A bicycle odometer (which measures distance traveled) is 4f*(jm.z5 x-ayhwiqf9pghz; attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle wpzf-5x( f jzh9;qh .g*ia wym4ith 24-inch wheels?

Suppose a disk rotates at constant angular velocitpmm.pf8 fx a8nw6 z.x7y. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either compon xmpwa68fzf.x.8 m 7pnent of linear acceleration change?

Could a nonrigid body be des4ya5+nw vuqu0 cribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force?cuy04u vak4* r 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 beh 48 hpt)omz-ddi/ .*.yhejhhpind your head than when your arms are stretched out i d..*8t) hhmjy ep4/ihpdzho -n front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel anul20li,+7 hghs.mmu 3d w nc.pd three at the pedal c,l0wmu hs2 u. nm+pi g3.dc7lhranks. 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 pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being abo .+rs(sz ym5hle to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34m(zys5so r+.h). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig.0 c8a2jk5rffl 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net tomct:8z .91nbt;ei xj;xudy o9rque on a system is zero, is thez.io ut:xe; tmnjc9b1d9yx;8 net force zero?

Two inclines have the stx*c fz/ jz11 cv-s9lsame height but make different angles with the horizontal. The same steel ball is rolled down each incl f9*1s/jcc vz z1x-tsline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (fromy0m 4;jki6v jy rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of64;jm0jyikv y the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder1 5z mgrsttta b/x9*e. have the same radius and the 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? Which has the greater rotational KE?5.b *trte 9 zx/agm1st

We claim that momentum and angular momentum are conserved. Yet mostvo5r ;pa-a+il moving or rotating objects eventually slow- 5 ;a+lvoraip down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wxzvnl3+ 8ppaimbe );i7-kl )vould this affect t ;-a7+l)pbn3 i v)pvxkem z8ilhe length of the day?

Can the diver of Fig. 8–29 do a sme; )ytp giy m-ym-3 p/tml/5yomersault without having any initial rotation when s3y iy-/)5mmmt mypyplet /g;-he leaves the board?

The moment of inertia of a rotating solid disk about an axis through its center x r9)z ski;aj.uoh;lvzdc483 of mas9voz8 ;a xhdujrkil cs43;.z )s 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 rotatinuy s*la1h) l,j-u p0mgp y.yk2g stool holding a 2-kg mass in each outstretched hand. If you s*ul2u-mpy .jygh1 la s yk)p0,uddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same m-cudot/j/ 2 y*5 l/qo/ zcbjvoass. However, one is hollow and the other is solid. Describe an experiment to determine u 2j/*cov/y jzc5/bo /dlqt-owhich is which.

The angular velocity of a wheel ro 3j0bx(*h ecdqtating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, desxq3dj(*0 cheb cribe 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 i ,6ir*4n4t.qevnjlq1r v v3z freely rotating turntable. What happens if you walk ton4iz1vre 3l .rqnv,4qv6itj *ward the center?

A shortstop may leap into the air to catch a ball and throw it quicxiq1,k-q rb7 )m1lxso,xd eg2k y7;qekly. As he throws the ball, the upper part of his body rotates. If yo,yx2l7ib ed,rsq;e1qg 17x o-km )qxku look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation ofq2syd+dbxq4+g7mpr 0 rsq*7v angular momentum, discuss why a helicopter must have more than one rotor (orvs*ysq +dq04gd 7pb2 rq+m x7r propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radian-elxjo7d3(v 9e(y +h gdy- roks: (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 Eart0ucfn5r1ca5yk a40 k lh because of an amazing coincidence. Calculate, using the informatiyl 5n0k 4rcaak50cfu1on inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at thehh i:(9rwuoe4 ygvd( i2c29 cc Moon, 380,000 km from Earth. The beam diverges atei urhy((d 2oh4 99cgc2iwv:c an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at j/1, ozkgdij;xxx-b0vnt ( 0t a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 (ti- jx1x;n x k,jdz/tgb00 vos. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the bahox,l; ;u a an02 o.v*knbvfk9ll makes 15.0 revolutions, what is its diameto0lnf hk*ao2;9x;va.u ,n vkber?    m

  A bicycle with tires 68 cm in diametew z/; ;.br/n )eoil )m)pz8eexz5jwifr travels 8.0 km. How many revolutions do the whn)z.wzozr/pxbe 8e)/e;); liw f5mi jeels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angyht 31 m vu4df(q)nd)hular m1v 3uf)dy (qdh t)4nhvelocity 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 )ab; y2h4mk mbone complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of k b42ya)hbm m;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) inrbbeu ;7nia:vnz10h8 z* t/ hq its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ok4 h5,))a nmk4cdjx /+nrt bibf 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 centriffhci+o q+2:,1rd,t(qtqmo;r zv/ k dcuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration o c tivk(r;fqo+tqoz , 2+m:,d hrqcd/1f 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm 5jf:sk az:756rbxma n to 280 rpm in 4.0 s. 6 mzx:75a: j5na rbfskDetermine
(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 radius6(p fks wtzcjt a1(,)* 5olfvp $R_1$ 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 r;m6 g3lqdlxh; ;pen5 spacecraft put themselves into a slow m;r65qel dhx; l3g np;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. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Through hows fsvh6 9lzf7; many revolutions67ss z v;lf9fh did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Cai q+wen) z 6k rwe0+i5etzl5/slculate
(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 strei21b e nsgs3ey3. .fn8vj4yov sses of flying highspeed jets in a whirling “human cegnjoib82e y3v. 41v fs.esn3yntrifuge,” which takes 1.0 min 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 diamnnhcrjw qa8 ;f .l 47ezmaxw y8r14j:1eter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this timey1nz fc;e44ajah x.1 mw 8wlr8nrj7q :?    m

  A cooling fan is turnedcgew+l9 k;i7 c off when it is running at 850rev/min It turns 1500 revolutions before it comes to a stopcl7 +i9egc;kw.
(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 redp 67,8jakkj8q 4 iidoxuces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.4i8apdi8j, k6 j 7koqx80 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 ) bzgjbq2i4l2the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0b2jil)q24 bz g.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 y:: cxdhcug;ja( 5pin+vx0 x5:hp v 2lbike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radiud hx0hnx5x5v(uv:a p j+2 li:p;gcc:y s 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 endmbw2xx3 wl)(kk.xv .b+ y2nrp of a door 74 cm wide. What is the magnitude of the torque if the force isk2v w.3.nw(x ryl+x) x2 mbkpb 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+qyxhe n *uo /)(glmmd7e5i/wxfp2 ,y–39. Assume that a friction torque of 0.4 lw/ipxeh /25dy7xemu+o)*(,q n ymg f $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless ro7( ujbc qx;uu+d which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the +x;c 7uj b(quumagnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engiyb3fq0tq-, hym4y 5na5zx;ib ne require tightening to a torque of 38b5y 5q40,hy; 3ziy- ft qmaxbn $m \cdot N$ 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 ol420 fu737chbe hhn+jh ;duikf inertia of a 10.8-kg sphere of radius 0.648 m when the aebh dlfiju h07hn2+kuh c3; 47xis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in di:zyzis 8t-; bjameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignory; :bs- tzzj8ied (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated irpj5chb6 yxv9*(aze:,g exd-i bld 7 ;n a horizontal circle of radius 1.2 m bb9*hpxeydi,lj ez rv7d:x5g c;( 6a-. 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 bojk(ao,a2 k-.ghs fad3wl on 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 totks (hf 2.aoakg3d- a,jal.
(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 objects shown in Fig 8/tx*+g8cs -me,-q- c i kcbmxz6fcfr. 8–43 ai cb6-/g fcsxmq8e, f c*-- tzr8xk+mcbout
(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 w015mslu zb8is4 a rgp-hose 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 sabmc 1ox(uxz* 3x o.c2pinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–43mzoox* ubxc1(2. ax c4. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniforv1 l7t/skihjca4p+,y m cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Cal1vhitp/+ys74j cla ,kculate
(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 jkr,e2 uh 5vscvmi6lix( (5*fit 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 tangentr,(i 5,ocr pflwtua+ 4ially 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 childrr4+p rtl( c,iu,wfo a5en (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shutah do5sytqw57ga 9,c c f7m/8e off and is eventually brought uniformly to rest by a9c 7wet7m/5 o fg5a,qdy ch8sa frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball at 77xp k3l(fefq . $m/s^2$ 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 v1e-fa0qjj f,)j pa 3ysolely by the action of the forearm, which rotates about the elbow joint under the action of the triceps musc ,-apf jej3f1aqv0jy )le, 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 conk;hp;5(brhhxd1ii6; eayy/z z43rjq sidered a long thin rod, as shown in Fig. 8–46.y;/a z5 rhzxbpk;1qdy4 6ji3h( hie;r
(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 cjcq(oh:d 8f2f:htg +lstgso7.4 ap/,i i*srbonsists 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 acceleratef/m6e7s w )6ecwvz-i9) p srces the hammer from rest within four full turns (revolutions) -ewp)6s m e/wrfe cs)9 vc6z7iand 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 inertia ofo50f s:i,rgdu5h vz;u $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine dev4uc ie9jo 3o9x*z t/ima /hlj1elops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg ft5 52wil.* +a9 hxyqzn0xl87p mfvpqand radius 9.0 cm rolls without slipping down a lane at 3.3 ai9n 8q*5yl5pv.f72xflzm 0hx t qpw+$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sn2bf p,.7* trcxk/5kjvy c fl7um of twotvcck 5jnfy7k2/b*fl 7,rx . p 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 m ()r* -yjuysyj *m0tutuch 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 som r* -jtsujt)(0uyyy*lid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and ror d0mzhmq(vj8/:1 y lpos.5 lclls without slipping down a 30.0d/clyjs m.oq5r (vh0 :zl8 p1m $^{\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 verticad8qi+fyegxe )fr q*5/ lly on its tip. It starts to fall and its lower endqyg/x) +85iefe qrf*d does 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 thxhhzxfjn f3 psml;; h m(3/5q(5eqc+qin string in a circle of radius 1.10 m at an angu( x(qf5 +scq;xefq /h;5z3j3m lhnmph lar speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylind:kwmi .um,+q ky /swkw(l56ocrical grinding wheel of radius 18 cm mc .wmo:kwk/(iyl5w6+ s kuq,when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platfo;9clea1 + doy(0srep orm that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to (ad se+ y1cpolo09e;r0.8 $rev/s$ (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 4sf5f)ipeyulh ,pb4- inertia by a 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 anguyhf, ls5 f4p bu)e-4pilar speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation raf9 w mpfob4*q.te from an initial rate of 1.0 rbfqw*mp 9f4o.ev every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating arom)b6wdcb3f6;bl-j6lyr nv. gund a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of nr)y . bjl;36b-c66v fmwbgldmass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3.mcrfk3 7;g b8ykr8gx: 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*1 jfisvirl;4 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 bt(2zeedcw59yy .*.5t lp gpd of moment of inertia I is dropped onto an identical d zd*gb5.2ple5wd 9(pyeyt.c tisk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at7abuo:0si dgf ,(d :ku 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 standpz,m b2k a s6c;e8 shy*ihb56gs at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inert;sc,iah pb5*zkm 8 s b66gh2yeia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotatin 4e/(rgmi:urvnm p 3g3lws.h)g freely with an angular velocity of 0.8 gnp( /ims.lgr whem3v:u )r34$rad/s$ 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 intdxdnv,i15 hi bla81vj +/u4 ggo a white dwarf, losing about half its mass in the process, and winding up withxgil8 1d/4inu1j5+g ,vh v dab 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 of7o,a z k40uxr( xym4vd1jeu1r 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 7vkc l2fh8pds0gh,j 6 $ 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 cayip5dw-0 +g z9- zfkgcn rotate freely without friction. The moment ok- pzg +5zyg wf-cdi09f 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 oiqhy8w i4h)d22 8 xq+tap7tvkf a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia ovphx7 k2qiita8qwy4) +t d2h8f 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 thekkz jg9ob16sqw )7kj+ rope lying on the )wkbjko gs+j6kqz197 top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces th ,9k9;fnsq7 a vk*ztm ebxvkzsw82,t0e Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momeq92vsfkv*x78waet,kbs, nmt ; 0 zzk9ntum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate -wnqm 3fz q90aevpm(5 j a+3veof 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 e -9wdbjdw: )lcylinder of radius 0.20 m acquires a rotational rate of -lbdw e9 dj:)w from rest 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 solid cylindrical disks, 6fj 8t0u-n7zl+ xgafmhk x/w9 each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from r0 9hufxn/+g a-txm7jw f8k lz6est.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how i 8rsx qcxgz2t:.pr9 +mxakj3;s the angular speed of the 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. /efe udh*53sr0 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 sp/fesu e3hr*d5 here at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pol*n*k6q4x u3zwoll, 5pgy.ds rlution automobile 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, 63 5zslk*opq,w.rn4lx*y g duand 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 rfjkik3 ;z29a u qvs,:$H_2O$ 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 1w srgzy( b*.tv*p- -hkg*gxfspeed 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 lengd 9vb+ j zsd gdnc 4l8:+yl2o8ez-cvv0th 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. 8–21gc4lz 2j+ l8s-d vvb:c9v+ no8ezg dy0d.]

A wheel of mass M has radius R. It is standing vertically on the floo1 79i,0r7zt*twepuuhdcc *g xr, 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). Tg0 e w p9t1tcci d7*x,r7h*zuuhe step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road i;g4ylh0rzemx)0 8 p uas making a turn with a radius The fo)egu0h0ypxa ;8 4z lrmrces 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 slikds/o :4j v+ jpo(l.wtng of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s o :j/s v.w(kldpoj+t4. 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 arms k8piczzrp8b ;k/+t(k/xu ;g m ; jmup7as thin rods, making reasonable estimates for the dimensions. Thezgtbc8 ( ;/kk8pu+zmx/; ;ru pkp7ijmn calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which cv ali*awkp(/,6yg 6b r z3:tvnonsists of two cylindrical plates, of ,wakv g6ibz/3tp( lra:v*ny 6mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ki3fm-u6 * g9iv5mhe3dnad* xradius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical hef6 5a-mg3kxevin i9*m*h3d duight h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do n,9aph yve,e v/u tmi,p/;i:x pot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unifldaed7dd/; w91 t 1ow:qq r0aformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of eac/9rl o 0qafedt7:aw1 qdd d;1wh 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