A bicycle odometer (which m ax77 :ntr jkta0l /*+auqsli4easures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens iq7 rx+ a7a0s *kajil:/t tul4nf you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates aaiwc+0kau 9 .at constant angular velocity. Does a point on the rim have radial and/or tangentiac+9ak.i wau0al acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by afaagnf1)* s20 xiq)sw single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque hs bp-c9g9d3bky3v.f 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 h b qesjg7-6ueq ibmtzi.7- k;0ead than when your arms are stretched ou0mq 7ibgtz6q7--. i ;uk ebesjt in front of you? A diagram may help you to answer this.

A 21-speed bicycle has si6va6dh :q,x k h.a1:2sjr2wwvy k s1a+r5abgeven sprockets at the 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 pedal, qa k +rh .,hy : xi:ad a26a1v2b6ws1s5rgvjwka small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs wj/k pgt( mo x:rw*:4.,dmp slfith flesh and muscle concenl:m.j ro/m(gptkpf ,:sx d4*wtrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carrza8svj++ ly(q y a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If thqzui+ zcb-dhp c qj(ttd4v94476 ct6: *nzfnk e net torque on a system q6- 74t9c*ztqcd :t pfnn(j4 4zbic 6z+dukhv is zero, is the net force zero?

Two inclines have the same hee o7gjiv1j-.y)-p m.;pj pap qya3i3night but make different angles with the horizontal. The same steel ball is rolled down each incline. On which y 3i-1g )jj;peaip-7nmvppj.y3 qa.o incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rollq sa1 gscr;80fing (from rest) down an incline. One sphere has twice the r0qg s frc8a1;sadius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the sam3cm m6bmrj(l 42:)qedy hiii2 e mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the grecme)43jdbqriml26 yihi m (:2ater 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 6u2-uxz me:oprotating objects eventu 2ozmu:6e -puxally slow down and stop. Explain.

If there were a great migration of people towairm.d +-6wjjwue 67h- u5xxc nrd the Earth’s equator, how would this affect the length oxej6 ij5ud c+- 7wmhrwn -.u6xf the day?

Can the diver of Fig. 8* 0*aplw ,naji;/v egm–29 do a somersault without having any initial rotation when she leavea ig0/*je n ,wplm;av*s the board?

The moment of inertia of a rota;c/ tpdbn2a x zw67:qcting solid disk about an axis through its center of mass inz 6wq;/a27d:tcp cx bs $\frac{1}{2}WR^2$ (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(ombzi6e m d9a5h8l8k holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocitmzlh5e(6 d9bmo8iak 8y increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same masyt ,.g(gfnneai gp 69 l57r)ho4q2jd es. However, one is hollow and the other is solid. Describe an exper7oie) glhe4 n2jryn5(, 9a p qg.gt6dfiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points94fm * /jcoa.rr4vfiazyn. cd,4f nl 9 west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangentia 94o4ciz 9ffr /nva. ,a djcfl*ym.n4rl 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 rot srdce)2vysv:;o,8nuo;k (jt ating turntable. What happens if you walk )d,y v8 esk:; (2rtoujo;svnctoward the center?

A shortstop may leap invwk wdrn:/7 3 ,acyvcpv*)e9eto the air 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 iny*v3) kcw n:pdar79wecv/, ve the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, d.(30s)uhu3qbb wsv go ;;jlhwiscuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the sec3h3sgju;blh( b; .s uovw0)w qond propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 3fqr2wz-1yjg l6dl x3, 0 ;0rie.mbwsl0 $^{\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 E rqx35isly5yn3(sa8 narth because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angula q xi (s5y8slnrny53a3r diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Mlu7q ywyc8v8+ oon, 380,000 km from Earth. The beam diverges at an +8q7c uwy y8lvangle $\theta$ (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 rate of 6500 rpm. Wherk4p (ggy0m0nn0kk -udlrd .*n the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular accelerationg *ruln kr-00.ny0mk( dgkpd4 as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level0essm jt eccd 1c259a-u)tr)k floor 3.5 m to another child. If the ball makes 15.0 revolutions, what emes 091 s- ajrckct2cd))t5uis its diameter?    m

  A bicycle with tires 68 cm in hgk6ja cv7eultc(1 9 :diameter travels 8.0 km. How many revolutions do the wheels make?lccv eu(h96jgk:a 17t    $rev$

  (a) A grinding wheel 0.35 m in diameter rotatesto dqu+)kjc;*.l ,v1b q binn4 at 2500 rpm. Calculate its angular velotq +ov; n)cbl14kd* .,bjiqnucity 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. 8–380:gjwl 9rswb5). (a) What is the linear speed of a child seated 1.2 m fw:gw9l5rb js 0rom the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velqnem(l3+ i oxl0l .yyskkav 9.p 1apq9/74kbjocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear s8 39nzpkhw+u g9q v x+sr8grm3peed of 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 rotate 7j5 gg s4)ika9l.ms wdif a particle 7.0 cm from the axis of rotation is to experience an a4i d.sj)gm a5ws 7gkl9cceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center freq6 * ogap*q3bom 130 rpm to 280 r*qg bope 36a*qpm 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 radius m rj*6-vnl2hu $R_1$ 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 -hhlqls: y44a spacecraft put themselves into a slow rohq hs:l y4l-a4tation 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 hod06uz ue:l eiw/4r+ *lza e;yjw many revolutions did ity4j; ei6 welu/ eud+* 0z:zrla turn in this time?    $rev$

  An automobile engine s-g:ttgxg /ttiu7v11 wh6 6ykblows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highsp.u;5r7yy v0x/y g horjeed jets in a whirling “human centrifuge,” which takes 1.0 min7yu.h/ xr0v j;o yg5ry 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 uniformlyq y9hf le97pp- 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 timeq97 lhe-fpy9p?    m

  A cooling fan is turned off wheno(m m-(v6,anu t qb,1pg*gd nj it is running at 850rev/min It turns 1500 revolutions before it comes 6,dut vn-b n(( gpm*,qmjao1gto a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniforma2 o k)f1qynk- h(q.xip)0e9kf pk tw/ly from 95km/h to 45km/h The tires have a dk- )pyfq (2awfnqp0. )ekoih/1xt k9kiameter 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 p8mjw.56p 2q )oulocvspeed uniformly from 95km/h to 45lop 2wvoq5m6p8j) .uc km/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 (pla + b4szrcl o/s9f( u-ygs5her weight on each pedal when climbing a hill.(r/fy+sos -lsc bla5g pz9(u 4 The pedals rotate 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 the enbq y9usr.xq+hh,5j i5 d of a door 74 cm wide. What is the magnitudexjyhu59h,+ bq 5is.r q 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 the wheel shown in Fig. 8–39. Assume 9c dyp la(0 du* f,x-.hgpuxf27r3jnythat a fric3x rx2ua pdg0(j u- ldfcnyh7.*ypf9,tion torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to thaqz hb)x rrd0tdlt3 3:,ar9a6 e ends of a massless rod which pivots as shown in Fig. 8 339,0r aaxq6h :tbrddtlaz)r–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque of: w1u bvmefy 3-u o (+9(hzbkas)qp-lp 38qv -o9mpw af ( e3:zp-b+ kyus(1hb)lu $m \cdot N$ 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 o*wsnm xp(zc(, 4muy u+f a 10.8-kg sphere of radius 0.648 m when the axis of rotp* cu +,4zymn sw(xu(mation is through its center.    $kg \cdot m^2$

  Calculate the moment of in kl0m6whc vadx2g 2jwi+eez5edd2 ai)) )v--mertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mvx d5+wj0)we)hzia dd-aiv2lgc 2 ee-k )2 6mmass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizontrd uo,m x6j08lal circle of radorl x6jd8u,0 mius 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 p5g)8( u oqcuqdotter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 Nou() 5dcq8 qgu total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inecdls) 0jzzlg5 kpn+t6up8d-9rtia of the array of point objects shown in Fig. 8–43 aboulj5 9slu6tgz)nzk+ dp-cp 80dt
(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 akxxcqb e+ ..p+-ml4 43ad w+mate, cltotal 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 cyli.yff4:x-, achcr ; nkhio0lb) ndrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite a-. nk)if byhchlx :f4,cor; 0has 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 uniform cylinder with a radius of 8.50 cm and a mass1s vi txk-h(j6c/zd8x:-elg h of 0.580 kgsc vg-e6x/k1 :xdh h-i8(zjtl. 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 bat, accelerating it from rest t/eyble jknc3dx/4mn 9 wou//2o 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a sdmc-hfi.e8z( q j it3.mall 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 the torque required to produce the accelei 3-d(f. zjt.e8hci qmration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventualt7+k9v5e kdptly brought uniformly to rest by a frictional torque o9 vk+k dte5tp7f 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 g2fgqxg-o ;o9e nj d2k8(k3rpball 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 ti7*jq1dap5f ho5 hrd8 hrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fd7r5op j5iq8*hf1d h aig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long t,(vf gyc 19mmy;jdvx xd7cn,5hin rod, as shown in Fig. 8–46 ccx597jmf,gv,x;1y dn myvd( .
(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 conszg*rghjg0 53f:*r a caists 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 froiwj))+ms uwp -m rest within four full turns (revolutions) and releases it at a speed ofjiw m-)pu+sw ) 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 mm lb33esj c9ypy o ;r2j0:ws9loment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque 8xcqn8 : nzei luu*ck(8 m*bt9of 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 22c9u02tu pe+ gw fjpjkg and radius 9.0 cm rolls without slipping down a lane at 3pjwe0 c2f22tp+uu9j g .3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic eub.*d46at*dil kjz f4a/ q8 8(ynjhcenergy of the Earth with respect to the Sun as the sum of two terf 4lb/48uk (zneih68d. ayqa*j*jtc dms,
(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 1nn42opaqcn11,liim 3k3kqw yntw 6,- 640 kg and 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 8.00 s? Assume it is a solid cylinde-tq3 l qca1 i2,w4mk3 w1,n n6ioynknpr.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and roj+/ m(ariyv1l57/qz ly2ougdlls without slipping downl(oqg l1i d yu+j 2rz/av5m/7y 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 itud) x.; /rwe/ts g e7fth-0p icn/pb0rs tip. It starts to fall and its lower0w-r 7sc /xrf t0h /d/ugen.;p)ieptb end 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 momentuto(f9yo2plasq9 *x( lm of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 10.4 s pf*y9l( to( xao2ql9$rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheel )u4rf -0t:.bv ndmncw of radius 18 cm when rotating at 1500 rbdv:)w-n fn0ctm. 4urpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a t1owvh (bv+kgzw.ul h*x;k( 8rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rota*kz;lwo wv(u1bhxg ( .k v8+thtion 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 xvc;a9/ 9 tgrlinertia by a factor of about 3.5 when changing from the straight position to the tuctx ;l9gcav /9rk 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 increahb 8wx;qwbuz xkni6, -yp-. *dse her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate ouw6- 8,x*kpyd; .-bi zxnbw qhf 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 verticalzsg *rm2m6jli(hf ) inyx: (n/e gt3)h axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass i( mng/fem*h (lrj2t:s )3hygxzi) n6 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 angul y8x)qm*c i1d p2tf--zlgdv,qar momentum 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 momentum of the ljgnh 8cadf r;91ih; -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 an idenq ebzw b;-i. ql/+(brev,d;dyticalbd/,y w;+iz ; db-(.leeqqr bv disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a:br5z4gitq5f*; lmn hmi- c8c t 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 kgc92 xel2tz3x w stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inw 9223ezt xclxertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely wiz, oq jcw85s3dth an angular velocity of 0.8qd 8z3 owsjc5, $rad/s$ 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 inf:bdqed+a: 3u to a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to thbd:qd+a:e u3fe 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 invol9vu .ey (owm1kve winds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass ( * cb1t4svjco$ 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, inifxjmbk 2i332p * dwqa3tially at rest, that can rotate freely without friction. The momemk3afb3dwqi22 x3j* p nt 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 5dg-;q:h sipwof a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia ofq:w -gih;ps5d 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 tb 7yrqx:4viq9r f;hm(he ground with the end of the rope lying on 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 fhm(4f9xv qy;ri qb:7rar does the spool’s center of mass move?

  The Moon orbits the Earth such that the same cq 9 yvo,bh )o8;r5vttside always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momen9ct;rv8btvo 5q,oy )htum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from r/c6(yw*b,bh eeaduh- h:g/r nest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cyl0xyw/f n(0x rdinder of radius 0.20 m acquires a rotational rate of r wxx/y0f(n0d 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, each of masvxi,/6rhs8jj 8vg d+js 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 ca 6djhsivv8xr8,+gj/ j lculate 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 rx;mgk e*-ip-b0wb)wj/o+m zoear 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 Su+ d+,cfzq my3nn, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times,3qm+, dzc+yf n and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to usr0gna4 n --nwme 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 m4 n gwn0n-a-rable 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 illustrateso1+r --xtjhqp h-b8zy 9ipe9s an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling o q w1.q uxjeb):+ln49gj:mks fn 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 (nbl 5+o8h2e/tifhyoe *hx:l6 *n)hln 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 toi n+fl56 )/et* hxbl2hn8*:yo hehlnhe center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing v+ kc6gxm; obcc3k*kh phb :.i7ertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55ckb cpb*khkh3 .m og;:ix+6c7). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turdt37lpn9 e(ka n with a radius The foa9tp7 k 3e(dlnrces 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 m and begins wyxa+ w s cjn:ctrhb4: +o6ku94hirling the rock in x y+tujohrs4c9:4 ca+knb:6w a nearly horizontal 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 body8 t :x-wsyx xdfd4(/on as a solid cylinder and her arms as thin rods, making reasonable estimaxwxd-/fo :ytsxd( 84n tes for the dimensions. Then 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 assemp -krsyf2rox /k-; r)fbly which consists of two cylindrical plates, of ma fr k2rxp-rf;o/y-) ksss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 i;ssp00fbcq 9the looped rough track of Fig. 8–58. What is the minimum value of the verticp qfc;is b09s0al height 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 ed2c2jsb2 e* snot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniforml aag;y+d0zd1o y from 90km/h to 60km/h The tires have a diameter of 0.90 1dyg +daza o0;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