A bicycle odometer (which measures distance traveled) is attached near the wh p*e.btre1w 0ueel hub and is designed for 27-inch wheels. What happens if ep0weur.1 b*t you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at const bu0 +*ocg+korant angular velocity. 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 rcoo*gu+0bk+ tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a sinlk*pqb8 vm64,f p qp2pgle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greate ,yej)atufz11o1t 3ngr torque 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 head toc 609,;btz yux0;a)l hp dauzhan whtblhpac0u)yod; ,0zaz;x u69 en your arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at they1i,ga tlr jh 1;(f9ok*x. mmg 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(1 ,hi;9am mjlkgx1f. rot*g y to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able tsdi/f/ ib5qq -k-zu3 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 dynamicsbd uqtkqf- /-i3 s5iz/, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bkr,j1ish (z b;eam?

If the net force on a system is zero, is the net torque also zero? If thea ji0ob-y9+ kruocco8.z 8/oy net torque on a syst/j yczo .i 80ua9ob+oo-ryc8kem is zero, is the net force zero?

Two inclines have the same height but make different angles with 28tgh5*qy).v olv1wrzq4dd kyzk(4r the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of (gdq1q r84zyy*t ) v4 k5zvlwrhd2.kothe ball at the bottom be greater? Explain.

Two solid spheres simultaneously stx8); 2guf6o m* hof1xq3hcarnart rolling (from rest) down an incline. One sphere has twice the radius and twice the mc2q ax;x*hfom1 3u)o8h g fnr6ass 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 raa ytk9i 3d g tx,mrpyvw),m:0;a3k2 fadius 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 ror amfa ,kk 9t0t2x3dgv ia,;wy)3my:ptational KE?

We claim that momentum and angular momentum are conserved. Yet mos1:gd**abr fj h9ib)yd,o2aeot moving or rotating objects eventually slow down and stop. Explain.ea9o1*ibrhj yd f2) od,b* :ga

If there were a great migrati aub9diybxl+l*s( *- uon of people toward the Earth’s equator, how would this affect thexbu9l* b(d-uy+* sai l length of the day?

Can the diver of Fig. 8–29 do a d8jjfjx*n;4)wo sk: kgsxlh06vro3b-r 3ie .somersault without having any initial rotation when she leaves the boa0 ivgjof4blhd.83swksj) rkr-n; joxe:6x3*rd?

The moment of inertia of a rotating solid disk about an axis througux,t9ip,lehf c8j:rvg* j0vr5(icr5 h its center ofrv0,:5 t*fcvj8 g rehx, jlcup 95ri(i mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holdi a+ubz2(oml. dng a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity o.u(2 abld +mzincrease, decrease, or stay the same? Explain.

Two spheres look identical and have the same mast.3b4 /uh w5qq mo;nuds. However, one is hollow and the other is solid. Describe an experiment to de4/3u; qnwqt.bh odmu5termine which is which.

The angular velocity of a wheel rotating on a horizontal axl q9crn)0)xrub e points west. In what dirx90n rcr)) buqection is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on b*02c5 aoprak dd:6sk the edge of a large freely rotating turntable. What happens if you walk toward the ca0*akpd : dr5 bsco26kenter?

A shortstop may leap2d.27kd (dgbnn4e*iqstj72i :wovp t into 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 in the opptp2n*2sigi o2d(dtb7vq wn7 k4e.d:j osite direction (Fig. 8–36). Explain.

On the basis of the law of conse3iw azu;07ysp rlhw t f.*5fnfwg3((yrvation of angular momentum, discuss why a helicopter wy7n 0*.swagt wrf5py((l 33 hfifzu ;must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles gjze u7hiv+jcu x cq(2ec969cse*v .-in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth *fvux2pj:jyp;8y9ux *, ypx qbecause of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the S,q8y uuf2y 9xxjxpp*pj ;*y :vun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 k8ab y *;,wnwuf,p uxh03vx(mzu/g-9 mzea xy5m from Earth. The beam diverges at an angy- anxw yu/;vm a3 e,zxub0m5x,gufwp8(h 9* zle $\theta$ (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 jz 9jo/bx6kan q1vg13 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the an jo1 v6k1/zb3gjqnax9gular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another childt/ gv ,4c* hy*qalnzprk()ee (. If the ball makes 15.0 revolutions, what is its diam ,t*ahe(pl )c4zvgyqerk n /*(eter?    m

  A bicycle with tires 68 cm in diameter travels ;y98o zu:/t,y q ndmwo8.0 km. How many revolutions do the whee ;m dony9/8t:,yuwoqzls make?    $rev$

  (a) A grinding wheel 0.35 m in diameh . o,btw. ))qrm,ga6fta-szp ter rotates at 2500 rpm. Calculate its angul) f,.)t6 zmob,wsqga-rpaht.ar velocity 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+e t(aby6 *,g ssvxju; (Fig. 8–38). (a) Wh*,jatbgss y;u6v+( exat is the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbwe7 5gi1,7dq9e e hyvvit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a pointim.)hjkixy +cf 9 h u9j -7fgkwo7q40t
(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 cdk :3vm u:x0gkentrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an accelermg udx:v30kk :ation of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accex h5 .nv+xfpofxv;pqr: ,)n r6lerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determineq;nfnxoxh +. :pv5, 6px)vrfr
(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 radiuslp0ht8js- p,h $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put them./sf.1ck( kz hk vdh g.ky/na1selves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Devn/1ds/ k zyg1kc(f.kh hk a..termine
(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 15,08pk 08 5,r1zyvoneru9uvre9 n00 rpm in 220 s. Through how many revolutions did it turn in tn19,re rz8yupek50 ov n8r u9vhis time?    $rev$

  An automobile engine slows d:lk0afr vpr* 1own 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 highspeed jets in a whirling “hu:hd s(;v,p9tb fcz1r3 xsksn* o(sce0man centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reacss((o0x*szk:f d hnp3 ; csb9c1etr,v hing 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 fri j:hq-q)b .vg-:mbg jogm8*aom 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveledgva*mq.bb)m 8g - : g-hoi:jqj in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It sv)9+ y xd.inzturns 1500 revolutions before it comes + v)xzn9d.siy to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as thufeva gqp60w8.ny+q(fr 2c 2ye car reduces its speed uniformly from 95km/h toy2 6v2qcaqgrf (0+yw8 fen.pu 45km/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

  The tires of a car make 65 revoluti u)t8z,dyezu+ons as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diamuz 8uye+t), dzeter 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 when clirx hxkk5-jg; -4jd )wqmbing a hill. The pedalsw kg-;jd-xkjx4r) hq5 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 end oxj+jczrqu 5-nb4f+7v ;vin-t f a door 74 cm wide. What is the magnitude of the torque if the -v v7xcbftijju; n4nq+z+-5r 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. Ass*hdp.co.v )p:cu+kguqdp2d .u 1k f)q ume that a friction torqhq c+ c )vp.dkou.)1fqk : pu*u.2dgdpue of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached bs b1h9r*fw;d 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 rel s;9f1hwbdb r*eased. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of0ng md 5el07mnqh s)cf)zkw.cp) vt75 an engine require tightening to a torque of 38hqk ts.0dn g0 zc c 7nf))mpel55)7wvm $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 1kpkw 7tp:p)e10.8-kg sphere of radius 0.648 m when the axispk1 pktwep7): of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment fi9,cn6b mir1 7k zm:hof inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a comiri19kn:fc7,hm 6 b mzbined mass 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, lighttn 98oj0y0mj,n;kr82eh k dkbb+y:q u rod is rotated in a horizontal circle of radi jkyn 9j 2y0ber8kkutnh+ d0q ,m;ob:8us 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 s8brc;o ray- s4peed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N ryrs8o bc; a4-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 ixij+msa 6;1 uknertia of the array of point objects shown in Fig. 8–43 abouj6+kx 1smia;u t
(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 oxyg:uo xd/ +ej:zqen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinningw*7 y(l. o6q kgtw.lzg at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3k*w(qgyl.z.w 7g ol6t 600 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. )wt(2xrcqn,rg3 f r zqt0t,g750 cm and a mass of 0.580 ngc,3rq 0(trz,rtt7 wf2x)qgkg. 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 6)v0e, r ,ln cjxnj :+ixczbk5bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven me3/v .aydwj:ts rry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume thw/s3v d:y ta.je 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 rotating at 10,300 rpm is shut off and is eventualfpl2ym l 9r2:le58g2i( miw rvly brought uniformly to rest by a frictional torque of 1.2 m5iepgl: r 2r l8(vfy2iwlm2 9$m \cdot N$ 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 ;y aeh t:2mw5o,kv3;ajxek.qa 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the ; h6) mn*bvn/ph )xzjhaction of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. b)jnhn / xz mhvph);6*8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in Fig. 8;z 7palz4ne8qeie k88–46. kip88lez7n ezaqe;4 8
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two mas:u sth npjj*-2vsef 57/1mqisses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest 7 b-(6pyfdpal within four full turns (revolutions) and releases it at a speed of 28p(-fby67lp d a $m/s$ 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 m q)s:heilkx/04zj92 icmw 0myoment 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 t5 e.z/bibwaw8 orque 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 and radius 9.0 ctd 78px/ ze+mv pa,g;nm rolls without slipping down a landex ;z m,8 /antgp+7vpe at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth withr,wm8e0 v tyxywp9g- s 4n/gv0 respect to the Sun as the sum of two term mg0tw/yvv9ns, px er84-w0ygs,
(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 much net woqw9rccd1hhtjj yx.w+f1 78k +rk is required to accelerate xhd9h+8w r1 f+t jk71 wyjc.cqit from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 3yir; 7f0pdtp4 cco aeyfb0 ixuf;.;; 1.80 kg starts from rest and rolls without slipping down.0t;ppo ;yff;;cfe 4 xricyu0 di7ba3 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 its tip. It star oj(i2 doxw 7rlvx5tjug1/5f +ts to fall and its lower end does not sli(x/1 i5fv rjtj ol2uwx+g 7od5p. 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 momentumqkioy7j 0;6js5q7i fs of a 0.210-kg ball rotating on the end of a thin string in a circ sjo70f 6ji7i qsk5y;qle 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 cylin)o :2ral ag o4ft/94 /xwt7wtzdrj l+tdrical grinding wheel of radius 18 cm whenttd a92t7/r4wo rt /gxllow)fja4z :+ 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 atigw tl 2ff-vp* 7dq(h) his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a h7(*vpw-q digh)f t2lforizontal 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 o6rc9 rpu4wa4df inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0wcu4r6 ardp4 9 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 rotaq1wiak8 zuzy -lafrl qc;8xe4* t);h5tion rate from an initial rate of 1.0 rev every 2.0 s to a fikl4*c) zial r-1x tqu8 yzhfw;aq5 e;8nal rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center at aa b+c t;nu0.k*m tbh+-g;pb jw frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, ojm 0+;*tbgh+nu;wpkt bc-. ab nto 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 skefw. ,p0g,oj /3 nct/6qqkstwi2x*bpater 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 they/ ad1d.dinf)4wc0mc 5xoez, 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 1r ki+umiu 2xlgsivq30b6 g)-identical disk rotating at angular spe sg)ugik-mi2xi 1lu0r3+ bvq6ed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsq4d 89*yx +ygjigimma gzlyw9 /:v+5 o at 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 fts- ok* -cc3 .ayps3ka rotating merry-go-round platform of radius 3.0 m and moment of inertkfc3t*op . kcs ay3--sia 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 with an angular ve7 m84jwa,go(o7:jwr t d)n jtglocity of 0. j w d7jo7 mg4ta(tj8r,n:g)ow8 $rad/s$ 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,4dbkyc:mzi *5 60ii7wkj la2v losing about half its mass in the process, and winding up with a radius 1.0% o5b 0a ljc2:k *wmziiid67kyv4f 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 excesn3 9ml0l.l1op4)cpzoj twa9os 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 rkdy26oa 50-wyqlj:f ra9e (h$ 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, init1yb o63uen p8tially at rest, that can rotate freely without friction.t 6n1oybup83e The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-round tunhc)ys++ (ycmr tor+(rntable that is mounted on frictionless bearings and has a moment of (+hrm nryy+o+cs t) c(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 on thlc cx 0u+0wrc0bt15e9xo8 (xe 5e8se byxbj8f e 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 thue xt0fr 58 8xeb5eys8le(wcxxb+c0109bc oje spool’s center of mass move?

  The Moon orbits the Earth such that the same side always nnc;w2y uju tch 19rsff/ (rlj b5cu0s ,y-2i+faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter0/rfyb,n(;+25c hjtuful- i 9uy r 2ws1cnjcs case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate n*z dnssi5 c;c0)nt p7qs.. swof 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 of5vxo h:nrr-f :p vmi34 a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate vr:4m if: -ovpx35n hrthe torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindric:; elav3qqid-om yswh o)o14/al disks, each of mass 0.050 kg and dioi a4 qvyl;o:qs-em)/h3wod 1 ameter 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 rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wheelwzp, k:w5 ykh; ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, w7s xw e:(6r:b*ng;yomc-ws fkere rotating at a speed of 1.0 revolution every*nmr( b6wg soe-ws7: y c;fx:k 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to ls (b9 j/0hjjause 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 salb/j sjh9j0( hould 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 illustrate a/klz5s.u b(is 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 on a horizontal surface at speed 6spz2mig;un 9;t, eo fv=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 lengthrno r 0(/v9c +6zzt.yrjtvr9o 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 t909+toryr. z nrz( vcv jo/r6that 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 hasdb;gg hym5kh;3vhq- - radius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that ig;v5qy 3dhgb-mh;h- k t 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 ojzhj+9 sjl2t+n a flat road is making a turn with a radius The forces acting on the cyclist alhs +zjj+92 jtnd 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 lengt4ni0 g. j gokx)t3i,nhh 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accohgg0 t nk)i3in4 x,j.elerating 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 cylin kp/z.obew:6 wder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with ar k:po./b6ewzw ms held tightly against her body.   

  You are designing a clutch assembly which consists ocpkctvu1 5 zct)5,ya;f two cylindrical plates, of m5kc c zyv;ac)15ut,tp ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough ,5:figq:h.jw eraw2)hol 9gh track of Fig. 8–58. What is the minimum vaio.wh h: qrg9wl2ag)f 5:jh,elue of the vertical 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 not asungp0okv pi-s)6fq+evz2 2u5sume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed xpnk1nm t+5hwf kup+; h,.le-uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of +h+nxhepwmn -kk;f.1p ,5ulteach 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