A bicycle odometer (which measures distance travele 9d 5)d3 ga/ o.uzwl2hj4yvixtyjn (g7d) is attached near the wheel hub and is designed for 27-inch wjt)yv4 d(h3o2 jil5z.gnxwy a7 ud/ 9gheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a vm-4bjb8wj s, .o vj (:ny2eixxoirsshm- 0:9point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity incrmb.0y:or vi4-:bso s2hij, j evj 8 n(wx9-sxmeases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be dff+qewr8 0 6qjescribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torquek(cko/jsn uq 783(f/b zwjv/pf)4f vt 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 do a sit-up wit78z-pbz ti 4vybfhau; 1o u(s4h your hands behind your head than when your arms are stretched out in front of 4yvft-obu1z ab(is p4u ;87 hzyou? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at thp;qm1e2v-hl:h9x/xzr str / se rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Whysh rpqhx/tesxrl19 -;2/v: zm? 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 lower6yxe t 99p) :lz)uhlnk legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamicsnlxuzkt9l y e)9)6p:h, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) cara:evn xv0ct:4ry a long, narrow beam?

If the net force on a system is zero, is the net tof x33kk;io fwkmeosl) o *;u0(rque also zero? If the net torque on a system is zero, is the net force 0o me f ;3kk)xis*l(owkou3;fzero?

Two inclines have the same height * c.3k psrz3xcbut make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of th3zsr 3xkcc. *pe ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (fd n bwc(l i,i-*rn+-1o3ddy q6rwzfo2f18 oiarom 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 speedci+1n2l 1f-oiio *(8 n-rwwbf6 d ,yqorz3dd a there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same ynwh++mc gfih*4; 9xu 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 ;hm+n9+i yg f*h x4ucwat the bottom? Which has the greater rotational KE?

We claim that momentum and akiz/0 (og;vo)qi b8djngular momentum are conserved. Yet most moving or rotating obj8i( d/0bkoo;)qvi g zjects eventually slow down and stop. Explain.

If there were a great migrationml*tx/i my ,o8 of people toward the Earth’s equator, how would this affect the lxi*ly8mo/tm, ength of the day?

Can the diver of Fig.2whulz0np/ci )bd5- k 8–29 do a somersault without having any initial rotation when she leaves twc/dh0kl2) p bi-z5nu he board?

The moment of inertia of a rotating solid disk about an axis through its cen+h9iu32xuwahk/)fa xzg7 e0 7 j9a qjqter of mahw a7fi0/khe929q+z xag73uua qj xj)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 each outstret) et7;z)v2bueqgw/c xched hand. If you suddenly drop the masses, will y)gqx;7ve bt/wc2e ) uzour angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the s2njgw7fi*p )aame mass. However, one is hollow and the other is sol 2)afpjn* 7giwid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points wn bd/jd0oquoxuk :c+3 m 10v;lest. In what direction is txov:b; u/0ud lndk+cmj130oqhe linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edgh*m2u5fysv7 ec5;qb9u/ bijee of a large freely rotating turntable. What happens if you walk toward the ceu57c9 */h5feyu2vmjbsqe ib ;nter?

A shortstop may leap into the aixd2y)v-iub,x cqd,6vr to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–3x dcqb-vi,dy,v )62x u6). Explain.

On the basis of the law of conservation of angular momentum, disc1lcykrs * h6d7uss why a helicopter must have more thacsl*6d1rk hy7n one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles inyg882fi4 juiy5s h*mu radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate, using u3rzsnsbo62 evga38n+ +h 4jd the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as8s6+ vej +h na3nzgubr43ds2o seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is direjm+rkcp4,5e yy a7u kgf )5ph:cted at the Moon, 380,000 km from Earth. The beam diverges at an an5guykck : m)jrpp4+7ehf, y5agle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blendq+d ,ghn1dmr)mjoer/ ;.t k6x2mg f k,er rotate at a 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 accele+ h;16,fm,2xke /rdqjgm d)r gko .ntmration as the blades slow down?    $rad/s^2$

  A child rolls a ballk4cm9* nk 1t 4brsnz)o on a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what4ko9rsz mn)ck*1b4 n t is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km.v2rl 8l) qwka:qf d6a: How many revolutions do the wheeqfk26a :qll8aw: r d)vls make?    $rev$

  (a) A grinding wheel 0lp;p.xv uc 9kgtg .h)13 gu9gb.35 m in diameter rotates at 2500 rpm. Calculate its angular veppgth g.u9x; blk)19. 3ugc gvlocity 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 revijcoeq204 3+ ihmefox uv3*z6olution in 4.0 s (Fig. 8–38). (a) Whaji4m+ocq3x z*v2 ef3h6 uo0iet is the linear 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 theahk;gk0i lu h43k39dq 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 5lm;bv4l4 skt,;k /. x f s:ppbxvqprb 4gr3+pa point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate+z bn..g1 d nko(x7cxvw klz2( if a particle 7.0 cm from the axis of rotation is to experiex+cv7( x1 b(z. d.n2lznwgo kknce an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about + hnc9sb.gya/9r iyj4its center from 130 rpm to 280 rpm in 4.0 s. y y 9r/j4 acbh+in9s.gDetermine
(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 radiuc3to3jz ( t8las $R_1$ 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 spacecraft put themsel/07o lr dgudc2ves into a slow rotation to distribute the Sun’s energy evenly. At the sta0 /ugdd7 or2clrt 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 mp glxlf pgie(-/) 2z1uniformly from rest to 15,000 rpm in 220 s. Through howl(- /e1gl pp)f xmgzi2 many revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate kgo3w 9.vf rmx aqdvn4oq1m1t2j / )d1
(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 hi oa8aes9:vh z(ghspeed jets in a whirling “human centrifuge,” which takes 1.0 min 9va8(:o azhse to turn 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 24ez)b+nql j jk-- hn)o1qba j(lr e1v+*0 rpm to 360 rpm in 6.5 s. How far will a point on the ed+-l jb nj erb)e v()1 *q-khq+ozl1ajnge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 revo :3mr 7q2waa dhgin50ulutions before it comes to a stop. :n7awg3 h dui0 marq52
(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 aa*c0 pcb:s,y7*nn0( yancl u65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m. a:na 7na0bslc*y (y,0 p *cncu
(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 reduces its speed uniformly np yoh3 sjn-:9h0u3t xx33 raffrom 95km/h to 45km/h The tires have a diameter of 0.83anryftohj0: -ux 3 xp 3n93hs0 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbiqtk+z:bpe pxmk i)73 zvr38 i3ng a hill. The pedals rota p zrqi3ixvkz7+tp km8)3 be3:te in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on 4 kggc n m1giwaaz1mj)k(5l:;the end of a door 74 cm wide. What is the magnitude of the torque if;51z1ag)nacg4 mgjkwi (klm : 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. Assuu,29byd4wp u ;o+rvu mme that a friction torb r;4u u+,wpum9 v2doyque 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 y9f .wxs7jq+a m rwd67rod 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 netj.q wydar+x mfs9w677 torque on this system.

  The bolts on the cylinder head of an engine require tightening to a toznuqsj 0w,b 7*m jukg0iy;,kb3r7 hy,rque of 38;znyy*wr bg70ukj0,jks,m,u7hib q 3 $m \cdot N$ 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 radimjtdhz-yz1 c+(t 87m jus 0.648 m when the axis of rotation is through its cet zzy1dj 8tm- 7cm(hj+nter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle ujzw(kv de( 8+wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).wuz8v ((j+kde    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light7+wj af66ovemdab9svi8sx m p 1:f9r5 rod is rotated in a horizontal circle of radius 1.2 m. Calcr1xdwv5 b9ef 668 7ssjipmf+9va oam:ulate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angulf/.+nb ukb fgb ht3zwe-+-hof.p55gy ar speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N tot/b5n.ou -k bf3.5zg++-hfyg fhwbpteal.
(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 point objecta dpo7znj x( vrx51v(h:x*s6ns shown in Fig. 8–43 aboavxdn((vrs nj px7z*oh65 :x1ut
(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 consist 7xgv9nmw r,n+s 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 spinning at the corr35lorhz :7uz4v q*z xt* vv)nject 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 forctzl)hxovzqz* * 4jr5u:n7vv 3 e 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 cylindel csdajvbg+96 jutq85j jp *5*r with a radius of 8.50 cm and a mass of 0.580 kg. Calculat9vu8 j 65jsj 5+pjabtc*lq*g de
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from restaqjq jlso7 )jfju16,9l(a.c m 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 taoov8(vo0 37:c*b km zjq q*lhqngentially on a small 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 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate*oc3(vlz7vmob8 : o *hqq0jk q 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 aa*dx4ftfdhm/0qjwv97c c7m * t 10,300 rpm is shut off and is eventually brought uniform*hax*40mcd7mv/q jt7 9 wcdf fly 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-k qb 7xr+nfub13hbb0u3g 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 solei4a z4fo+ rtz mk7d.n/ly by the action of the forearm, which rotates about th/4 otrk.4 i+ n7zmfdaze elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be con+ ;/mot/jb bfxsidered a long thin rod, as shown in Fig. 8–4j /xb+;obt/mf6.
(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 consis6snrdq/ 4wnt* .vj6iq ts of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns (revotxw z aw:3 (fvql)0cy3lution:fwq(ly3w3xc)0a vz ts) 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 moment of inerxi hverc5 qv1.8*k 3k i8ztti7tia 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 m9osj2y 6+mgnof 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 *(x (kaqbod8vand radius 9.0 cm rolls without slipping down a laqa8* d((kov bxne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as thep6cdl10 8uimh sum of twc6mdui80 hl1po terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How mvx6va 58chyd i(8jd6 f:y ou7much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a sol65f(:8d vd xy oy68v jihcuam7id cylinder.    J

  A sphere of radius 20.0 cm and mass 1.800e) e6(0 rwt6hn- btu1/zpwqhvs6x cu kg starts from rest and rolls without slippinp1x 0 uht/h6q6eunzcr0(v tw)-bw6 esg down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on pwtdm hk0( vdk4* .5rwits 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: Use co tmkk r4dd(h. wwv*50pnservation of energy.]    $m/s$

  What is the angular momentum of a 5sn 3vj4fbx:1( qha lvop5tjrf4-t:k 0.210-kg ball rotating on the end of a thin string in a circle of nj-sv t k f:jpqf3o:1r4h5t5x4 a( bvlradius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum z55 ;imv(th 4f xjiae8of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm zt54f ;v5x(eam j8 ihiwhen 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 sidert mvc pz6v8k/)f1)4 u3aiih f3o r1ivcn0(cm, 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, the smf kn68tcc rrhfoii)iva v0)( muc14 p/vz1 33peed 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 s;q7nd+u /x5 mzeyn5veq63vs Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tu6/;ss+ dy 7m5 5nvevnuqqx3 ezck 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 rotdnbq:f- y :g7a.q wep7ation rate from an initial rate of 1.0 rev every 2.0 s to a final -7.nwqpbq: :g 7ae yfdrate 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 axis through iop:fb/.-pi7)qf k*nv azmdt; ts center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flatq7k.bfd -t/:vmi n ;fp pazo)* 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 momentub*;vd(s*b;t f)waxj)uyg lq fgrb :/ :m of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentc2 .r dqoxy+(he fg0v;um 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 drw fv:zb il ;g1ko28*of moment of inertia I is dropped onto an identical disk rotating at angu ri2l* ofdb1kw;8z:v glar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2hlrtt8etga:bipk+ 5 w vb)i-i f)+v9 ).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 siiny)fn-7zh ny 3u 9*g-.dybdtands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia bhi 7y )9-n nnd.ygd*3y- fuiz920 $kg \cdot m^2$ 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 ro:r6 )ggw8ku;xhpj9us tating freely with an angular velocity of 0.8g uhjw8s x6p:ruk;)9g $rad/s$ 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 wx 5 ew-8x9n6dkwetdk8hite 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 angulan8d8 5xd ekw-ke 9tw6xr 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 excesdul i6jx2u/8 zs 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 pea9nd-(jr 2a $ 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, init l9.1ldxuxt i1dzj:k/ ially at rest, that can rotate freely without friction. u/z: lx19xi. d1tldj kThe moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-;x)bf85kko c fgo-round tur8;ffkb) xo ck5ntable 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 rope lyin+yd rot*ma8)og on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holdinod)a o*rmy+8 tg 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 6.ue ppo: 9*ps1ywtkuEarth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth..u1y eppp6 uow s:t*9k)    $\times10^{ -6}$

  A cyclist accelerate 0kbh pcs6lb,(m;wsho .o b15is 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 ofl hxb) .hv x93 -fcqfpuf)w8e6 a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by fuxp lx9c v3))bq.h 6hfwe-8 fthe motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg and diwterlt8c/ xmm74.pq- ameter 0.075 m8/- lqct74p.we rmt mx, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of thre. ),1fd2c 5 besgch tw*v07zvd9hcee rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, )vlp:23bikiurr9) fjwere rotatii)jv:fku b2r irpl39)ng 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 momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is fotj7ttz ;k2h :ko p6,x6x.bcj er it to use energy stored in a heavy rotating;ez,6t.: x p26hbtk7ko jcxjt 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 “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an wy12:sf2 zz1 * dy3jgllyl(+vo; pfrd $H_2O$ 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 horizontal surface at speed v=3.3 n9(mtm3p7deu$m/s$ 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 andp 7ljg5o nfx/k6:h 4f;r4fspf length 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 the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 4sf; 7 flj/:xr6gh f54pokfnp8–21g.]

A wheel of mass M has radius R.u yofquy,.i73mbfc ,ys4f 9t1 It is standing vertically on the floor, and we want to exert a horizontal force F at its ax 4cf1y73myyi.o f,s,bq utfu 9le so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat +dd zp8robld fe +m) o5w:pir)ql,/2kroad is making a turn with a radius T rbewmq+),r 5/d d d2l)+ f:opizpkol8he 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 rock into a sling of length 1.5 mkw xk8 mph-2x+c4lw3 m and begins whirling the rock in a nearly horizx8wlk23c m+-kpx mh w4ontal circle 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 h*g) 8f:vm,zyhww (bn aer 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 held8w) vam g(*,bny fw:zh tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates,ila dchr+/* 1l of mass l*al1+cr di h/$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 lo1c ;j vln*f+xvoped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is t1 ;xlv*jnc+vf o reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assume bbvt0x*r+efkzs/8 -j$r\ll R$ h =    (R-r)

  The tires of a car make 85 rvb3qy,j7w hje-uf l+s;14 eusevolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of -1eu3wvu qe7jjl;by +s sfh ,4each 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