A bicycle odometer (which measures distance travelhl,7bnd-z q7po)16ydni kqzly 6 77vs ed) is attached near the wheel hub and is designed for 27-inh 67d6lp7 s-7,1 b)kn 7yqyn oizqdvlzch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a6 sm89xb6gje z 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 casesm6 6bg 8ejx9zs would the magnitude of either component of linear acceleration change?

Could a nonrigid body qb g/5q,b.2juoo irky(srw+7zg-a )l be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Ex 1j))2/x,wbs dzb 4ucaohta0qgn en;2plain.

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

Why is it more difficult to do a sit-up with your hands behind yvp8ug8/ x45mubut*tl our head than when your arms are stretched out in front of you? A diagram may hegxtu*tm u 8b5/84vpu llp you to answer this.

A 21-speed bicycle has seven spz g;xoo3thz+.rockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it hardehog ozz;t.3+ xr to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower)0dc3kd-3 v*5/ow5x8 r yyrtl mrzypr legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamlyr kz)c 558rwyd*3yxr 0 /d-top rmv3ics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a loezsr 7v)8alo7ng, narrow beam?

If the net force on a system is zero, is th;ogsl4 e//rtne net torque also zero? If the net torque on a system is zero, is the net/rl/to e4ns;g force zero?

Two inclines have the same height but make different angles with the horizontal.2f r:u6npkjy u y*j4wlbpr,,d hw w39: The same steel ball is rolled down each incline. On which incline will the speed of the ball at t*u jd6r2y:394fpr, blwp,kuy :wnhjwhe bottom be greater? Explain.

Two solid spheres simultaneously start rolling (fk)jf- vt/ r1throm rest) down an incline. One sphere has twice the radius and twice the mass of the other. Whikf/)jr-vtt 1hch reaches 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 same mass. They startyk 2g cu tc5y0p9p:cukdoc:5; from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy 5ouc90;yuky5dc c:tk pc:gp 2at the bottom? Which has the greater rotational KE?

We claim that momentum and ang;ia20q cvz-a qm ku*,gixut 0(ular momentum are conserved. Yet most moving or rotating objeci* 0tzigam,cx-0vk2(qau q ;u ts eventually slow down and stop. Explain.

If there were a great migration of people towamnvamr- w(h:sy(1 nb/ rd the Earth’s equator, how would thi:ya/(h (w1 n-sbm rmnvs affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotatio7hh: u03lg gkun when she leaves the boaru g k7h0l:3guhd?

The moment of inertia of a rotating solid disk about an axis through its cent n(v0oe(ec yk1mi);ea4 b8r2u3tvbpv er of mi;me 2erov(k3) ey(1pav4 bncb v8 tu0ass 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 rx(cu-z gog(lq6s+sk0 otating stool holding a 2-kg mass in each outstretched hand. If you suddenly dropx +c6g 0-ssokguq ((lz the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and ha6/s6nbt uar 9qve the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is whts/ ur9 6abq6nich.

The angular velocity of a wheel rotating on a horizog+(i l-f8gp txntal 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 l8x fgi-+p (gltinear 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 large freely rotating turnt1u v +q5,x,i+wpjq s kvt1r;heable. What happens if you s,i ;q+ 1 wu+jre vt51v,hxpkqwalk toward the center?

A shortstop may leap into the air to catch a bary+tmor6s+8bmg k6 u2l6u lw9 ll 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 ou lm k+86 tr+br2m6gl s96ywu(Fig. 8–36). Explain.

On the basis of the law of conservatioz8 aju82dl7n in of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss 2l8u7djin z8a one or more ways the second propeller can operate to keep the helicopter stable.

  Express the followingc0eup* e;kfe ; angles 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 amazin8n27)h:nuhs nx hq 4peg coincidence. Calculate, using the information inside the Front hux4qh he:p)8nns2n 7 Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges a7+j lcc1;ww/ ie 7xhhx j*8nyat an y7j+/x c;wi h*an8jhxec 7w l1angle $\theta$ (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 6500e9ll))wam:1x .r ,dcggi j7br rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. Ww,rla m.e1l gi9cjr):)7dx bg hat 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. If the ballh,bf(pkd mine7 * ga7n.(b/zukev.* u makes 15.0 revolutions,(pungef bmvbk kae. /d.uz*n*h,i (77 what is its diameter?    m

  A bicycle with tires 68 cm .qhb-ht5p ga:w y:+wx in diameter travels 8.0 km. How many revolutions do the wheels w:g.bp w5-+tq a xhy:hmake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculufwz/ nuh8zye g;t9; )ate its angula9w nhyf8tu;; z)uezg/ r velocity 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 makekc4a4w 4pkw g9nc6: ;so6nwh ms one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a 6p a wh6gocs4kww4mn:9 n;c4kchild 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 Earthqbvmj;0fr u32y-;g l p (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speer8l c om)pqvwn* i;pk2f5go0f144j ind 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 cen2-fv ;w6)p i rbpl3pzptrifuge rotate if a particle 7.0 cm from the axis of rotarbp pf-pziv p;)w62l3tion is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly abwjb uz85+wp* :) fkfs3pgqae 4out its center from 130 rpm to 280 rpm in 4.0 *bw43j+ pqz8k gaf: p5 wfs)eus. 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 radiu8+wwcaxabw8ef6 .*p /7dhndh7 szx2 s s $R_1$ 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 Aposeny.2g0+d u wllo 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 touny2 s.e0d +gw 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 frowgwa5yw 3utac yww7g637y )c64m)lts m rest to 15,000 rpm in 220 s. Through how many revolut76mg)6yw 7)u4ta3 c swtyl5 aw3c wgwyions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 ichjx; *8q q4d;k kjho5m63lwds5(zy 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 m +(9*kp .fssh aj2psahighspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn t ssj9* ppak fha.s+(m2hrough 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 rpmpd mv +55ueub. in 6.5 s. How far wilumbve . 5pd5u+l a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 15000s izrg h6da0( revoluti60 gdraish0z(ons 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 .u3f nt)3nonq5 vea6 vcar reduces its speed uniformly from 95km/h to 45km/hnu3e5)6nav t nov3 qf. 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 carwvbv 2nt)js,ocgl.tym:t/jer)2j ;4t wi34k reduces its speed uniformly from 95km/h tow mvc o4;))gtnjtwi: vt. jltsyr4b,kj2/2e3 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

  A 55-kg person riding a bike puts all her weight on cv;+mhd(t7wjdv 0dkpk: / movl- e)1eeach pedal when climbing a hill 0 kj) cdep;/kv -1v lmd:h(ew+tdmov7. The pedals 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 doo8;qmp qww s2i0r 74 cm wide. What is the mag swq;mq2p8i 0wnitude of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel sh 1goejbqc0m2 uc*cs8k8/3 3x pfcv-caown in Fig. 8–39. Assume that a friction touf oxv2j08mb/1q-ck3 aecgc 8cs3p*crque 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 massl o slf. 6ap5huizm/53dess 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 direction5.m6 zs3u ofiha/p dl5 of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque of 3wk )uzyz:thee t1 el -u1:u27b8u1t e 71t: :e-uu2l)kybw hzez $m \cdot N$ 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 7h+j1thb o(mta 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its oht7tjh (+m1b center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicyy1zzm3ffv-yx( k. 3,uq;deb acle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignob1ffue3 (q.x 3 dvy;m zakz-,yred (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a h32ioho hd d.qs 3o*mu*bkl; +xorizontal circle of radius 1.2 m.o2m xhdq3kloh +b3;is*u* do. 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 3kg 5z)gom4ez angular speeemg4 zz3g5k)od (Fig. 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 ofo8c+wsxr nn-8r4j fapg r3k12 point objects shown in Fig. 8–43 awaj kr32p+4sc1x88o -fn rgrn bout
(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 cokvu/j/.c ik:w /gd+*ncpm4jpnsists of two oxygen 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, uniforonj( w:5.djfuisvuix 6 6bt :1. bdd5xm cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the requirev xbd516 snd.u.xidb:6 ft:wjjui o5( d 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 c2 7gr,vgi6gdl m and a mass of 0.580 kg. Calcula2gl rivgd6 ,g7te
(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, a17xqnuq sk:z4 mmw. cmg 24c27hg uo-iccelerating 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 tangentially on a small hand-driven merry-go-round andgxdbx1; ,by1w 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 k,wx b1dby;g 1xg) 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 bro-r 9 p30vr+d,rs*yzt cqa9uk rught uniformly t99zp-ua3r r0s cvtryq+k *r ,do 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. 8–45 accelerates a 3.6-kgu z 0k9zm *1 . tqspax-dcbd 4wm-rb2osq5,6au 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 bsvd)k 4/i b;paction of the forearm, which rotates about the elbow joint under the actio4d)bk p/; vbsin of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade1 fd8hl8epd 9 kyfpco0c6as4 ) can be considered a long thin rod, as shown in Fig. 8–46cal1opyff0k e8ddp4 c8hs 6 9).
(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 conse;i lx 2c0iofiz;j *q/t x:a8xists 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 foj9q i6 /2iopzull turns (revolutions) and releases it aizpqo j9 62o/it 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 genr5:k9nl . /l4rurc a 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 develops a torxh q*gf at)dq5,4n zcb -tn,u3que of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7xe m;dpl n 3yrm(1 jj1y28k1kr.3 kg and radius 9.0 cm rolls without slipping down a lane jmy1(pkyxrr; jmk2 18n de1l3at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth wi4 +haw/crq .zcth respect to the Sun as the sum of t+h ca/4cqw. zrwo 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 radius9 * d3/: sufl 7igrtnj20nnwpx of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 172pws*0 ndu:3nrntgji9 xlf/ .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 and rols) 0;tpnuy 0av ,jct,zls without slipping dowv n0p ,u,jytc0t)sa;z n 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 oe154xdt 9e*axos )a zmn its tip. It starts to fall and its low*o m ta9edxs)xz45e1aer 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 the ez87vsyux/.n m 4vo2brnd of a thin string in a circle of radius 1.10 m at an angular speed of 10.4 br2oyvs v /8.u4 zmn7x$rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg unis,o 00f3spgswml1xx y h ((a1jform cylindrical grinding wheel of r(jpss 0xasf , 1hmgyw0 xol13(adius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a rate1fuko p( ; 7lmea dfr*4merk+6c 7h.cs of 1.3rev/s If he raises his arms to a horizontal position, Fig. *1pc+.faerdmslc(7m4 r;h fkk6oeu 7 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 onep2ukm0t;h+ *.k7 uajp2c lsym shown in Fig. 8–29) can reduce her moment of inertia by a hyku2mc .ma*tu; j2s+l kp07p factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase (sc:+ f*z rwdyher spin rotation rate from an initial rate of 1.0 rev every 2.0ysdfcr:z* ( +w s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical ax+-( y 8wpsyaruis 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.8prwayy s+-(u 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 after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum r0rl6e(qcm*fwgpg 5zt us(5d 9qq7d1 of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentuqza7qau-*5vw; onj0fm 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 inerrajfl vs8 c(vpi )-emk5f41:atia I is dropped onto an identical disk rotatingp:sr vmki1fvl4 j 5fca)a(-e8 at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns,pl ug0 l+upxi5)l)+pw u p4xu 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 csq55p5c4nd1l8n xnw e enter of a rotating merry-go-round platform of radius 3.0 m and el4pxncd5 s8nqw15n5moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round 6ak +q x0 , iabm(ur4erm0mn9gis rotating freely with an angular velocity of 0.8 r0 m abgnei9m,uqm a+0(xr k64$rad/s$ 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, losiess 4ax5exv0 5ng 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 Sun’s new rotatio5e0s sa5exv4xn 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 wind8xhrdx)u:;7zp 9y n ccs 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 k :/ze1em 8jqr$ 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 plc)jn01w8 jwrh;s i 6pgatform, initially at rest, that can rotate freely without friction. 1 h)ww;86isrcpgj j0 nThe 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 stands at the edjt jepsg7i /:4ge of a 6.5-m diameter merry-go-round turntable that is mounted on frpj 7jig4:/et sictionless 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 th lc4xp-ps dg pkk).kk686b8xf e ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and wasgb4) 6pp6 8pxfkklxk-d. c 8klks 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 te jes)xs9*s+(k qyr1the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, trea k)e*jr9xs qye1 +sst(t the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate ofrr94xhj , (++s gtk27yhptgw8wbp8h y 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 1w2xjcfnl 4lbpb 6,e)sky:g0of radius 0.20 m acquires a rotational rate of from rest 4g bf 6x2yne)p0ljlbsw:k1 c, 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 dis zwrn8* ej0lo1ks, each of mass 0.050 kg and diam8onlj e10z*wr eter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is cvi( p+sb se;1rj0j.lthe 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 .4x+rtk mway 6nwo7c.great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost maso+ .4w.tncmryak 76wxs carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use e -sbb u;kd2d6w/5nq4*ce qqo4wx c:r knergy stored in a heavy rotating flywheel. S*:dckqweuqr/ks x b24qw6b- ;dc4on5uppose 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 illustrattccpidj72o + 6es 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 horizs1)cc c her. h:j2h8l 2jv.esoontal 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 L can pivot freely (i.e., c nc9m -b6np /0wrjlpoaq8+5t)c 2dciwe 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 relcn cc/ mo2 q5c tbwad p98)p-0nilj+6rease, 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. fjx6y ,q cb*g3ax(a. nkaxytxz2 6m*2It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Facn,a gbxf2ty 3qx*x. *xmj26a6z( kyig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/m:) 8koom3.; ayau jevs on a flat road is making a turn with a radius The forces acting on the cyclist and cycl.v8oe)aam3 k oj;myu:e 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 oqp5bf7w9kok du f;.4*b0ucke f length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from restu7kp9;fq e 4c kw.buf0o*bk 5d 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 solid /7umj5z. d cshcylinder 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 outj.d75/z ushcmstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consisp39c8l /ar/ .ubnva)ed 6ae8bjq c/onts of two cylindrical plates, ofnr/pqdu3eel68c.bcaa o /9ba/)n8v j mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ;rkf o:ti,eh9 the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is h9,k tf:ri;oeto 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;tb . kwzmo+l. not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as thevn81 b.li26o wvpt : i.1cjjpi car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What wasj6.bcjii 1oipnlw1 2v:t8 v.p 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