A bicycle odometer (which measures distance traveled)45kol-t vvj+ktn9(lylx+ u ,8rbkf+x is attached near the wheel hub and is designed for 27-inch wheels. What happens if you u+ tvf vuktln,xkx(+ y br49 5kj-ol8l+se it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constjluf ch8j94iheo (4i hn2;o9 nant angular 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 acceleration? For which cases would the magnitude of either component of line9;hoj49nh24u clh i( ie8ojnfar acceleration change?

Could a nonrigid body be described by a sin.k7 ,2n xdbwvcgle value of the angular velocity $\omega$ Explain.

Can a small force ev+zg bmr4ppubbwkgi;9t hg/ kx x : ,mn239/n8ger exert 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 8rnb0+wb m, 4oj/r e,zvhvyus: 9va p0do a sit-up with your hands behind your head than when your arms u jr/8nse zb 04y:v9rbmp h+, vo0vaw,are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets a-2 mdb7m04qkz:akttbi-6b x svgt1d8t 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 or zxb0 4db:6ta--g21t k stbmiv8kd7q ma large front sprocket? Why?

Mammals that depend on n1c8qgzpx j kyklq728s30d 9w*e3aqkbeing able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis x3q92k0g apy8d37nl8s*kw q jkq1zecof rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35 yjec1c5tp7,;k tt5)e:eflya) carry a long, narrow beam?

If the net force on a system is zero, is the net torqueauq(;bzz5 anm)a 0ow)9uto9 w iqh+b) also zero? If the net torque on a system is zero, is tha 99b);zoqm t )uwa()zn5w ia0ouqhb+e net force zero?

Two inclines have the same heightf3y+h3 ph/ dyt but make different angles with the horizontal. The same steel balhtyp /y33d+hf l is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rvk:cl+o;ent8)j r :wu olling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of theu:jv l:8r kt+ne)cwo; incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder haveqsl g15t8b*zu-ssf )w;-nj j f the same radius and the same mass. They start from rest at the top of an incline. Whs -8;lusgqfzn bfj5jws) t *1-ich reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are c *chgye;jh,;ew*2s ujonserved. Yet most moving or rotating objects eventuallye*gh jyjcse,*2h;u ;w slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how woulmy 3*cku-0.dqsof/z yd thiysy qzm/3do0 k.fuc* -s affect the length of the day?

Can the diver of Fig. 8–29 do a somersault w 1fsaocw ;.p0oin6ae(vkiqywk n3 oq *9*;- phithout having any initial rotation when she * ia3op*oow n;aknwqpev;khq-9 s 0(61fiy.c leaves the board?

The moment of inertia of a -es0xou9g w 3iy1; qqirotating solid disk about an axis through its center sugq wi19x;i-0oy q3 eof 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 on a rotating stool holding a 2-kg mass in each oug3jo+ xh5( mjsiihxg) +.0x shtstretched hand. If you suddenly droxxx+5 .so30hjig+mi (gh j h)sp the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Ho: (weshikturt-4 y*c4wever, one is hollow and the other is i *cu wtyt:h4k4-rse( solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. :; wn 6:oqnqrkd(e le-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 decr:q w-k6 (:nq;ldeeonreasing?

Suppose you are standing on the edge of a large frcguz/ih1 s) v/15w hqaeely rotating turntable. What happens i5uw/ha vq/hs)g 11czif you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it q yz9kfd( )zer 3mtyp,67cxn2s uickly. As he throws the ball, the upper part of his body rotates. If you y)mt dp3 ys zfkeczn(,7x62 9rlook quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a helra1p-8+kkp3ewls5 w k4 ztd- eicopter must have more than one rotor (e5-e -za81k tpr3 kkw+pl4dswor propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following anl:m zx,y)qjuktjz0/t1wd+vh-xa4 1 cgles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth berby hj-* 4;dqacause of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular da-yr* h4q ;jbdiameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directhj.vkjgdk a8g- u384l /smp4g ed at the Moon, 380,000 km from Earth. The beam diverges at a4g4p8 gd hmjg v.ksla-3 j/uk8n angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 j0;snz2 7tsmf 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 sloz72s tsnm jf0;w down?    $rad/s^2$

  A child rolls a ball on a t:z.lyodbc w; p0,zi 6zb,.ttlevel floor 3.5 m to another child. If the ball makes 15.0 revol:oyczi0tt..bt,ld 6 z,z pb;w utions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How mcri).yv9air i 5,4 +yco+ puyr,1vvlaw e.g6q any revolutions do the wheels mak.6gauyrv i+awy5 9ceo )r,ri4 l .i,v+p 1vycqe?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its anx9 zjs wv, qs r,/xi-bic7ff0;gular 90;jsfic f z/x-q,wxs b,ivr7velocity 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*hhq1f-ew d ein89ciz ndp*5) (Fig. 8–38). (a) What is the linear speed of a chi)wpnehchi8dn*i*d5 ez -f9q1 ld 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 ik(s wlbg n5v,grm/e yq:dn*,d 0z.zw+ts orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a po4rt ;1m,slsi pint
(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 paksc6 ge,.s(px,sstxcz/ / 1kxrticle 7.0 cm from the axis of rotation is to experience an acceleration of 100,0k. sp/z tcs/(s,eg1sk,cxxx 600 $g’s$?    $rpm$

  A 70-cm-diameter wheel ofdyd77;kic0 nv. xp5umg )u+ accelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determivm ; uyp5cn+x0 7gdfk)d.7iou ne
(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 crxu cq1hhgh* av2k0)y56z 3c$R_1$ 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, astr *lh pozvh0z t34ndb06onauts 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 n4d z6n*30 otlpv bhh0zo 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 15,0bw-(i hlx d;5zp iom(700 rpm in 220 s. Through how many revolutions did it turn h;ozilx7d(5i wm-bp (in this time?    $rev$

  An automobile engine y g:ow-3vf-wkslows down from 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 m:iw.y- y fj+aflying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min y:a- mwy.+fji 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 accelerates uniformly from 240 rpm to 360 rpm in 6.5 szfvfm/to *n--. How far will av n-*tmzf-fo / 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 d az w.:k vh30z;hb7vrrevolutions before it comes to a stop.v 7w.:rzbza;3 0hhk dv
(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 car reduces i n2tg6*ar)wc kts l a-:2rxw8pts speed uniformly from 95km/h to karlwg-2)s: * 8rc tpaxw n6t245km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed ue 3dfz(z2s5fnpxriw* ie(q3 +niformly from 95km/h to 45km/h The tires have a diam* 5f rzx2pie iqd f3w(3z+(neseter 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 when climbing a 0 j3sh3ksl *xwr) bt0chill. The pedalk)l0 w xjrt bs0s3c3h*s rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is the ma(t m wbo ;ukj+b;h**xykb* / :p+grbbfgnitude of the torque if whmr kk;x:+y;tuf+bo/pb (jb gb*b**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 tuds e ri;jn gr0v;if25,9e c6phe wheel shown in Fig. 8–39. Assume th,6 dv0pr 92fs5nue;cj gi; reiat 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 wm tq3ya5 7f i6d)zd8zwhich 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 nfm 5)w6dqd3ty8zz7a i et torque on this system.

  The bolts on the cylinder head of an engine require tightening to a tors/qp m*ge9 .xaque of 38x.q *m9/ apgse $m \cdot N$ 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 10.8-0p2mpz y(xy3 gbap1q*4(gc vikg sphere of radius 0.648 m when the axis of rotation is through p( px gzyv4*1y0bq3mpiag2( c its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 c5mx 9vr,jx1x7;c ss m;r7ksv6jni*vem in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub 6e ,xsxjs*rrmkx 71 m9 c7;ni5s;vvjvcan be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizontay,:v4rpjhzj 15i2 l8sg.j wsul circle o:8 ,j4 szh2yrivpuj g s5jl1w.f radius 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 bowl on a potter’s wheel rotating at constant angular speeyqam-r9ca 8-6u) ,pb 9ipmf omd (Fi6 -o9pq amm-bpufm,8ar i)y9 cg. 8–42). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fig. 8–4r:)srg hc e6a43 abou )rg 4:s6haecrt
(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 whvmf ha ;kz- b34t7p/qbose 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, engin 58.kuhwkzl r0eers 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 requirk .58rkh0wzlued 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 rad*13:dvf i75urvo d ghbius of 8.50 cm and a mass of 0.5:5 vd*1b7ihrfd3 u gvo80 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from res/kyc5t1(j c gu0j0mcet 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 tangentiallpcfu,v *7a0fzidk) 2 ky on a small hand-driven 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 of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, nvkz*2,pa ) 7 0ucfifdkeglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,3009 k+ h)z1ohtiuq6y/ ni rpm is shut off and is eventually brought uniformly to rest )yio/6tn ki z1u+h9hq by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerwtrpmrn zop mxy4, u. xtjzbyh23 +.qj.:9p29ates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, whiw)q0 qwyfq ,w6ch rotates about the elbow joint under the action of the triceps muscle, Fig. 8, 60 wqwyqfqw)–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 longz2:imm8 6imr k thin rod, as shown in Fig. 8–46. ikim8r6m:m 2z
(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 consi9jbf7l:4 /lmz/xo xc1 udw 2justs 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 accelera.zqglqm2ym/b)xg)j8zhsi ) 1 tes the hammer from rest within four full turns (revolutio)ql8i zgm zm1hsj/qgy 2x)).bns) 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 azh 0ixpsk84tr jfs53rzday.ur-3,i+ moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine dentv3z;m*d) :z(w/f (iexkywcyd dd 3(velops 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 andjo2 h ).l6dla3vpva:s radius 9.0 cm rolls without slipping down a lanavjl.:2l o advh3sp 6)e at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the xyoa2mf 8.(wk sum of two terms,m x w.ko(ya2f8
(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 nnp; ; lp tqvau9*ggfp30s3u.rhkv l+9et work is required to acce. vu;;agpvtkpn* 30pqul39slg f9 +hrlerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest a u8hzn;2k gk1wnd rolls without slipping down a12 ukk wnzgh8; 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall and*jgt3 m rw 74o5hwc;kv its lower e*c4 g j;ro5wv 7k3mwthnd 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 energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on thg.q wnw1 dc7sv;v(m0n e end of a thin string in a circle of radius 1.10(nv7v.nw c;1 d 0qsmgw m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform c1dk dsfb ;/9usb2ih) bylindrical grinding wheel of radius 18 cm whenhb;dd9bu 2)ss f/ i1bk 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,bzy rktt*:kc vtqqs5vx+ 20+4e jq+r , on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotr vz:qbyvkkt+ *2qt +40t+x q ce,r5sjation 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./ kz89-ts df.plv(ylm e;(lon 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she n dsle;o./tyzv-f 8 mk(l9(plmakes 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 rate from ap5wloh8 ne00 an initial rate of 1.0 rev every 2.0 s to a final ratowp80e a5 hln0e 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 vertic5 3tdbfy0bu- mal 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, onto the center of the rotating wheel. What is the frequency of the wheel aftetd3mu-5y0b bf r the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinnined k68y7 rdja1ag:a7bvlin+alf00f + . csig.g 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:lpw8 fktpgn 80bg 2-d 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 dropped onto xi4/h uqfdqpt;2 94tk0zmu1a an identical disk rotating utd;zp 2hm9qi4a10f4/ qk tux 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. xch ix8gw /aq6lyxe50:c;hq;xr09gzd r( pw,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 centz i)y 77;cujk ey3prv9er of a rotating merry-go-round platform of radp7rc)z7 j;kvyeu y3i9 ius 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- q7kld 7y0(htbgo-round is rotating freely with an angular velocity of 0y(l7h0k dtqb7 .8 $rad/s$ 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 eventualyi hpa/ m2cg(3ly collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Su3m2y/acpigh (n’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 wo+; gwoz k sy3m e6/v1i7ctf9hinds 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 +6qbixo. h0lh$ 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 pla kxm i;x b(0n5e 1eshbh32f( rmmft6b1tform, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the plax1sekxbhb6f(m1hbf t ;0 (mremin523tform 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 diamikug6sm+;g5c eter merry-go-round turntable that is mounted on frictionless bearings andg+6mgk uic; 5s 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. f b: dhqd3nh,m8p(pc 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 spo (m8nhp:3dhdpcbf .q ,ol rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earov as oyag+-4s r0h9b.th. Determine th -sa9rb. ogo yvs0ah4+e 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 orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest aiwv*q q4-f s;ot 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 of radius 0.20 m 7e ud8ak e cw.4/zpkdxokk8-5. evug tjsx33.acquires a rotational rate of tj53xw.8exed8 k 7kdog-k. zv kscu.a4e 3up/from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg and t cvcm:c5m9k w7 b:3uodiameter 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 sk93u: tbw:mmcovc 7c5tring, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is de-v7jjdib.u*)o9b d the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were rotatits vg,myq z.bk8q t9k2 l)pk( v34a5bing 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 rot,.g5t k k b(8paz)i4 2tvbqyqs kvml93ation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobilc3cax of;xyp: 8r6 ep7e 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 and mass 240 kg, and should be able 7yac :;xp 6e3porf c8xto 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 illustrati(f2 +frhh h-yes 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 horizontalghjps1 c*+)uupo3zz )s,sfx; 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 lehgj4t cxt )*qj0it65ength L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as j i)e4jh 0 gt65ttx*cqin 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 has radius R. It is standing vertically on the floor, and vf-lrz 18xvk hd29g ,mwe want to exert a horizontal force F at its axle so that it will climb a1 dh x-m,rfvvlz 829kg step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn withuh96 e a3t.ikb7g nnc( a radius The forgan k.c63he9(tb uin7ces 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 into a sling of lengtpmae5s(dhv peh5 .9 2lpxro,,h 1.5 m and begins whirling the rock in a nearly .h ,sd5 hepl2p(vx9m,raeo 5p horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a 5.ud)yn:mc.xn ry 7)wm285 lmyxkz bpsolid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinni d nc .ymmn.my5)2kx:8xwy u)rlbp7z5ng skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylin ,;cxellaq p(6drical plates, of mxcpl;q (el,6 aass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 lolc/3wc l m/5aehjx-1xoped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the m h/l5lwx x e3/-m1jcacarble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do wg)uiilp*p6 fx +uj5-m 8h x7rnot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly hsqd0tf72 ai/3o1n*hlebiq r je3d:9from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular /bd i3t s7j*q:qr0i hd12eahn3l oe f9acceleration 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