A bicycle odometer (which measures distance traveled) is attached near th e+kaitkk 6m3 0esg)(ve wheel h( 3ve k0 aiksm)ket6+gub and is designed for 27-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 the rim haqe ln:-6z*fbz62 vt kjve radial and/or tangential acceleration? If thn6bf e*jzkt62 ql-: zve 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 linear acceleration change?

Could a nonrigid body be described by a single value of the angular velocityls zx v1zr;v;t6mp4 +y $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expl7 9g ki-aakj+hain.

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 pdo3fqf a (xai3 yz d48:k 37wmj0 td/bbd7:brhands behind your head than when your ar(3 of pad7dkqi0mdybjd4:8 7t x/zab3b:w f3 rms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at 8,mf .xuttf6y6q+ r)qt) w s 0pdr4ldwthe 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 a large fr.d 8r6pwtwfrd)y,f0 )tt u+xql 6smq4ont sprocket? Why?

Mammals that depend on being able to r5.u13r t+ok,4 gaxgooued +x dun fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–o+due31g ,du4xo+5axtrok.g 34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) c6yb( r6fbrxc:lwmru86 8zc 4tk,q e y;arry a long, narrow beam?

If the net force on a system is zero, is the net qcqtwf+zrzl2x 2(( s0:qd)h jtorque also zero? If the net torque on a system is zero, is the net lq: )dcwqj+2t2(rqx (sh f z0zforce zero?

Two inclines have the same height but make different )ph 9+sa*8s,-x/uc v rb)a d:ueeapcy angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Exx uhce-)as)8 urcsy9ve,app/ *+d b:aplain.

Two solid spheres simultaneously start rolling (from rest) down an incline. Onzlc-ui ghor72hxo7s)a l y, )g p*s1a5e 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 tha,x7rsl)2h 1 - 7)guh osol*5czpgiya ere? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They s:4 r;sa9m8k v0fh/jiwn5zy l btart from rest at the top of an incline. Which reaches the bottom fmh0bzj alr;w9n8i4/s k 5:yvfirst? 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 angk+ocm p1 x*72eyn8v mvular momentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Explan87kmvmc+ p 21oy*vxein.

If there were a great migration of people toward thm3z4yoxs)1 a,hsnq 8 fe Earth’s equator, how would th,1h3zf xoayn 8qm)s4 sis affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without c6pibci/pkw 7g 0pq39having any initial rotation when she leaves the ii c7cp/6qpb p 3k9gw0board?

The moment of inertia ofo0hw 3pzfzv)g 9zh7u 0 a rotating solid disk about an axis through its center of massh p7)gvf09h zwo 3zz0u 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 p .7arh2d-qzva 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrzh. rdap2v-7q ease, or stay the same? Explain.

Two spheres look identical and have 9sjd2;z8z u5i8upzu8b+rnym the same mass. However, one is hollow and the other is solid. Describe an exper 88 m+9uzys5;r b8znudiz u2pjiment to determine which is which.

The angular velocity of a wheel rotating on a horizont7eyt;svn- 4)dk t;fwyal axle points west. In wh ; wnv4ys;t7 tk-fd)yeat 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 decreasing?

Suppose you are standing on the edge of a largcdl+1d2vk; x se freely rotating turntable. What happens if you2 v+lkd;sxd1 c walk toward the center?

A shortstop may leap into the air to catch a ball an9 6tdxr bux.0h*u -wj j;:yufvd 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 (Fig. 8–36). Explv9b w-ydux xjtfh6ruj0; .:u*ain.

On the basis of the law of conservation of angular momentum, discuss why a f 5q1 d*n84ii irb,apfhelicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can open5,fi r48 d1*faibiq prate to keep the helicopter stable.

  Express the following anglll+ lgbk* 9g4ses 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 because of an amazing coincidence ch:sxx qj, -x2,hz0oe. Calculate, using the information inside the Front Cover, the angular dxq 2 oh0hs:e-,zx j,cxiameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Mtjepv -).v vdhsh9zx)pt3)- o oon, 380,000 km from Earth. The beam diverges at an angetth )ovpd-9x.3zj) shvp-v )le $\theta$ (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 rn0w*hc+e6+ 4l2slmevpl m t1ipm. When the motor is turned off during ope+weilc2 vl1 sel4tmp06*nm h+ration, 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 floor 3.5 m to another child. Iflk,mhd6 (*d)xcf-dmjzx:h1 z the ball makes 15.0 revolutio 1d zhfdh-l()z:,6x jdkxcm m*ns, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How maa jz6*/-j ab0fuyuj76fs(gkgny revolutions do t6g/(6uujjjf*faks7 0a- zgb yhe wheels make?    $rev$

  (a) A grinding wheel 0.35 j6 y0ye/bk odjm +-dp.m in diameter rotates at 2500 rpm. Calculate its angular velocity in e.o0d- j 6bdm /yjp+yk$rad/s$ $\omega$ =    $rad/sec$
(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-rou e8.p.3fsh t/6 g9z luyywcd l--md:ofnd 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 centers p.lgdl-3th9zcudff8o: yw6y e /.m-?    $m/s$
(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 ywl-:a3/ux*u .de uh hits orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spee bt7; c mbux+,9gkww0td 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 fr /jjnh9z ntkx4q5/5bvom the axis of rotatio5bhx/ jkznv jqn /45t9n is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uni+sqg0vvqby; l.h (b6jformly about its center from 130 rpm to 280 rpm in 4.0 qjvq(hbls;60ygb .+v s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiu*u5+gciwr x8cl b.-*dya yc*ss $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apol,auj*)xngmxf+ xo5v * lo 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 afo5jv gmxx n*x+), u*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 m;m1zau7ez4u ,000 rpm in 220 s. Through how many;aem1u4u zm z7 revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm xni8 p(g :mmjh(2va(re /wn1dto 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling “m sis50 l z*vlh(e5xf( kpex4:human centrifuge,” which takes 1.0 min to turn through 20 co5xmp*i v k f(hxs4:(ll5ez0es mplete 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 rheagvp8q4vj:x s6o 3 *pm to 360 rpm in 6.5 s. How far will a point on the edge va46sg: *83 hjqoxep vof the wheel have traveled in this time?    m

  A cooling fan is turned y)5: kgai7 e oyeh0(zooff when it is running at 850rev/min It turns 1500 revolutions before it comeh)7 ao:o e5y z0yge(kis 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 reduces its speed p8he72 )cnj dtuniformly from 7cn2jptd8) eh 95km/h to 45km/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 revolv8,ok wt x);-kbvt+my utions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m. , tt)okbwv+yk 8-x;vm
(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 all9nla jqzpt3bki0ne 1a w6q/ q j.ko,2g9(gsd0 her weight on each pedal when climbing a hill. The pedals rotate in a ,.i9qkla9dz spb j 60k(q3j /20gown q gae1tncircle 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. Wha;hzi nby.aw g;c d,( o8l** -q5lyxkezt is the magnitude of the torque if the force *zalhi.;nyk wocgde 5(;, zb*-qx8y lis exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. Assu 75, ddo+.zse s5u yl;emdw4qlme that am +ldod; ye .7uszd,elsq55w 4 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 ofec tl)a3o+)yxhb+iz 0 a massless rod which pivots as shown in Fig. 8–40. Initially the ro +h t 3bie0xoycazl+))d is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinde :;;o;19 hhbzmjp.ix5 kgswzl r head of an engine require tightening to a torque of 38b:1s9hih5z; ;g wxjopkzm ;. l $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg k 9.e n3x+:mxdpwtzsb5nv:(i sphere of radius 0.648 m when the axis of rostvw.x :9nm bnp3xedi kz+: 5(tation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diamet5.ys dtzd .np-er. The rim and tire have a combined mass of 1.25 kg. The mass oft. 5dzsdp -.yn the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod isv1lvl6g)xfcex3 g+ s+ rotated in a horizontal circle of radius 1.2 m. Calcul+g1vxclex vf+ 6 )3lsgate
(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 r q kov(penae e)d(:gidilp *62s6n6/ootating at constant angular speed (Fig. 8–42). The friction force between her handsiqak d/e6nsg i2e6*:)p(6e n(vlopdo 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 mb ohf93tkp)m . :,sdhthe array of point objects shown in Fig. 8–43 abo ts,pbmfdh.:ok 39m h)ut
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose to w76osdhrox/* tal 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 correcq( a- zvrpfq/;t rate, engineerr ( qa;-z/pvqfs fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinf-z,pn7 oon waz06 jvod )nv2)der with a radius of 8.50 cm and a mass of 0.5)p)v f0-jvna,onw2do z o6 z7n80 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 f:7 vulhq *1jlzrom rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-gor x 0,/ aq/(quo3,lhbssud6 hq-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 otheuhudr/s o,6(a qqs/3q h,0 bxlr 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 eventub.e gu .vm4d fe+-pl*sally brought uni+.ef-v 4.mds* pl egubformly to rest 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. 8ofhn7 6)h,rzf7vt ljd (xhgovk )(-f.–45 accelerates 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 the1fr1.7 mlkhxm forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated u xm7l.f1 k1mrhniformly 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 chgy)kbh0j ewa;7ldc pm )uc(9.b1l0aan be considered a long thin rod, as shown in Fig. 8–4.(9)jc dwbek1gla)0ah 7 h0myl;bup c6.
(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 con4t v3wlw jol;.sists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns (rev(9/9uwzy sl8n4 iamq oolutions) and releases it at a speed of9y/i o 9slmnzw(8uqa 4 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 inerq7lz;)c sz 3witia 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 engineg xd-w)d/1q wr develops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping do8 ae g5td+vr9a* z3)lqlzy8xjwn a lanjla + z9lg dqz)r*5v 38at8xyee at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic n-p2pymw927(ubsrf4le6/ n n7 3yowq0 io vdnenergy of the Earth with respect to the Sun as the sum of twop2o w4 ny i6f7qe3o0mduvr 27lnbwp/s nny9(- 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 7.502 s 2ozdqa832nyrwi1 x m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolutionq2i3 8y2orw1z x2dnsa 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 and rolls without stqm -/vpirr3; q;/p mrv-rti3lipping 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 anq 6z 8e11tzmy1(arhvim ,k a,zd its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the groak8z,yr1eiv1 ,1h(6zmmqta zund? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball *6v sx zmh-l9drotating on the end of a thin stmh- 9dvlsx z6*ring in a circle of radius 1.10 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 cylindrical grinding0t5kd5b /y sh1zqcx9 s wheel of radius 18 cm when rotating at 1500 rpm? y 5sds501bkzq ctxh /9   $kg \cdot m^2$
(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 plaun(r 2 eumio fxec6x6i c5)5*htform 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 rotation decreases cn*( e xe hfr56uo)ix6mu52ic 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 F /a:69yi+ljjmf*fyuqyth 9xky3/ y:v ig. 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 makes 2.0 rotations in 1.5 s when in the tuck h6 9ijfyyk*tf:yy x/vym39+j ul /a q:position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation ratu0z-wa:z;6fbglp mj 1 e from an initial rate of 1.0 rev every 2.0 s to a final rate of 3 bup 6am1zjlgzf w;0- :$rev/s$ 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 center3*hiflf+gni odpx,( . 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 whl,nf+dh3i (xo fp*. igeel. 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 spinn(0) xsmgn gnz0ing 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 momen:f7u03c cbfnw/g k fg,tum 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 an ma x:7ww5mk :.oq ue.jidentical :ea mkwq.x .j5mu7ow: disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a p.jyyj20pn8 at 2.4 $rev/s$ 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 g ue b+,hpvytbzf/9hm 8 24m(frotating merry-go-round platform of radius 3.0 m and mom+yffbmzh, 2mue vp4/9 8 thb(gent 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-t- kwyq dro3/s/j40qs go-round is rotating freely with an angular velocity of 0.j0 ts-yk/s4 qqord/ 3w8 $rad/s$ 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 collo gcnplr*a0 -.apses into a white dwarf, losing about half its mass in t.p*acr n 0l-gohe process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to 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 involve5pqu. 8h;fh 5a)by mkd winds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass l 8z6hrr : 5rkwmay c;o*k4d1ue*jj1z$ 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 rof aovej wj 2,2z qht3chf8r*s35l-ad )tate freely without friction. Thj w8eh )h*qlv,2cf fatzo3r2j5s-3a de moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stazq.: btqa,u4s(2cj8ac(do v o nds at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of ine 8 cuq2:jv.baqs,cot((4 dao zrtia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying on ylqp f76l aox2(u4b3lthe top edge of the spool. A person grabs the end of the rope and walks 4l6y7fp2lu3b loaxq(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 t(4b;dut b l;asame side always faces the Earth. Determine the ratio ou;; t4b(dltabf 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 re/6 xrg.mah bt-ze3cj :st 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 unifo i,u;cn1bhk c5rm cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angu,k15;bhu cnc ilar acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of qvi1:pgpf u:pcbek98 rx )va:e ,98 wmtwo solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.: mf1:b9q epc9ap8guw8 ripve ,:kvx) 0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wheeu5d 4fjc3pax- l69svcl ($\omega_R$) 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 sizemh g kdv zz c71kb-8p.g1u.b4n of our 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 ahvzmz8g-d b4.1gu . k7bcn 1pk neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a lowpo c-:tuvn04o4hntv 8-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg,4np:nh tv4t-0cu o8vo 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 illustrates an xc/w7u(qx up,$H_2O$ 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 r8m+pg .p.uks* 8dzq za:c,no7kyvpf6olling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length Lakz.t6h;yi +)sr ua j4 can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume t6u yik.asrjt+)za ; 4hhat 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 onhek.reet3i7 : the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step ha: kr7.iee3 eths height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat * zjqbdf 038scroad is making a turn with a radius The forces acting on the cyclist and cycle are the normal f3jqcz80f*s dborce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 begyxswyh2/4-vtt-/ e s7yvb ahv37 pi2sins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torquhpesvsvb/ w y 42x/si32-7ht- tyv7y ae required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body tq57x,asl27 j, qqm imas a solid 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 helm2q,taxq m,7sj l7i q5d tightly against her body.   

  You are designing a clutch assem :x ei2efc wfzw. ld) *7tej8ne+ps;+nbly which consists of two cylindrical plates, of mass petle cdf+. )8*7 zs :x;w+injenfew2$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 loop0r3/ :ux fcnd cc1,rtned rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it :n/udf cc0rx, nt3c1 ris 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, bupdy9sb*f gt: ln,pgy 8z;9 im.t do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces vf: u::ojlo x+ne84 9xnacij,its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90lcno,:u:i: j+4va9exxj8 on f 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