A bicycle odometer (which measures distance traveled) is attached nearr.uh+ wg4 9qha2 eark, the wheel hub and is designed for 27-inch wheels.,kwr uag94eh q2ha .+r What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does z mg*6wvw)xzmejwu717 /t,r pa point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, d uvxt67zm *e w,zwjgp/m7 1)wroes 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 valup+g yhb )mm.x9bnpzy.5; ey2rw7s e5jg70h rse of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than-ejjx+ns2-s- yq i9 :q bb0bpw) dn9zh 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 sitleyy7t o8dd7w;8ne/aq /c-+q bpq3kynfc .)t -up with your hands behind your head than when your arms are st3twf edp/n7/byceqod ) 8y7tn+; q a 8-.qylckretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the reart2 )eigm:,vvn xq)ch: wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sproc:cqv)t:i h en)vxgm,2 ket 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 w ycm(6drce79 qith flesh and muscle concentrated 9yqde7 crc6( mhigh, 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) carry a lonv qd01x8q r,gmg, narrow beam?

If the net force on a system is zero, is nj x*b 5hv3q8xthe net torque also zero? If the net torque on a system ix8n *5hv x3bqjs zero, is the net force zero?

Two inclines have the same height but make different angles wit/0l -g ;;o1wwrvrw slah the horizontal. The same steel ball is rolled down each incline. On w / w1owar svlwg0r;-l;hich incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously -7a57rtbqyp hl 8n1z:9dgpd6u bdn5t start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the qlr68td-y d9ubp nt dh1g 7: bza7pn55incline 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. The+ho(n(* vr 4yrbv2s yuy start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Whirns rh*v4uv(o y+b2y(ch has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most movingl(,v;4nwr g iq 4 6jct.2cmr5dk5o+mxd,msb o or rotating objects eventually slow down and sto ; mmwdt(cj.qgo+ v4sk2m6 br5,nod cx45il,rp. Explain.

If there were a great migration of people towxmtd, 6::m whry4l5w-u5 czcdard the Earth’s equator, how would th-rzwdt,5 d6 5 cxm:lwh cy4:muis affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any r bnpg/ qf3t.,initial rotation wrp tf,3 /b.qnghen she leaves the board?

The moment of inertia of a rotating solid disk about an axzqtn 8kgw0- (bazo35zis through its center of (btokwang 0q-5z83z zmass 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 sittigkmlq9w*- 19rtdsa 1ta 1l61. r ozftxng on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses,9xwftrl q-glkasd1m*91.1o6t 1 t azr will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow anda1wl6ry95: tnsz jy0 eb o(dr. the other is solid. Describe an experiment to determine which is wh:l.srownejy 0y6t b1r (az59dich.

The angular velocity of a wheel rotating on a horizontal axle points west. h/ :2bt:lo oekIn what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linel b: khe2to/:oar acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the ed8,auwzm4af /5-d rj cjge of a large freely rotating turntable. What happens if you walmdf4ua,/aj8 5zrcjw -k toward the center?

A shortstop may leap into the air to catch a ball a01i4f1uw,e )eopvt sp nd 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 aw fiuo1 1pe,) pes40vtnd legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular mi44h tqz-t- fyomentum, discuss why a helicopter must have more than one rotor (or propeller). Discuszqyih--t4 4tfs one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radiansi/9d)bsqaq, o ajx 2c9: (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. Calculatesvd 71z7z ovh7c pe3m. f(+hto, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Eh7o smvt e1p.+h7o 3(dcz 7fvzarth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The be r7 43vu4lpv 1o ewkgith2v6f+am diverges at an a vkr 2ouef44hp3 l vg16vt+i7wngle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. Wo3 ;cwi)3z-kupge1 mv kof ;ce+y(jt 8hen the motor is turned off during operation, the blades slow to rest in e8w(cgti;u+ve3 fy o-k13o pjc;)kzm 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level osrfhj2a 1h2a 7dtc rxpn:7am12y,1zfloor 3.5 m to another child. If the ball makes 15fjch22,xpy1mst 1rn ohd: a7za7r2 1a.0 revolutions, what is its diameter?    m

  A bicycle with tiresem;pc.ukz 8.e 68 cm in diameter travels 8.0 km. How many revolutions do the wheel mpz8. e.c;keus make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angqn4z 0ltx e76 (cwxj.pular v.qwx(txz j7 046p ncelelocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig.mk+1c,ni (ve p 8–38). (a) What is the linear speed(1 ev,c+ mpnki of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular t9ux1t6 e,lm o vzhrb-dq,- pbojdt g/.5(j3o velocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poin29.mqds+ y ;wncfx(f,fq;cu ct
(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 bih.dzwdp3d* eq*9*yif a particle 7.0 cm from the axis of rotation is to experience an accelerati39 *h*debwpd yz .qi*don of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm*;y)i8 uchxnw t7r ym* to 280 rpm iuy8*tyn h)w* rmi7x;c n 4.0 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 radius c(i wq, l mlyedw2;q)($R_1$ 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 Apollo sp ba.+.bj-hki z9d.7en e/ mosb8mof*lacecraft 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 interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Detem8dz bsn97f l..eka-. mj*oobh+e /ibrmine
(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 15,0a7d yu8p 1)xn4iw j*qr00 rpm in 220 s. Through how ma1j *yau)wni7x r4qd p8ny revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcuky:np (7u/ve xlate
(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 whir sta, rp:yc;-ujmnx89ling “human centrifuge,” which takes 1.0 min to tu r 8c:tnjy-sup; ,9xmarn 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 eis6urlsn,v1u+g 5*t ((rd ogrpm to 360 rpm in 6.5 s. How far will a point on the edg vg,6(g+*seiuu1tnod(ls 5rr e of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It g+t 3y(o-o57k v5r, guixttm eturns 1500 revolutions beform v(x5r3i gtoutgt7+ oe,k y-5e 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 reduy)wa- j hm*w3uces its speed uniformly from 95km/h to )3 hj-wuw a*my45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as theak ;/tm1eops2 car reduces its speed uniformly from 95km/h to 45km/h The tires have a diamtep;1k osa/2meter 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 weom)5 s a m8p*)jiiro,pight on each pedal when climbing a hill. The pedals rotate in a circle of ra )pai, 5soim mp)8rjo*dius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is thea0tr s),fsx th 38yd-e-g yge*u pu.z/ magnitx -u ,-r)aye3sstt p/ zu.0hd8g*geyfude 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 shown in Fig. 8–39. Assume +l viz2/dxr7rthat a fric/lrvdrix +7 z2tion torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod whic;v2 bhijl zwbr;+/r8 ih pivots as shown in Fig. 8–40. Initially the rod is he brh;r/izl;b8 j iv+2wld in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine requireakrczl xk3 ) ny* :0:-snge-ph tightening to a torque of 38 h gkra-3ypnn*c:z-xesk0)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/xe 0z dxs5qk xz005kh 10.8-kg sphere of radius 0.648 m when the axis of rotations5 x00kzqkzxx5d0e h/ is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm i. 2o-b fnm**duw ha94 qs.wqrkn diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignor9uqmk-wd* 4q.nw b2.aosfhr *ed (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rom/ txs +va cspjw,;8+otated in a horizontal cir +cs/w+x8 p,astv;oj mcle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowy f6wm mp 4/okt1;m+vvl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). Th6mf +opw/ 4mtm1;y vvke 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 a6es:7lp ww5 uj7h 7z85ri yibhrray of point objects shown in Fig. 8–43 abyje:i5r u 77s p8bw5wh6izh l7out
(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 atom qpz;ttjsyk 2d9) );nws whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spb-3p bliw8z. dinning at the correct rate, engineers fire four tangdp. bi-8wbz3 lential 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 cylinder with a radius of 8.50 cm and a masskpqi0zsrrm+64az ot,5- 3x x k of 0.580 kxzqr-akt+5p,r 463kx zim so0g. 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 swingdk:eq3jrjjh4 */ f5 rgs a bat, 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 tangentially on a small hand-driven merryb2o5qp e2 vyjx )ada((-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 ((d pyoe)2qv 2 baxja52.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and .9ishv-hta6mlc1e*q5kv , n lu 1wq.eis eventually brought 9 he qh ea,tuv.l1is6 5 kn-1qc*.wvmluniformly 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. 8–45 accelera0awe54h.1m1):la 5 vyvpk3 nipkgof mtes a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the fore 8ag/499u8gttp/i ulw;ye wluarm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. Thep 8g u/y9t4uu /;we9w8gtlail ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be con+u g: 1;,wk,smzc h veplqijh: fiate7*9w u6*sidered a long thin rod, as shown in Fig. 8–4*:vu+gf :lsh *j9p,mtc;e,z iw6uhi k 7aq1we6.
(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 of two2t+w z;w,p8* rgrrde w 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 hamnc qzt. )-o (ei kktvv4i 1wlk2u8i)x9sx*g1dmer from rest within four full turns (revolutions) dkkiiv)48(ex1gq* ux )-k2tcl1vnsi ot9 zw. and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a mt8 u5pgd6+ :8erk12os lv lpzloment 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+f/ : tw;y8bjvy/wmsc0crjn . 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 faby9hmg 73)kkj 2uj8down a lane at 3h)7 ju gykakfm829bj3 .3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic enr( vo+6:ui xt5b(bhlw5y y 0jgergy of the Earth with respect to the Sun as the sum of two to5l htb(5(uybjw:+ygvr i0 6xerms,
(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 mo yl)7+g :sejo. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revol:o j+gloy7se)ution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 c-h dea:5unz :lm and mass 1.80 kg starts from rest and rolls without slipping down a 30- dz5ln :a:ueh.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 verti av1yhl-rh0xqzs g0(uz/*k d*;p,ssqcally on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Ux ;ad0gh, *r pskhql-(sz*vz 0qy u/s1se conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg basufl xx7r(6l. rspxvpo p; ;g f*.-rz3ll rotating on the end of a thin string in a circle of radius*v g (.lp;63o pr.xxsp-x;urfl7sf zr 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 gm xes 3:ydb/zu)f,q6mjc)3nqzsj6 i-rinding wheel of radiz zms3m:je3xbunij6d))y /6 q,qfsc-us 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 rdi. bkc*+nny9j9 a ie680u qfgotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, +ybn d0ufgj98 eck6ia9q.* in 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) can reduce her momektho9nd hz: pd6b;.xc/ukv5 v )a. oi5nt of inertia by a factor of about 3.5 when changing from idt5)d ok6.va hpbzhxk 5./: c;v9nouthe 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 rate3m+jh r*hpgfc rme 801o:0og l of 1.0 rev everm+o h8 p hcjom :*0g13egf0rlry 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vy,vpa13fb.hq ertical axis through its center at a frequency of 1.5rev/s The whe y3hq,.ab1pvf el can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinninst4;oy; w0jr.-bspr n0vxnt 2g 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 m ok,7r dn;j7h dzf 4e+.;g7rkbqb eii.omentum 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 mow4s4o)ze vedb 7c;5qpment of inertia I is dropped onto an identical disk rotating at angula e75 bp;vz)4q eo4wdscr speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnscbkvlzlxkf10a-+ i1 * 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 rotating merry-g7cu yq 3 nlz 939a1uq)- bn(:ztv +onfmxlrf*qo-round platform of radius 3.0 m and mo7z +)y3xtzur1 99n :a3(lq qq flnv-ocf*nm ubment 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 i6t-xwg w4*q0ux ux jd(s rotating freely with an angular velocity of 0.8 qw0tdgj(u *w- xxu46x$rad/s$ 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 isccd 8ll+as )2)zqh6 white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its eq8hcs6al ))li +c2d szxisting 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 involve windt(4 s:hkwkw(l5 jt n 4kr+py;hs 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 (fm-dta .+me ft9o3gr$ 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 rotate frjp-y pkz1 bb)9eely without friction. The moment of inertia of the person plus t 91bpj-kypz) bhe 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 d :dr.)eac,pr edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a mr:d) de .,caproment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope pt,9mww n7 es(,*pz yqlying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center*p9eztm7pqnw,y, s w ( of mass move?

  The Moon orbits the Earth such that the same side alway bwk9,3urlc bi*l145vsu0k vspj72 prs faces the Earth. Determine the ratio of the Moon’s spin angular momentu 3p,lkwvrss74u0bi 5jpbl rc9uv1 *k2 m (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at dfyxty;j5g7 7 a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radi*h ,oo)iax u++d .hn2;t4 ,h /xpyjtvmf+ggcsus 0.20 m acquires a rotational rate of from rest over a jn*fu+4d tgp,o i.,/ 2vyxhom+x;gah+t)h cs6.0-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 digq+d8 y-*yr/ - w33evjgorldysks, 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 sp33wrevdqylj/y-* gdr8-og y+ eed 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 rhm7s6z*jnm);ps( cf vear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great,8r yxw+ 2vd:7.9xghoxat4twi 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 mass carries off no angular momentumx2wrg to.8y9 aiw: 4xv+ 7dhxt.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pow r0 )cijb/a.bllution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a tojwa)rbb i./ c0tal 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 illustrates anu ;;ivok ,qs-bud qh,0 $H_2O$ 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 gpfy7h7v3;kf5 )0,bd gaiml hhorizontal 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-)6ddy6xmg5hx u3f6tp us2ul.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 that the force of gravity acts at the center of mass of the rod, as shown. [Hint: 3ddxu5 h-ug)6l 26ysxp6mtfuSee Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, an 1c5tul(mbk :oz s5xr(d we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Figx(os(5z m5 ctk: blru1. 8–55). The step has height h, where h

  A bicyclist traveling withsqd:d s 2 ddeki2z, n9lod7wn4e8vz95 speed v=4.2m/s on a flat road is making a turn with a s ddddn:2 zln7o8 sdi9ev q,429k z5weradius The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rocdq9ygz star61fk+a, 6k into a sling of length 1.5 m and begins 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. sqr9gyt a6 dkaz1+6f, What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater*bbfl6jw7d5 du,0 up c0h++r*jr vlwf’s body as 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 *r 06f ld wj5hbfrcpu+d,w7b+v 0*ulj skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plat6k2som 8bqyx; es, of mass6syok m xq;b82 $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 a rg.pk;a1dt;y long the looped rough track of Fig. 8–58. What is the minimum value of the vertical he;1 pryadt g;.kight 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, bzrsjip6z 2. 2rut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the carjkj znw+c/0 *w reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.*0/z jk+jwcnw90 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