A bicycle odometer (which measures distance traveled) is attached nea+vcu;6n;yw:8a+ o uw)bm pwgir the wheel hub and is designed for 27-inch wheels. What happens if ygm8bowi:+p cuan ;y;v+6) wuwou use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angula 5/jk9 enq/kphr 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/ k pje9k/n5qh component of linear acceleration change?

Could a nonrigid body be described by a6et(s0 kuqxh , single value of the angular velocity $\omega$ Explain.

Can a small force evemr9aa50* g*t l jzxxzp0f nu/;ww-lk9r 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 do a sit-up arde5w ly1uq fr6of/1 ueihn ,8b/*8bwith your hands behind your head than when y wn856eo diebl b a1u q8r//,fyr1*ufhour arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel anz mii,1x05xozi k*hs *d three at the pedal cranks. In which gear is it hz0h,x1 so* im5*izixkarder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with fle wx6lfy),-h ukiy;b *kshk ,- ;hk6 lu*wixf)yyb and muscle concentrated high, 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) hkbyx3z*:1 tz carry a long, narrow beam?

If the net force on a system is zero, w28.qkyx .sv+k bxwy iodzw -.dl 8g/yuhc 957is the net torque also zero? If the net torque on a system is zero, is the net force zeroyyi.l.h8 72sqwbgddzxx-kc5yvu./o 9+k 8ww?

Two inclines have the same height but make different angles with the horizontapy:u.kru98 -oncd/h gl. The samudpo n h.y: 8k9grcu-/e steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneouslmmq y i ii63b1loyw 1r:+yec2co:m4;ey start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which rear34w y16;ml +:me bcio :ci2i qe1omyyches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the sa wn;p4gzbbgg;xa 1+kb)wtr83- f3 x jgme mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the botto4g3 gajwb xxwg- ngp;;r)f1 kt bz8b+3m? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular mome*/:dzhodc /b2h6y nmu0z*e ni t/k -sjntum are conserved. Yet most moving or rotating objects eventually slow down and stop. Explain/6ny dcjhz0ebz:- d**2s/u /kit homn .

If there were a great migration of people toward the Earth’s eqxbu ae/q 4,y5quator, how would thisq4euya5 q b,/x affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotatio0yyeq f+ml1*3is3 mmcx4 bg,rn when y+c30r*ebilqm ym14x3f , smg she leaves the board?

The moment of inertia of a rota7apnk7*7)w n ,dd+y3l ooqt3qypsrx( ting solid disk about an axis through its center of mq3x y*+rad3s7)q(tlnowpnk o y, 7p d7ass 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 yx gl/4*fbee, each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or s*b lyef,4xe /gtay the same? Explain.

Two spheres look identical and hav (iii2/lzly2u e the same mass. However, one is hollow and the other is solid. Describe an experimenuizi/ l(yl 2i2t to determine which is which.

The angular velocity q:pggn21qwa+g hpf* 33 ,pzsw.w y+rd of a wheel rotating 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 the wheel. Is the angular h2q, pq +wwgapw.3*1gdgf s p:3zr y+nspeed increasing or decreasing?

Suppose you are standingh1yapq5 dm x0e67z(gv on the edge of a large freely rotating turntable. What haz dhp5 1(vy6axmqg07 eppens if you walk toward the center?

A shortstop may leap into the air toxo43w niy5d3oekq 0)i catch a ball and throw 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 rotate in the opposite direction wo53kix )iqnoe4y 0d 3(Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a .)d4z9wki9lkeuz5ozjk269p mi qi 5 u helicopter mustz p6imlku2q)k izdikw 5994j 59u.oze have 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 i8 -hedo9ukqj 3n radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coinc;wo 50rrda7t4 +gv lluidence. Calculate, using the information inside the Front Coora wg ll5uvrt; 74+0dver, 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 t9h- 0.d1cqvg97b1qvutu: yt)zlxn h diverges at antqt g.9d0tuyvv-u:n)1c7 hh19lqb zx 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 rate9k1 n(boidsr/;0r wst lry d)6 of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the ad ;swyls1t(k0bri drn9o r)6/ngular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. o9td3gk g)p:cIf the ball makes 15.0 revolutions, what is its dio9:ctp3) dg gkameter?    m

  A bicycle with tires 68 cm in diameter travo5bg9a9x di luu9zp8 *abrb0)els 8.0 km. How many revolutions do th9d9o 95ui x*gprbu8b)la0 a bze wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Cvigcyq(2oz +.yqr2p- alculate its angular velocity in pqvgc(q+yiz.r2y-2o $rad/s$ $\omega$ =    $rad/sec$
(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-ro oycj32/2 zfop)s+ atyund makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the cents2/yz j+y o)at3fp o2cer?    $m/s$
(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 orbi64ev 4 :cjx w6.62/shtmout4d zihgfat around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a 9q7 d 2+fm-zr*v-oyd mu2ywwhpoint
(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 cent5ktyr yy6ucpi,+ kt97ad6q2 y rifuge rotate if a particle 7.0 cm from the axis of rotation idq2kti yp, t6au975r6yy+ ckys to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about i94g s uq(w5 ; oxh+d-dmatx( mtblc8, zfoo.+pts center from 130 rpm to 280 rpm in 4.0 s. D-(( ho4u,xcpg5 dxzsbomtf;9mo8tl .aw +q +determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius u9wd2 /d z4a zrzw;51o2g ssqtt/k7fo$R_1$ 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 Moo ck9897srjid7mh 5azrn, astronauts 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 minute during a 12-min time interva9 c 7d8sh9ramz kir57jl. 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 accelerat)ghk: :y0n3x.rxpfolgklz 88 es uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions didxg8yl.h3 k zpol ):k80rgfn :x it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 16rp:u - 8no 9ng9xvejz a1w6pu200 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 hi1hx9elh/z1dzye si/ 1ghspeed jets in a whirling “human /1 xhy siz1lzhd/ee 19centrifuge,” 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 accelerates uniformly from 240 rpm to 360 rpm in 6.5 seezv1 /+u7;n q hj8eov. How far will a point on t8env1jhe7v+/u;o zqe he edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/minl8. qctow-h m0 It turns 1500 revoluto8 0wlhm. tc-qions before 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 car reduceskvg)i7hcg6 gd2 n3gzw) io0r; its speed uniformly from 95km/h to )vh60ndk)gz ;ggc7rig2i 3ow45km/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 re1 gww+6 zzgz9u;. wiywbcp y1.pz10a kvolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tgzbw9a1zuz1ik1cw0. w wp+z y6g y. p;ires 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 pedal when climu:bfm0 o;gr 3f0qyu7aez:) vyi gr72lbing a hill. The pedals rotate in a circle of f0q7 g auiu0lv)7rzem:fb2y 3 g;ry:oradius 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 -h 52ps7np 7ypnl-valend of a door 74 cm wide. What is the magnitude of the torque5sp-l7-nlph a 2pvny7 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 z/c0kd4eo c-(jlous885 l2p*f o n yroaxle of the wheel shown in Fig. 8–39. Assume that a frictiop(8nuoyo24zcfljlo 5 *0 r/oscdek -8n 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 myw8uadofvpip (:e k6//-hx/ ends of a massless rod which 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 net t/km8u f/y-(xd: a6vwip pohe/orque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque ofry33 fn8dtfi;5p b/ bo 38 b3rp35/;dfnft ioby 8$m \cdot N$ 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 inerjsh aa kjt671;r9atnet x58 d/tia of a 10.8-kg sphere of radius 0.648 m when the axis ofj5/7at;srh a9 ke861a xntjdt rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rim 5xqwf 3 a8sq vooc79w5an9c8 v5osq7wof w3aqx 5d 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 * eopagsl0wqt9q q7,4ykf ;v7rod is rotated in a horizontal circle of radius 1.2 m. Calg9k s7 7*a0qvtq yq ,p4;ewoflculate
(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 anguluy8se)siqgz e1 tm0:3f,v.) 5lr1q fvm t;it war speed (Fig. 8–42). The friction fort0 sm q v),;8m)l1ifef5z isr:vgt.qw 1tey3uce 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 tnz ztn)edi(6 ku4v6k8q f)n8 of point objects shown in Fig. 8–43 tv8z ktn(znkq6nuf4 8) ) ed6iabout
(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 oxygeny i55b+v awzmw)2)jrr atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindricalez6gug8z )r l+ satellite spinning at the correct rate, engineers fire four tangential rockets as shown in +l6ugez )zg8rFig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of gco5 d/akrj*hvzw-6z(0q 4zx 0.580 kg. Calculawx6ha0go c-z kv/z* d 45qjr(zte
(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 batooqc6g2h -z0z, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentialvf9i. wm7 503 oqcyycbly 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 ofc oy0m7bvfi9yw. q3c5 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 brou 2rj( 9c,cadwught uniformly to rest by a frictional toduca 2(c,r9wj rque 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 4 r6h mjdcg5va.wi,27nmb n-zaccelerates 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 +3oqhly1ym n 5solely by the action of the forearm, which rotates about the elbow joint under the action of the tricepo 3yy+hq1l5 nms 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 bla.7p zru3 uuau+de can be considered a long thin rod, as shown in Fig. 8–46u3 u+.zapu ru7.
(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 +bc2bz2n vd n7of 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 hammep ewa,zgoy )jp7b-/k *r from rest within four full turns (revolutions) and releases it at zbp/ kew7y),o pj*g a-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 moment of inertia .*enn - pfm;. 7szn-rfsgr4zwof $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a tor22-flier5 eoa4 p hy1xque 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 rp7 sw,ly56 urzadius 9.0 cm rolls without slipping down a lane 56w,pyu7slz r at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of (/ bk pe4;vif kt;rh9mthe Earth with respect to the Sun as the sum of twvbi;fmhr;(9 kpte4k/o terms,
(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. ,tbe .zaet/v1;dmz4 d How much net work iavtz;1 ,tdzbde em/4 .s required 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 2 1 nw55 qxa2u)dp7))xx wqpzqe0.0 cm and mass 1.80 kg starts from rest and rolls without slnpd x a)27 pz)5wq5xquxe)1wqipping 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 verticae- l4u 0 eov2wz6ymbh61o (utqlly on its tip. It starts to fall and its lower q y( zl obhov 4u6twue026m1e-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 energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on jd*1*es4gw3duuc bi j 6 5jpg(the end of a thin string in a circle of radius 1.10 m jg *s16edgbdp 4*u (53 iuwcjjat an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a cpt2rksfp-mwq6-)p9 a/ o/it 2.8-kg uniform cylindrical grinding wheel of radius 18 cm whenq tr-it92p6m-koswap /c/ fp) 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 at a rate e4cj ,0 ikn/xb (aymd;uprw0-of 1.3rev/s If he rai(br, -mud c/pyk4ixj;e0w0an ses his arms 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 shown in Fig. 8–29) can7;m(v2e:yf a 0nak rkt reduce her moment of inertia by a factor of about 3.5 w2 atry;nf(e7mvk 0a :khen 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 rate from an initial rate of 1i (6n7hsl xh td:gt d.znb/-j2.0 rev every 2.0 s to a final rate of 2-hg : sdntdx.(n6h zlij7t/b 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 through its center at a qefb4f 2 c5:cwfqb-x+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 sc b2fqcw- q:4+befx5 fhaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning npb;f 0xrr9 w* n)v2z9xau8heat 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 momenqpd,fa1 dg ixr h mg92c:)a1jjk3z00mtum 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 diskmd5 z+:zu ev flpx.b7dl /,*at of moment of inertia I is dropped onto an identical disk rotating at avtfd7ump5xdl*. ,z+ :eaz bl/ngular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.ye0h)3lii*ez;zc 6xp 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 ibthu13 i .lfdlk a*mdx;632 qmerry-go-round platform of radius 3.0 m and moment of inertia k* .ifb;3lt 6aq l1dh23u xdim920 $kg \cdot m^2$ 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 velocity okf;tt -uk/zy1k 7vl0wf 0.8 t zfk0vt k;-yk/1uw l7$rad/s$ 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, los8rzw*47s/ykh5swtwt/ln3c g ing 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 angwwzsl sg/5y4 *7h/cnwr8t3ktular 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 windbky qu4rg9-p w .1xch4s 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 y 1yvygnrd;vrj 9)xe4: s5h6s$ 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 platfor3eblqf3j 4mp h)h, ipr2+lz-gm, initially at rest, that can rotate freely without friction. The moment of inertia of the plbple)hp +4i,jm32r fzhqg3 -erson 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 diameter merry-go-rouruk0r +-)cd :lyl vjq(nd turntable that is mountq c: +0-j dlvur)yr(kled 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 theu4 y4r kq2rrb0k8o( gfh9 qvb8 ground with the end of the rope lying on the top edge of the spool. rkr42gkbv4qy0 f( o 9q 88rhbuA person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces hb*wx, )zu8q, 8ngnsoqvt0)vthe Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital xo h nvt)u,qw*q 80zbs8 n)gv,angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist acceleratem9k od*y;j/kj/iy 1z)todi;f s from rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape v 6 2txahet09fof a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calcuxa f 6hv9t0te2late the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrirn 4/n xkx:m;1/uupd scal disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when rum:/nkn1 ;sd/xxup4 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 s2/kaltkznga+ f5 lx(2peed 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, butw- .fi szrl5lr.(e,kg 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,g(5f. kls . erwl-zri radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy sto9def0 onr)*4dvn5e otejx;v ;red in a heavy rov9od;xn4 f;evtjd*e0en)r5 o tating 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 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 illustratesacp83b-. kbhx.oe x6 h0ksdb. 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 speed v=3.3 r5 :0z qoxuvryo1)u(nzs0m 7c$m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore p 3h l x5knhomev((-y4friction) 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 t(4 (pleox-5k vhnm3hyhe 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,3krf-wq 33kemr9ryd0 and we want to exert a horizontal force F at its axle so that it will climb a step a-r 0wfk 3ky3mrr 3qde9gainst which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with jz zq(,+3q.xwkcax2 mspeed 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 q azqk c.+3( z,jwxxm2normal 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 and begins whirv d- iufij3zls 8-7hc0ling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rzi-07hfc 3jdu 8- lvisate 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 s 6m.+g6ov vuafolid cylinder and her arms as thin rods, making+mo6uf6.av vg 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 body.   

  You are designing a cnvs *+-v gy)xelutch assembly which consists of two cylindrical plates, of mvnx*+s-evy g) ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 loop-a*eohm0qz2f1,t a l9/ uiuc sed rough track of Fig. 8–58. What is the minimum value of the vmelasq 21ui*z0/a h u,-t f9coertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do u ils ijrqzu:dgpo3j) 1a 679(not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as th19j (b6fqavb ke 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 each tire?1(bqvfb 6ja k9 $\approx$    $rad/s^2$(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