A bicycle odometer (which memdb ym:1f,mh d*2j gt9ick 2(zn 4x4znasures distance traveled) is attached near the wheel hub and is mhz 1j*d2 m g4tfi xnd29bkznm:(yc,4designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on 5yj.d*z 0b3 qq e-do 4hl5kj3uf.gmcf the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential fc..d y053* 43 -g ubdokfqhj5mejzqlacceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value ofs(iy )m69 7 2ozmpbkec4 s0toz the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque thamofv*t6 4+ eva cj/erz;ew(7un a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind )1b:7d-cu eke9fx2xfu,z0 4dlbzsyt your head than when your0 ulybsz 24 kx7 )eb9fzx:e-cdtd1u, f arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel) dy)22dff da1 ahl3h2-ibpz e and three at the pedal cranks. In which gear is it harder to pedal, a sm dz2efa2f 31)i)bdyh lp2h- daall rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on beinu1*uo9gi )je1gajxa3 g able to run 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 j1ig o*g3a ue1j)x9uawhy this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, y bq c59u82; ,kwjionpcyf.4yi ;hbc3narrow beam?

If the net force on a system is zero, is the net torque also zero?lw+(v8h95b a twpuittp *g:1s If the net torque on a system uti w (lta9s:5btp+ hwv1p8g*is zero, is the net force zero?

Two inclines have the same height but make different al.lfh pv 6o66c6vzb* ongles with the horizontal. The samez vc6v*hl .pf 6l6o6bo steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultannfyty ysa7;mxr m07tl(r gs5 d/+5/lceously 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 incline first? Which has the greater speed there? Which has the greated7mryr 0ls(/ycy5 xmn5 tlsg +;f7/t ar total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and tgmu1,i08ns97 lcy grkugi3 6lhe same mass. They 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? Whichk7g ,6ng3u 9m8yiglr c0i sl1u has the greater rotational KE?

We claim that momentum and angulaykaj2j h*49pg46 rg0wvbwk. k yr)*xfr momentum are conserved. Yet most moving or rotating objects eventually slow dow4j kh v 96kgprrj* w xka.bw0fyg*)24yn and stop. Explain.

If there were a great migrap:r5 jeg+ :rtrtion of people toward the Earth’s equator, how would this ajt r5g perr:+:ffect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any inisdk/a 4 w:6h;bch: kwhtial rotation when she leaves the boardbh;ww k:k/hca: 64s hd?

The moment of inertia of a rotating solid disk about an axis through - 13jsbdnqoi(hj - mr a2l6ik42u,jwl its center of maowjhj qj2i4in12l,s-k(6b uml 3r-d a ss is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in c1h4zb1dj 3.xhaec +oeach outstretched hand. If you suddenly drop the masses, will your angub1a .4z3xoje1 hhdc+c lar velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However,lwgu)da l fv*-3*1gwn one is hollow and the other is solid. Describe avwl3 *)wguf*l d g-1nan experiment to determine which is which.

The angular velocity of sj20s 4bl*cgj 5 n kv:1jdiq.lrr/b4j a wheel rotating on a horizontal axle points west. In what direction is the linear velocity of a poin.nl c2k*vs105s4j r/lq ib:jj bjr4 gdt on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating (sbjl)n70w /n v;teohturntable. What happens if e l0hw )tv(nn7sb/jo;you walk toward the center?

A shortstop may leap into the air to catch a ball and throwuao b- ng6-io2j4rv 9d 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 2-r94gi6vujn bao- odlegs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angularzy0d+um7lhz(l( cq dj7 uv1w6 momentum, discuss 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 stawqy1u ( +ud ml7cl(vjd67 0hzzble.

  Express the following angles in radians: (a) 3flalzdzk 2ah3l:ie fhc)/csuk (1- 3 )0 $^{\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. Cal8-qy*u, c2y7o8 y0 ygxpb cwn 3pdel.zculate, using the information inside the Front Cover, the angular diameters (in radia8w3bpygz*,2loudp 8-7 0x.yqc y ye cnns) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the +ldh.q 4k 3mjpMoon, 380,000 km from Earth. The beam diverges at an ang4qmph 3+ .djlkle $\theta$ (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.2tv 90 edux;zkxk et7 )/xrwn rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as kx;.nr0 u2)ewxd/k z 7 ve9ttxthe blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3uam0c;j qeuiuvp2 ,6*tk- 6vq .5 m to another child. If the ball makes 15.0 revolutions, we, 6 uti0k uuvc;6avqjp-mq2 *hat is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions do 04/v: udrgo fqthe wheels make?d4 o/0rq :vufg    $rev$

  (a) A grinding wheel 0.35 m)*aeafltx7yl1dj.r -e- i3qw :co7xj in diameter rotates at 2500 rpm. Calculate its angular velocity qc-t *) .3lxw7o-7r ej:lajea yid1fxin $rad/s$ $\omega$ =    $rad/sec$
(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. 8–38). 27 :wn4, 5obetlb)d2lbe*dum8osuc m(a) What is the linear *s edu)8dt l4c bmlw:u5omb2ne2,o7b speed 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 velocity of the Earth (a) in its orbit around the Sa 4xc- ;p(c-g:znv 8y1ou xrkiun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poi,l6y4qhmm bz0( :uba5ya9heh nt
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the axiq h gvk:,7b)u5o:vjfe 9a z3zjs of rotation is to experiencez,jkgz:e5)7voaj q:b9 h f u3v an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly n:aj4ze j m0e*about its center from 130 rpm to 280 rpm in 4.0 s. Determine : ajmjee *4nz0
(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 radiusybhfd ehb:9hg z.(-5f-w d /bs6ws ;szihv*, k $R_1$ 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 Apolro:x /gis +:rglo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m.ggiro+ s:r/x : 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 fr)yu,- 4jidet x et1l 4n2el2n-corr.com rest to 15,000 rpm in 220 s. Through how ma -cet)x2-tn 4eri c ljod2 r.y1ne,4ulny revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpcmt0 g. z5sbw(n t tolc7.v0j4m 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 flyo6,8hx i,ip fjing highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 coj ,8 6hxip,fiomplete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6.5 svz:*f5 lxdgm- 9b5gfj +jmc/ y. How far will a point on the edge of the wheel have traveled in this time?+yjbf5md 5 *g/fjzclg-xmv: 9    m

  A cooling fan is turned off when it is running at 850rev/min It turns 6 n5g 0gz 6zlg(k;aqhyoh3*by1500 revolutioqy0g aybz 3 6n*hhgokz6 (5l;gns before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car 2 j1yyq 5lhd54(fnwfureduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m. q 2uf1 yfn4wdjl5h y5(
(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 au2y(,hfone -z i2 uad,kz,( cts the car reduces its speed uniformly from 95km/h to 45km/h Th,o,zdeh ac -(y (uti,nuzk22fe 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 weighhyjctpf:9 4. fz93qde;+ f cojt on each pedal when climbing a hill. The pedals rotate in a circle of radije9z.jfdf:4tc+h cyqfo 9 3;pus 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 ofemkd)b5 *i:-ulyrxe ) a door 74 cm wide. What is the magnitude of the toi:x*bl) k)u m5-dyree rque 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 wejb;;v q6fp.t:bg7gbu z s 03theel shown in Fig. 8–39. Assume that a f3bg.7;qj0gf: 6pbb ts tez;u vriction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are anh7rsyk- v43l(q m*go ttached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially tnrmykvs73 *4lh- g(o qhe rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightenhquz:+gf3/f ks9 tp k3ing to a torque of 38t 3z f9k3pfuk/gsh+:q $m \cdot N$ 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 sphere of radius 0.648 m when the alno k y/)s sd9w-k;wd3xis of rotation is thrw;k/dkosy w9-sn l3d)ough its center.    $kg \cdot m^2$

  Calculate the moment of x81f z8aj5voo inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined af jo1v88xoz5 mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball sjrh 7--;kd0)qc:k w6//tch)y ethhm hpo8kson the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculahmr qhh-) p/78kecwc y0)-j d:st tk6 kh/;hoste
(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 onqprdb,rl5l1,xs y+c/,r h c1 z a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N to lzb rqc5cy1,,drxrh,lp +1s/tal.
(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 of pouo/kl58 rf;* gozz 2em, vg,mn3vkmq,int objects shown in Fig. 8–43 abogmmzv, 8qo2e/nfr;o 5vk*3, gk ulz,mut
(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 atomsmn3g/ )q czmn: 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 spinnw se/sji(5k 6bing 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 required steady fsk /w eb5s6ij(orce 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 ma6 )6g li(0beblaz /3rxa,wx)ph-bffpss of 0.580(bir ,a x z /3p-b)xgwa6p0bflelfh )6 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swingsdfdf ; dgw(0/e 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 me cgm b- z8i,1yni k6uoc-d9cz7rry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictiouczz1gc7c nd, k8i9by -imo- 6nal 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 broei, 3y0bs.js q l+vc+ought uniformly to rev,lcb jo0+q3sy.+ ies st 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 accele :idf hfp(, k-rblgg+2rates 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 bal:k 7luuiz fg :ekk/((zl is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, k((lf/g: zk7ui :ekzu 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 blade can be considered a long thin rod, as shown in Fig. 87c *8.6u hx qtt*nj5iixqks6l–46. 6qunc*5 xq s7k68i*h i.jltt x
(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 qqyled0 ) i4k0two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns (re ) 2/j+k1agxnr4ppjde volutions) and relpp4dej gxka2+/1rj n)eases 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 mmhr tu+c)vy2yx5ele bt5+:) d oment 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 66c()hx/45w7n guvl wxsym-beo,ni7 gy 7 d zf$m \cdot N$ 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 wi3,(;pjgynr 1 vgjdkwc+)n:r qthout slipping down a lane ,)+rp3rjykgn gdcn;(jw1v :q at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun q 3 p(xbg6jduo:r8ya)as the sum of tr)d6 :o83j(xgyup aq bwo 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 kls+ - mw14ay( d kvsn+wur0cg6g and a radius of 7.50 m. How much net work is required to accelerate it from -vmdg6+ar yk s(lunw0w1 4sc+rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80v. v3y u,lnp;c kg starts from rest and rolls without slipping down a.3 ,puv ;ycnlv 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 3jd).z 00ynemnx ncd3 on its tip. It starts to fall and its lower end dnd 0ynjm0zn3c xe).3does 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 end of a thin(ypt7iw )1qf7lq bc4yct5h 5b string in a circle qbtyyi h15t(c77wlb45q cfp) of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grin9(tv ud/xuk,onj1 zqy2/i p0(e,nop s ding wheel of radius 18 cm when rotating at 1qypv ,zkj //9un1(u sxto e(0,n2p doi500 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 histtqtbwrd20oz+ bksz* 0g0 0)u+t9 vf e side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, + 0dq*os t9zg buw0r0ett0kzf+2v) btthe 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 moment of inek0. co+ud kwn)rtia by a factor of about 3.5 when changing from the straight positionk n.du +cwk0o) 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 rfz5*/ obe avw5ate of 1.0 rev every 2zwe*bv / a55of.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 vertical axjk 0bs: muuyzarrk :43hg . n--+tanq7is through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diamets-a0. uza+brn:kuj3 :r -m qknt4 7ghyer 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 db*8h, nwy5ida 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 angula3 zt1*c qtuki3,zjll+d (yag w*j3p t(r momentum 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 ivgf 7 t(a61) dv1v:c,xnyiydfv1 3hb cnertia I is dropped onto an identical disk rotating at angula)fac vb h3(n7cyv1x: t ,1ddi1vfv6gyr speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atbmu5 ke :(rgnx39*xviw yj;a3 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 bz*ou eyck9)7merry-go-round platform of radius 3.0 m an oyu zc9)e7bk*d moment 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 i4 i21 -tgbvds fg8zen;s rotating freely with an angular velocity of 0.84gsg2i; - 1ztv8bfe nd $rad/s$ 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, losing about halflik +wemwpv14 1jco qtue*);0 its mass in the process, and winding up with a radius 1.0% of its exisj10loeiqt1wp ev m4kc)*u; +wting 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 winds inypiq.r tfxi +q7f/7/.bqpz5 v 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: o ex0ywvsx2n(-dx.ly a w($ 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, initie99cgv5c mooj99l )bq9ey c)w,e (wmwally at rest, that can rotate freely without friction. The moment of inertia of9 w( 5ecqmm,v)99gocol ) 9wweyc 9bje 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 6.5-m diamet n3e6 i4hk4 tms;m6vw,leppf8 er merry-go-round turnw,et3lm4p 6p m6sik v h8;nef4table that is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the x*a4q kjz jr9-rope lying on the top edge of the spool. A person grabs the end of the rope and walks a d-qj4rkjz9x a *istance 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 the Earth. Dets8hmx7 lffl1ze0 yl :e(m3gg9ermine the ratio of the Moon’s spin angular momentum (a1m3g ey0ell(z ms:7f9lh8 gfxbout 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 acceleratesjj:a d4o);fqto d6q :x from rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 2 ff:7+p3f x npt qax8r-v9foam acquires a rotational rate of from rest over a 6.0-s interval at conq9aano f:r2t7f 38f+x px-vpfstant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg anq++*bj) yj ww.runi9. t tiwo:d diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and 9:*+ jy.n+. wjwoi b )ruttiwqdiameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the r37i jp(. snozf*wzg m1ear 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. ak(sfzho),; a (rkkv of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to 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 a.r;f(, kvhs)oa (zkkat all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobvi-wu7p c9fmw7 gvnbi2; eml;6x: ;od ile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spi wgw7m;vb9v6xf e p; 2i:cduonm7l;i- nup.”
(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 hn9) m e4f.rqb u6yj.jxy j34ran $H_2O$ 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 horizontalpmf * asdra5ms9x9* z) 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 l4yu -4f z6pnj:- stia(v j0jvsength L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of tiv-t(fp6s0 4-4yzjs j jva:nu he 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. It is fujg.3i h)uzd(*bd(wstanding 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 (Fig. 8–55). Tdfg3h)(*iubd. zuw j(he step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turnh /tdpew.-lfe4 s/, zj with a radius The forces acting on the/d.z ,hf 4twpsl/j-ee 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 slingk c/ .;f) sm8n8o7fajdo6mflm 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 ofmof)/ n8.skd7jmf moa6lf8; c 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 skate x1:gjpdda./e r’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 skater with outstretched arms, and with arms held tightly agj1p/xd d.ea: gainst her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, 1owjao 9c*a .fof mas *a9o1cojf wa.s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 track of Fig. 8–i3) ldpa-s. tj58. 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 lojs) i3 -.tdaplop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do notuqcmghe*;1k i3:k2 ga assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uy+ch:w kp;m8ndrk g.yal. x 14niformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. :pa.h8 n1. ;dwrxyk l+y m4gkc(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