A bicycle odometer (whizcfu. ivc0i,e-g:1 s ofjr9 f+ch measures distance traveled) is attached near the wheel hub and is designed foro 9irf,i.+u01:zv-scfe jcg f 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 the rim havejtwzpzll(5)yd3 y /:7bwu 4n+ss. iye radial and/or tangential acluw5y w4.+/: ) 3e(lybsz njzy7idtspceleration? 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 of linear acceleration change?

Could a nonrigid body be described by a single value of the angular vm2py g:hydw3-v9 0rx4mjm a9 celocity $\omega$ Explain.

Can a small force ever exert a greater torq.du cp+drrw; 3ue 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 with your hands behind your n;;o6 nxlt0dgh qq4p9head than when your arms are stretched out in front of you? A diagram may h op ngd6htn94;;qlx 0qelp you to answer this.

A 21-speed bicycle has seven sprockets at thevde*-yh s(y 5x rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to p5(xdh vyy* -esedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on beinginzpp 5/1 fcq6 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 dynam1pz5/q fnpi c6ics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) mhow-gxa4 x-vbfw u:y,.1l9ncarry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If2og ru9fdc(e u*d2 +h;4zlmoa the net torque on a system is zero, is the net force zero?megr2o*9uddh uczal 4o (;f2 +

Two inclines have thp8amdm5/kxnl1g eox -t 4y/m5e same height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will thx5/4yka8t1m-x mp gn 5edoml/ e speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an i ,q4c7ogck r--x3rgd rncline. 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 greater tota-rqgc c3k- dgo,xr 47rl kinetic energy at the bottom?

A sphere and a cylinder have the same radiu3at1l0-uuec:n gfuuvy f: d/d n2e37bs and the same mass. They start from rest at the top of an incline. Which reaches the bottom firstf7f3be endc/ d :g uuv2au- :y01nutl3? Which has the greater speed at the 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 or eb i 4nfg52h4vrotating obje4iv2ehb4gf 5n cts eventually slow down and stop. Explain.

If there were a great migration of people toward the Earzh;aazs 6bm9oak97hf)-j2lq rzc+ , e th’s equator, how would this affect 6;msjzfq a-ok 7 bl9)ze+,h2c9hzara the length of the day?

Can the diver of Fig. 8–29 do a somersault withousb4xe 5pd5 r);pjmg; gt having any initial rotation when she m5grd ;p 5s)pb x;4egjleaves the board?

The moment of inertia of a rotating solid disk about an axis thrs. j,/u1lx jkaough its center of mass j,k/ 1sx.aujlis $\frac{1}{2}WR^2$ (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 ma ackxbc(y 8n,2ss in each outstretched hand. nc8a,bckx2y ( If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same gcrak d 8psv7 r f,yl2aa2m/ 6m+rz-z8mass. However, one is hollow and the other is solid. Describe an experiment to determinz+ap2v - 6r7 fm/rdly,am8zg8scr ka2e which is which.

The angular velocity of a whv( rg8gw) 795v xqhr;3okxfk weel rotating on a horizontal axle points west. In what direction is the w)7kgvxv h;xqog rfw (9r853 klinear 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 edge of a large freely rotating turncnk4 n+p:i- eotable. What happens if you walk:nec 4 +-niopk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. d46v 09lqytrx,a i:gjAs he throws the ball, the upper part of his body rotates. If you look quickly yxv,irtgl 69d 0a:qyj4ou will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law o qlvuu7rbe-4: +t-:vwizkcg/f conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second pr uilv tq7 +z-cv:/e4-krgubw:opeller can operate to keep the helicopter stable.

  Express the following angles in radians: (;p lzao0rt/ tbthwg36 89 lm1ha) 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 coincxouq06 qnjhr5 3v cxen:/j; 8kidence. Calculate, using the information inside the Front Cover, the angular dix/x5n0 uro3e;hvq6jjk q: c8 nameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam di 4as7t5o0sdbrmum)3 rverges at an ang a5)3um 7rd04sstrmb ole $\theta$ (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 rag+ywhv03m t/mhx 1 d*pte of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular 1x/0d gm w*3hth+py vmacceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another 22/z tr-l/0hf+ly a3v5. itoi blkonf child. If the ball makes 15.0 revolutions, 5l lh/y b+lfk2totrzv i.3 0n2aif/-o what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How manyom4 /u4c7sxwvz0 * mchac;6 tso,q;9fs,bmqb revolutions do the o ac;x q,*sz f4cwb/shm76uvmsq ob,49;0mctwheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates anr qp)a:n 2d6ht 2500 rpm. Calculate its angular velocira:)6nphq2 nd ty in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 8 cmgb9c:4ahfde 72 g/t2x+z)e+cew cx–38). (a) What is the linear speed of a child seated 1.2 m fromex eedca/ f4wc+2g th9m)2c7:cb+g zx 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 orboi y*ww6lrz- (it around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of4 mq2-leg.pnb a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge )d ysw 1 z+h7/qvud:wgc; -bnarotate if a particle 7.0 cm from the axis of rotation isb v;wy /1)hqugnz 7a: dd-csw+ to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly ayt8 5 zd;l(a gb-w;j2q4j : q0fleijwybout its center from 130 rpm to 280 r;fyldl52jj8w;ig04- taw qjezq b:(ypm in 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 radiuto h,fx:-7zg dq+0qnu 7l i,los $R_1$ 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 spacecrle f43m( lsx3maft 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 fxl3(3smel m4of 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 f:idtef3,/ zh-9zer vi4w hubs *5;mtqrom rest to 15,000 rpm in 220 s. Through how many rev * ize:vi4sm-,tb5 9e dfruq/zh ;w3htolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1m i,oj -zw f3r,6fu smfolxc08,ip y*(200 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 sl-t)ezc6 0 ru;ekvsl;tresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 completer;t) szlue0-k e6l; cv 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 t 4v am15 4ua1fiai4zj8ex7pzr o 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in u 14x5m8zz4vi r4fai71aeaj pthis time?    m

  A cooling fan is turned off whenwzwa9yp ,+f- .fh ye q,nk43 ishx/oe+ it is running at 850rev/min It turns 1500 revolutions before it zo . /ay y4h,q-+pefih ,e3nxf +k9swwcomes 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 revolur,1e(j smv)ww2j1 tcpwvk03 l2ka1krtions as the car reduces its speed uniformly from 95km/h to 45km/h The tires hj(2wvrs 3p ckjwvt, k a0k121)lmrwe 1ave a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its spe+ gww4svxl fzy4+(vdw4jd*rj t42qd* ed uniformly from 95km/h to 45k dld* +wdf+44wy*w4rzvs qj j(vx4tg2m/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal.e p587p qf usac*5wip when climbing a hill. The pedals rotate in a circle of radii.*spp pfc57qa8 e5uw us 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 ghw p:a n+**4-o7exz:i pyezuend of a door 74 cm wide. What is the magnitud- *ehuna i7zwe+ y:g4xo :*zppe of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of 07025 )lbv+aom,zkjxgymm46a4m/ opwfofu r the wheel shown in Fig. 8–39. Assume that a fri2xl0/7f0owgp +yo4zmmv ao b 4mmu)ka jf6,r5ction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of ma *mrk87efev a9l il-0yss m, are attached to the 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 magnitudee80rl9-imfyl7a* k v e and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque of udsogxv/7, pg7ld3 1 d38 3d1od gd,spuv /x7lg7$m \cdot N$ 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 inert, a:ql6agnr;ia zb29p hq(a 4xia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation ilpgb4;qqxza :arhi,6na2 (a 9s through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycleg2 wlf8(hio+g wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. 2gwi8of( l+gh The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on k)f5s+zx nm/zhxx d8/ the end of a thin, light rod is rotated in a horizontal cir +f/xx5hdm8x skzn/z)cle 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 on a potter’s wheel rotating at constant angular a:z jxi*jh.+x. 8lmaxspeed (Fig. 8–42). The friction force between her hands an* .+j8x.z:a xa imlxhjd 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 h/wonl0n;t wfjkf5 ,9of inertia of the array of point objects shown in Fig. 8–43 atj5f h f;9nn w,/kl0owbout
(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 atoms whose- wy4gg (6(bixyc mu2s 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 s1 l4oojfu5 )sjatellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a rad51s4ooufjlj ) 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 uniform cylinder with a radius of 8.50 cm and a mass of wmapkne 2g9sw-7fn 3r/y j x300.580 xymek30/sg9a-jpn7 wr 3f 2wn 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 swings a .uae1sx*gw l 0bat, 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 tang+4mb uq8wb s.ientially on a small hand-driven merry-go-round and is able to accel4msb+u8 b qiw.erate 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 frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotatin:/a 2d0pupp lng at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictio0nl/pua pp :2dnal 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 u5od-/-z+h jab o.sbprvd1 y96x/a jp 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 thqls 0c*)vey x,e action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly frox sc*yv l,eq)0m 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( yoj xx 26l55x)ln, jj/oefyj8aiq7ssidered a long thin rod, as shown in Fig. 8–46.o)n 5 2yqx(68jjx/xl l7 jsijy5 ,faoe
(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 conr(zk8d9- vl onsists 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 8k owpi r7-j ,sui1oc-from rest within four full turns (revolutions) and releases i8u1i p ic7okj--wos,rt 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 momeny tuzhyuv5e.d8 wtbg (i b(564t 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 torq;a0:h i 1:)tvu5oq3ge i mbp-n6pbopxue of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg ank klb 5in-q o0y9(w)yxd radius 9.0 cm rolls without slipping down a lane at 3.3 k(k- q)oy5 wblxiny 90$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Su j o7i3hue7sh mkd-:l skk47o,n as the sum of two7d-khuk4 l os ,: 7kio7mhjes3 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 5/r+dcpx-sc wnt2ow i(v.h4 aand a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per vat cs i pd.-/h(wwo5 4nxrc2+8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest:lwd(:z6ujxagq ulzf i;2 ;(u and rolls without slipping down a 30.0 w(l6ziuaxl:;2fug j (;u: qzd$^{\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 balancz)9l ;v+qxr . th wjlur7:c/vfed 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 the pole just before it h ) lqwr79lxvhj;/+cz furt .v:its the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momxzankd/.hk:0 jl ud2 *entum of a 0.210-kg ball rotating on the end of a thin string in a circnljd* /uka0zx. 2dk :hle 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 wom tw 3phs7ha .400 oye-x0azcylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm? ht0hwoo maay.p0 7 0-s34exwz    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his sidd.s5qw6 en(7 yswj71u+ lxwbliucg(3 e, on a platform that is rotating at a rate of 1s3(wnsigw( u ulx+ 77wjcdl61y b.e5q .3rev/s If he raises his arms to a horizontal 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 one shown in Fig. 8–29) can reduce her moment of inertia byj7m5c ypo14c 4hpvqu; ajpy 4hpvu cmoq4c17;5 factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial ra6anvw v -hsfa8yfb, js*4(wq.te of 1.0 rev every 2.0 s to a q6b,ay 8vvwhf w-(s n.as *4jffinal 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 rotatm ox2opwusr2,1z)p bl1 3 ell)1en,(njnc ;lning around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 n3m w1s jn,xoc2benll1prp 2eozlu(l ,1n)); kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3 pkvj1n+3 0dt0f xs-mh.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 momentum of t aq gpgw0 j87.ab;62he 1kgfrr;kn n+rhe 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 onto an4g/*vceh8z yv identical disk rotating at angular spv/8y4hz* cvgeeed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at vgt(tv24nu4cu k(2 oe 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 /d jksr21+ 2g veogw)protating merry-go-round platform of radius 3.0 m and moment of inertia 9s)g /v1 2wp2e+dkrjog 20 $kg \cdot m^2$ 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 freely with an angular velocity wulrdi/l8ea.1m85 i1 k:dvyy of 0wdkrdu a:1i m1e l5.i 8lyv8y/.8 $rad/s$ 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 h-6dpy/6 8uaak o +uo1am)qt baalf its mass in the process, and windi)a-b6do 6 ku+muq yo/a8ta1apng up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new 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 excess jx.muty:-c6b+hu tg7of 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 ;1 wy1 r;vhgsfe4hxb -$ 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 rotv ckfj3en7 iiu q.8i9 7(j,f qee:s2usate freely without friction. The moment of inertia of the persos fe:2i8uvkqj,q(ieeci7j7u 3 sf. n 9n 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 gwmx oz 2*ry/,the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearinm,g 2z yowr/x*gs 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 lying o. 7 1x7smcl w.omfmhfk cb)p,:n the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does m,.7 x.cpocwlffs kb m1)hm:7the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. Deterzyf6.q/7skes tq 6 z r5lie(3imine the ratio of the Moon’s spin angular momentum (about its own axiszfeeqits(i/ s7q6zy lk3 r.56) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates mcudbs:0 ro53k ) gvz.g2qh;gf s;am*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 unif;6lxn4 :vo:e hap9vtiorm cylinder of radius 0.20 m acquires a rotational rate of from rae:ln;4htv 6px :oi v9est over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solt8ev7+svi6 xq ;b i,gmq-4 v:5bekoldid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thiobtmg+idq45 bve7 qs8 :lv; ev 6kxi-,n 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 the rear wheel k();g1gb.xgf vkv e /d($\omega_R$) 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 q 6cvrn3s h/7:/3thvnuyii0rfoq3 w3Sun, 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 spevifho : 3s/n3vr3/u h rtqwi03y c7nq6ed 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 fo cw3ia3 h,xy.g*vm)i. xmm( slr 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 3xc(.)miv w i3m*ahg.lmx,sy“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 illustratei,7zdd2;8 fqvn ,ofao 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 (hoopa qh kwf0x46ip :zcc*.jr;r5m ) is rolling on a 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 igno87 bmc ;upeuy4tkt1i.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 t78.epmb;uytci ku14. 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 sn-q5k g ljzwyww1g3678ou 1c btanding vertically on the floor, and we want to exert a horizontal force F at its axle so tj lzk6gyb 1u7ww5-831 wo nqcghat 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 road is making p5 xwk3; ifxyz-ez4 l(a turn with a radius The forces acting on the cyz e4xxyz5 l3pf (ki;-wclist 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 slinohmq ywvoc(:d* n; c.yr 0bf)3g of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head;c)bwvmofn q hyo*3( .y:dr c0, 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 armsfpk k5br725s oo,eq+ s 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 wi rs +qk5pk2b,5eof7 osth arms held tightly against her body.   

  You are designing a clutch assembly w ,gic8qr t gj2:xgrg;*hich consists of two cylindrical plates, of mair* t 8gqg,c :g;xgj2rss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alo(ycusk4+glb+b qk x gw)o* *v.ng the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach thegvy+sqc+*boxw)b.ku g 4k l (* 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 v:fxvl3z+ m1te(d5gv7symr2$r\ll R$ h =    (R-r)

  The tires of a car make 85 n o g/+0 yy3p+bp-nmhpw7wxd)ga)av ;revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have an x++mph/)0 bypyv3w adg)a7o- pn;gw diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s