A bicycle odometer (which measures distance tra;4k:y);c-zuus pqh stveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with :skyqu;h c -p4 )stuz;24-inch wheels?

Suppose a disk rotates at constant angqve 8tz( i6:byular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component ofq:tvby8e6z( i linear acceleration change?

Could a nonrigid body be described by a single vo sh,tyvn- /9hdbz3 jafzd-,7alue of the angular velocity $\omega$ Explain.

Can a small force ever exertu8jfg5d7cy:tjd69l8 00 xciio v ,bzt a greater torque than a larger force? Explain.

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

Why is it more difficult to)wgc*o fuu vu/(c y,c7 do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you cc/,yf uouc(vw g 7u*)to answer this.

A 21-speed bicycle has seven sprockets at the t/0 h*z+ep)-y ebvh (,gn trjrrear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or j-rh /()h*nre+e,gz vt0by tp 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 8 rdh3*wmj k0trun fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mas 3d8* tmj0hkrws is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beamg:-.fuvif0qbym9bs. em 9 us 8?

If the net force on a system is zero, is the net torque also ze(s .wjzof /s+h:vwro (ro? If the net torque on a system isv.zjhoo w(f /(+ ss:rw zero, is the net force zero?

Two inclines have the same height but make different a 4e4(kfxm :thsngles with the horizontal. The same steel ball is rolled down each incline. On which incline :ks (h44xetfmwill the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (fr; wfhx+hr0(tp-k6 qthom rest) down an incline. One sphere has twice the radhp0t- qxhf;( +h krtw6ius and twice the mass of the other. Which 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 stanu, fav9 /jt+m:ef 7kirt from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at th 7afn:ivekuj9,m/+f te bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or7bs.b/v;s h+w,bh ap83wzlzl rotating objec a+zw; bv.87zh/l, hb 3blwpssts eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how woe l zeseec6qn2rlg* vdx3ah-(2/a zl/l n1(.buld this affect the length*a blnn .ezgrxqlaec/v6((e2/- 3l1s ehd lz 2 of the day?

Can the diver of Fig. 8–29 do a somersault without having cv.7n1y9wui dml1kv8 any initial rotation when she l1v 8k lvycu7.d 1in9wmeaves the board?

The moment of inertia of a rotating solid disk about an axis through it ifz ** -gs+zubp ht9l 8,afo:kfwi+8is center of mass is p,i8 f k8i9lz*-g zi+ wsfub*o:taf h+$\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstrenu1p epj4j9 3etched hand. If you suddenly drop the maee1j puj39n4p sses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howey+ )scpqp d:l)ver, one is hollow and the other is solid. Describe an experiment to d+cdslp)py q: )etermine which is which.

The angular velocity of a wheel rotatingd6u-,r 0j6l:h fwww nu77vpgg on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the wfg6 wdu6:n 7rv jh0,l7gw-pu tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on tr/3oue)+ o-mc ugwx)v d(ml) hhe edge of a large freely rotating turntable. What happen)+/g wvu(h)m) coruxl -m3odes if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly.0l nakbm/0 (m(bo.bzs As he throws tbns/( a0b.mk(z0lbom he 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). Explain.

On the basis of the law of conservation of angular momentum, discussrnr6 c1:9d2g o9hnqf p; qho+z why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stabl+q6h9zr:on;fq nh2cogp91 dre.

  Express the following angles in r7xh ;6. v98re zymbdnradians: (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.+g:kq xtb.hnje 8+-d- a:sow m Calculate, using the infor8x kh.b:t-o jd:a+weg mnsq-+mation inside the Front 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 beame- at:18q,hq pixk: m7 to) ax0ruzp.q diverges at :rq8u ott- xzpa.a,7 h)1:mqkp xiqe 0an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at3*p h;p p(ikhasy4e1e a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3 see;hai3pp4ky*p1h( .0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floozoq84 5w(9kui dhn w **muif0or 3.5 m to another child. If the ball makes 15.0 revolutions, what is its di*o8ioi zkh qnum0fu49d*ww( 5 ameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. Hm*h / /hov*)l4y,kh m bdbjghm1az:+d ow many revolutions do the wheels mgzk*vdm 4m, ol/hj)b/y bahhmd1*: h+ake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500jgg1k3,k lx va0+ed3a ,shs3o rpm. Calculate its angular velocity inh0j 3o3v kk gsg, 3da1sa+xl,e $rad/s$ $\omega$ =    $rad/sec$
(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-rou2 owr51xf*ugd nd makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated *f d 1guo5rw2x1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit ar-,h 4vtkwt;tz txjyl4 a28ht 5ound the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of +9i kir snoubs ,mseg7.98q (wa 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 centru 0g mhpei;vp uax*b94ec2-l9 ifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,0009 eh9gmb;l -uvpicx0p42e a*u $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates u a8f3 (cqxl,oj3n6t2ovg1mfeniformly about its center from 130 rpm to 280 rpm omjf a, xtg3q18( efcln632voin 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 okx )6w-53uoqjvgtdde 5j s02$R_1$ 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 spacecrub g of;*g5c)d2dx-pzaft put themselves into a slow rotation to distribute the fggz2*xd - d);b5u copSun’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. 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 15,000 rpm in 220ddxee,(c0i at: yp;5fm2+m rv s. Through how many revolutions did it turn in t2m 5e:xdatf ;id0,y(c+pvemrhis time?    $rev$

  An automobile engine slows downtphbm 3cv38*t from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in) f ib9hhv42dju eaf1q4j)ra; a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revole) u vfj; 4badr)hj24i1qa9fhutions 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 b w3fpx ujkoh4;o/ )+v360 rpm in 6.5 s. How far will a point on the edge ;xjob+3kv /fu)ow 4hpof the wheel have traveled in this time?    m

  A cooling fan is turned off when it i 5z+1dqm*xidkr+q s0ls running at 850rev/min It turns 1500 revolutions before it comes tl*+5+1dqi0xrs qz mdko 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 redu f mhd69cs lq-szx567qces its speed uniformly from 95km/h to 45km/h The tires have a diam -5hdsfmc7zx qq69sl6eter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car redm: *:ko;5wj v)aaspnduces its speed uniformly from 95kmw)ak*aojmd: vp;:s 5n /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

  A 55-kg person riding a bike puts allh- -dn) ozeo)tfd xzsx21 c1g2 her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 cm)dcz11-g2)o os-xtf zxn2 deh.
(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. Whate1hb 8u d*)p1xzs0l pd*by-l, z:z nmg is the magnitude of the torque if tl g p)yu *:bpnzzx-8sbe*110,m dhlzdhe 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 xvqk1vm37t p (wheel shown in Fig. 8–39. Assume that a frictk m(3vpx1 q7vtion 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 then/a19a*y eftj oun c,3 ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on9nna ,/u1*jtefocy3a this system.

  The bolts on the cyltmmj2(e 4. kfn6fa2zhys+wz 2inder head of an engine require tightening to a torque of 38me(nw s2m24a+jyh.ft2 zfk 6z $m \cdot N$ 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 spheo k)p8y3f:cn rre of radius 0.648 m when the axis ofro3y :fp8nck ) rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia9r s lgdw56( t(zd)hhp of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of thep5h9td6(hl z( )gsd rw hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a voi u5a+n0nq0 horizontal circloai0n+50 v uqne 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 bowl z x/m3d) ;vezih 2i/qjon a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friije3z/ mhv/i2 )qdxz; ction 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 ij*ta3 q5 etbln/ y1cs0+jtjuj3u wz. )nertia of the array of point objects shown in Fig. 8–43 abosj5 uaeujlt b jy3/ t)w.+*3 jnzctq10ut
(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 co8dt,n;j, ijfrhh ka9: js(+h fnsists 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, uniform cylindrical satellite spi+xx x e(:-7gshggnsg9 nning 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 rad:xesg9gxn-sg7(+xhg ius 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 uniform9 .k erp9q4o6ejm2jyy cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Cykj 4m2p qr9oeyj 69.ealculate
(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 a9.fon-vbo+x ;ofw-j9. tb5y/ glkklw 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 smajr ;y 2v (6)gbyduapkg; 7bd6qll hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 76 v ) gy jgb;ur267;dpyaqk(db60 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 shutsiq o 38fg*6vh off and is eventually brought unifori*qos3 hg6fv8mly 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 accelerates a 3.6-kg vy duy.jlt.:5c /ozww//e4ov 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 br;*9 y; nfnfbgh/y:lof the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated unifol /;fynhrgf*by :9nb;rmly 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 c15qcq ;hu;d9v:kz/efuux q- oan be considered a long thin rod, as shown in Fig. 8–46. zcq q/q9u ufho;1 ukv-x:;ed5
(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 two masseshq k8zey4/9ecdu93 8 hd5ouw v, $m_1$ 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 wiy l ci;9ubot*l+lg;3sthin four full turns (revolutions) and releases it at a speed of 28g;9;s*t y+b clu3li lo $m/s$ 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 momen.rdcwlv;d gh nd 20;vsxq. abl7l32a*t 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 torque of 280 3)9*xp hdi/ r0owmq od$m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and rajn+6ld)*5u:azn le 7gdelw+9m8 vi fgdius 9.0 cm rolls without slipping down a lane at 3.+) w6guf+j*8 d5z lnd :lmeivea9ng7 l3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum eyhhsfdno1 g j)i63q)g/o) e2of two tege3h62o1f d eh/) oq nysi)j)grms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much net w s)et iuj:b.c,m*yqz-ork is required to accelerate it from rest to a rotation ratme-t b):z*cqs .,yj iue of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg*7(po(x.bfh q9 eekyy starts from rest and rolls without s9xe7y.( ohbkpeq(* f ylipping 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 yk s b(e)chgfe63o)0p vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of )obep0f6h) 3egyck(sthe pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum oft 6 x7 7w52 ;h,zmi,jefep4n4unr tzue1cuba- a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an anuth, -nreuce m4u6a1w pf 245 7nt,z7xijz;begular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angul5;;pa*ne9rav1 ee k4exg 9c-owrva7s ar momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating 4wo 9kce9as5*;g e;arex- v e7avr 1npat 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 t uqj*kv06.rvrotating at a rate of 1.3rev/s If he raises his arms to a horizont*k0 6t. urqjvval position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the on 6-uc7 rkq e7b2bz1ftze shown in Fig. 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 26 u7cfr2eq- zb1bkz7t.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of ;tqx 5 2bpqo 5ul7i7tr1.0 rev every 2.0 s to a final rate o pt75i;luqxtbrq527of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its ce jz7lw;c(0 ybxnter 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, approxi(cblwx 0j7y;z mately 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 spinning at 3.tlupu2j*+*p s 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 mou ji);5 t:piepmentum 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 zo)jy7xrd w0uao,mit a;-: z,onto an identical disk rotating at utr)-:z,o7 0zmaxiw j; y,aod angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at obmh9c 7bk;av172d;xc t9ium2.4 $rev/s$ 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-go-gx-8mejt; o3e round platform of radius 3.0 m and mom gom;xe3jet 8-ent 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 is rotating freelkj : ucqimtie(y 857:sy with an angular velocity of 0.8 8 (iq5tjkyiesc :um7: $rad/s$ 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 intr;frbpe6w8 s0)9 lmf/ dkeq(to a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no ansrf8; 0lbe9(k) 6wd fteq/mprgular 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 winds in excesdcnyq.ke9 96nhdi,oz4i.ma/s 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 fyrsimrek a7 : -,g am1z+jb3,$ 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 freely without 5cm47 kj1j+ri en/ 5 snqk(k)/ bmjzt7bb7ejt friction. The momm m1 5b ci4t e/kn(qjb r7/77)kntzjek+jjs5 bent 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 edge of a -u*py)ui,w xntlpu9(n :ke mfae-b81mzs0b / 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of puueenm,/m9 p(x-) bzyktswu:8n0 *fa - 1bliinertia 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 .dpyr z9k -4clon 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 sl-r4z.l dcy pk9ipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the ) z8ys7wefv2 nEarth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its or2nz w8vy)s7 efbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates xagp4 s 8r,d/ jbaqbhr:- nh+w.,5rsjfrom rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 +cb3p.qs 6nqndm6 n-ne9 a7lrm acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calal pne6nbqr-n q+ dm3s.6n 9c7culate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cyli,gmurk zjr w*b68 ( 9e)arqd4xndrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long stringd b u648x(,gk* wmr jea9)rzrq, 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 wheele6h)osx7ln 9kvin *5 l ($\omega_R$) 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 Suvdb*0rwi: v,q5 l lu d10ymil+n, 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 a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rovy 50dlllv+r:i uw0bm , id*q1tation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy sto u wl jrq-;)f/7zf6takfs9 1bmred in a heavy rotating flywheel. Suppose such a car has a total mass ofjf7 fbs lwrt ;)6-/fuq mk1a9z 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 illustratesiwnu 77 zw,w,s 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 mdguo em+ 4(mz ed7l4: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 L can pivot freely (i.e., we ignop:x j0ycsec5 ;-z)rss re 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, asszxs;c )yejsc -05r:p shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on tq6+nf4kpy ad .znlvx+9 k0n8ghe 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 has height h, w .y9 f+kn pa dg0kxnlq4v+8zn6here h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a tuk-18if zi:vr1 * ma a1kafrn.crn with a radius The fr r11aca f.f1kn: za -kvmi8i*orces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a slingkg ) .cv23qebd)v9mla zl3ep8sv-*rg of length 1.5 m and begins whirling the rock in a nearly horizontal ci z vvb.ak)gcrm2del*8 3-ve9gp)q3 sl rcle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her jo5/ hz)uhj2 warms as thin rods, making reasonable estimates for the dimensions. Then calculate the rath2h 5/jjz)wo uio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of tw2-xdmmvr0 3 gfo cylindrical plates, of20mvr3d-g xfm 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 the looped rough trspk buz//s:1. 9tj wqbd))hezack of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop wiz/ejuq9)tbs szhbwd:1 )/k .pthout leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not ax/c)l lk76(w i,e moppssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the carg+ju7t*+i: rme 0uaaq reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the +e q i*j7ruma+:ua0gt 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