr pg/3oi 9xy. h9kjv)chrkg. 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 rnb,8;uk(ep 0sw zn;vwest 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-driven merrgf2b ikqcodj+ /t+d j3e.ol 70y-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 radiuifj jq2o3 d07b.k d +/c+otgels 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 10,300taeewk. r.7) t rpm is shut off and is eventually brought uniformly to rest by ate ) wre7a.tk. 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 acce( rr 5)fseq1gv43b c2t3cx kiplerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thl;hqr zl9.sdn/n a. -jrown solely by the action of the forearm, which rotates about the elbow joint undh l ;jd9nqraz.n./sl -er the action of the triceps 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 long tb 2pc*dg5/mhkq85p0jtgl zq . hin rod, as shown in Fig. 8–46.p *m2l8b.q/h5jggpkzt q5 0cd
(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 col7li.0yt7:nn tfa t*x nsists 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 aqs d1.r / ksh/*r:ubil /do4crest within four full turns (revolutions) and releases it at a speed of 2uoc.d1rkl*s/i4h sbr :q a/ d/8 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment od 2ca9r3 9t*rre(( fj-kltxldf 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 develops4 ziz,2 dw;gow*)be hk 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 radiv; hi8 lj2a6ggus 9.0 cm rolls without slipping down a lane at 3.36ij 8 g2gahv;l $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to tlfqu (.e:pz 0cuh0x8qhe Sun as the sum of two : zx 0ul8qpu(0cq.fheterms,
(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 wo6 esrq6qf+0,;u0k c5ec sttdk 6v8d tj8d2s of 7.50 m. How much net work is required to accelerate it from rest to a rotatios kvsor0d65 ,fcw6dekdes j;2qu 68 qt8ct0t+n rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest vrvh(l,dfmkp-y 32rlx m 3r13and rolls without slippiny3p (l3rk-rmlfhvv md3rx 12 ,g 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 andw3w yytg9-w (g 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: Use conservation of ewg- w 3yyt9gw(nergy.]    $m/s$

  What is the angular dckf7p h)giz:l:y6l-ghsg (5 w8a ws0momentum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m alg- 6sfz cwl:h: 7gd 0i)gwak85ph( syt an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindricp:qy; p1xr ;fyal grinding wheel of radius 1y; y ;qpp:f1xr8 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that isk 6 bg9wrpu(h4 rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotati 4wg(kp6bur h9on 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 momek ghc*p-d 2clo6q );q6i x3eezxn03 iwnt of inertia by l;c *x6 k2e60-qnp3qi3 )oghceiwxdz a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation raprxoh1 t/ oz e ,;i+4xahbaq2.te from an initial rate of 1.0 rev every 2+h z bet a,2h.4i;p1oo/qx xra.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around oj7ee 1jp*wn .a vertical 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 clay, approximately shaped as a flat disk of radius 8.0 cm, o 1 n7jeo.j*wepnto 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 zlj :6kjarv;5*l5jmfa figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Eay-n*h)l,roo4 po vb)re q13 uarth
(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 c1et;:sy3y in I is dropped onto an identical disk ro;3n:yisc1t yetating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4asr ya/h4nc*(uua -ypd * s:f2 $rev/s$ 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 rotatimacdprr8++:g n 4,cd ing merry-go-round platform of radius 3.0 m and moment of inertia 9:p nr+r i4c g8ma,ddc+20 $kg \cdot m^2$ 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 merryb9+6lk- kwwk 0 q,lfko-go-round is rotating freely with an angular velocity of 0.8k ,q+klfb0- o6lkwkw 9 $rad/s$ 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 )h9m f;jazwh8 (o*cqn collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing r)98hq* ( ajm wozn;hfcadius. Assuming the 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 of 120re; n0 qlf0 ,js;o:exd $km/h$ 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 7 cps abi47i 3g7ckay7$ 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 rogw n0kw/ays .f6fs/qy hk; m57tate freely without friction. The moment of inertia of the person plus the pw /yshks qm;y/gfn .76wk0f 5alatform 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 diameter merry-go-round tugb6gv ya0u *qqooc*8, rntable that is mounted on frictionless bearings and has a moment ofy ,qub* go*8qoca g06v 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 rop5 hrhr/7ngkfx; f mke i9g+0bi k-u+m/e rolls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from thk; kr+g7ihr/05eg 9hbinm+ mkf- /fx ue spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Eakq jjk1j5* .qt. cdm;frth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle oj f*c jdqm.15kkq t;.jrbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest ,3ggw39(qc8 z)as54f yu*h qlibwzja 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 cylinder;l r -bujs(hl4g3hi- e of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at cli b; -3h-grus(4heljonstant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, e*e + ge2vrkg 36m7zscrach 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 linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released fror*r7zv2+ eg k3c6em sgm rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear whee qb: )cyihr--wl ($\omega_R$) 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 o-eo-l) seaub4 v *yn i;v)azoo.zm;j 3ur Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo 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 v*zuyve-;4b)3o. aeo-zj ;lams io)nall times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is;0qswc 89j k0 3g *qexyomx2yp for it to use energy stored in a heavy rotating flywheel. Suppose such a car hymx gy e3j*0q9 w co0xqk8;sp2as a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustratemg-oz6sc7u6a7vn 9l01e qvz os 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 surface at s1 tx5+ m/ ntezznb7zxzai2 48f:y8b9o,m r xgypeed 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 ina3asly/2k8ay 6e l w)gnore friction) about a hinalyes)wl 8a6 2/n3ay kge 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 shown. [Hint: See Fig. 8–21g.]

A wheel of mass M ha:qv+tt * y(leas radius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it ayl (t*:vqe t+rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speeja::i,;i/d yd xh* m5dxgwro3d 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:,;ag 5dx ymx :irihjd/dw*o3 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 1e0a2 6:fu+3rjyf baha .5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to af+b0hj 6: yrafuaa3e2 rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid bmj0x vu5d m7.cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her 7v50d.bjx ummbody.   

  You are designing a clutcd r42jxjo*3j fyzt7pv t( v+vko15/wk h assembly which consists of two cylindrical plates, of masd/v7 v3jvpz5fkkj 2t4 oyr 1xw+t oj(*s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 track of Fig. s n9jy)(m zg09cb9wfhxky:p18–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the 0 w9b z1msc( nkj9)y9ghfyx p:loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not +imla r s. j;v5)dn:kbassume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions asip) 2.hpz5wiq the car reduces its speed uniformly from 90km/h p)5qz.i phiw2to 60km/h The 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