A bicycle odometer (which measures distancel5x mmlqom./)/i9 xkl traveled) is attached near the wheel hub and is dl5lx.mox /i9mlmq /)kesigned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular v7h6 8udwlsm g7elocity. 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 ad7wg6 l 7su8mhcceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be -c ):.z cv;fmtpe2t kudescribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a ldmh6j(49rd w8vj 5 tthb z9f+barger 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 youd7bq )tna-2 bzr head than when your arms are stretched out in frd)7n-2t bqazbont of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pedncoh kg 81ecj:,2 aqe(al 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, a small front sprocket or a large frongaj(ckh82oe: ,e c1qnt sprocket? Why?

Mammals that depend on being able to run fast hav m8mah c)d9uyh3upk:b/ -p7 tke slender lower legs with flesh and muscleph9yb m 8pauh3k-)/k m7du: tc concentrated 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) carry a long,sq0)b: yigj+an h0wh t*a+q9p narrow beam?

If the net force on a system is z 7*dt x7s 4tfftlb3h:fero, is the net torque also zero? If the net torque on a system is zero, is the net force zer:tthf37f 4tx b7fs *ldo?

Two inclines have the same height but make different anglepu3nq8kz2(l m nd* dg9sbi2;x3 a;eaxs with the horizontal. The same steel ball is rolled down each incline. On which incline will th xl3;92g*im z;q(dx3a 8 kad n2nbpeuse speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down a /./b ,)4 /3k3xlx jr,eepywuyxhdx)5 mnohbjn incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? hbh j x3joyx,4/e)b nxdmep)3/ ,./lyx uk5w rWhich 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 t8z**az fk3mip+cruk1w -g h.a7/e qwshe same mass. They start from rest at the top of an i8.3srg7kw p- kczq1 */+aai*zmuf whencline. 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?

We claim that momentum and angular mocfpq69+ba7u+m1 qz0rorn e1j mentum are conserved. Yet most moving or rotating objects eventually slow down and s+f9 czo0 a 6pje b7mqu11+rnqrtop. Explain.

If there were a great migration of people toward the Earth’s equator, how woulaom +ni74t1o vd this affect thm 7 no4io+1vate length of the day?

Can the diver of Fig. 8–29 do a s1aw9n i8+kqwhu ,k,fsomersault without having any initial rotation when she leav,s8u +9, iqwkk1hfan wes the board?

The moment of inertia of a n0u pp7 srvj )l7tng1;22pj1cy22*ck dbqjj arotating solid disk about an axis through its center of m; n2nvrjck*7)j227ypq 0pjg1aljd 1s ptbuc 2ass 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 sittin/wmgyx:.5og eg on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease,mw .eygg/:ox5 or stay the same? Explain.

Two spheres look identical and have the mo2q:*e 8v aipy uz7y. f0m2xgcnx(y1 same mass. However, one is hollow and the other is solid.uain0 qvy1.x: my*2 2 cpz m7x(eoygf8 Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle po v remgf9pg+(3ints 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 tangential linear acceleration of this point at the top of the wheel.er3mf+p (g 9gv Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rota :qs9ff 2)(znseks)j pw-0o)8db ud2 jwaahq3ting turntable. What happens if you walk toward qs :db0dsp2ju9jah zwk n f a2()8 3)ow)s-eqfthe center?

A shortstop may leap into the air to catch a ball and throw it quickly. As yja kp.k.54vm6 : lxwahe throws the ball, the upper part of his body rotates. If you look quickly a. v l6k4axw5j:mkp.yyou will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular mk() ( bqruuj5,x 4znokomentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can unz(ro)kk,q5bu(j x4 operate to keep the helicopter stable.

  Express the following angles ismxl0 602suh tn 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 Eary*ns ,) sz2.fi/rrdhq th because of an amazing coincidence. Calculate, using the information inside thez)ds.r/irs ,qf2 h*ny 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 the Moon,(l3 6,lzjmjrk8a y lde3ee ,*o 380,000 km from Earth. The beam diverges at (o3y3l ,ee*a8jzrdj 6m elk,lan 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 a rate of 6500 rpm. When the motor i2ni /7ipcea 41ysw (w1w+l bmol t ms)b8h,y.es turned off during operation, the blades slow to rest in 3.0 s. What is the angular acciybls./m sh17 w)ot+mp ae8cylwn,( 12 w4 iebeleration 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 e,te5; t/t/liv:e p huball makes 1evt:/hpt;i l5/ eut,e5.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revoluryj: +-ph 5f*1kf1 sh d,op 6un8xmknluxs9 )wtions do the wheels maken96hfoyux* k1 n8ur:,kx1)sdm-p+ pwfhj 5sl?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate o4vb(l(9 hyu:r-mjv rits angularjv4mr u9rh - ob(ly(v: 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 innf5n 2tnc .z;r 4.0 s (Fig. 8–38). (a) What is the nr zcnt2f;5n.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 orbit azkogd2+ ug( :hround the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a pofix/n0/u:sg+up w 7o )a;tau 2 oq/jpsint
(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 if a particle 7.0 cm from l k 8nrcr1+kq6the axis of rotation is to experienckqlc+ 8k16rr ne an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its cz(pw.wh+x38mio)r qsenter from 130 rpm to 280 rpm in 4.0 s. Determ(.hp8siw) mz x3+r qowine
(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 radiuseo/g, : snh)xb $R_1$ 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 Apolf 1 a;v i;gjjhi;r;kd5lo spacecraft put themselves into ak5if;v; j;h;1j idrg 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. 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. Tho/t(iv5ibm +prough how many revolutions did it t(p5 oivmb+ t/iurn in this time?    $rev$

  An automobile engine slows down fromchio gu)8 s1pe 8n6qg)sxs)p: 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 wv0kl9 owisz,+6p2v1;ib tdy+oij y )ihirling “human centrifuge,” which takes 1.0 min to turn thrvdj+l)b1o6o,t2k + pi i;iz9ysy0i wvough 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm m54aah1a.g)o4 v/9dgvz xediin 6.5 s. How far will a point on the edge of the wheel have traveled in this tim ox dhaag/ei )vm1azd4vg.594e?    m

  A cooling fan is turned off when it is running at 850rev/,d9i7 8 qh-.7 7)wxuiqnomtdx ywao3imin It turns 1500 revolutions before9yt x und.aq7-7ow7 dwq)ix,m8 ihoi3 it comes 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 re( 5yjsmzd 0xk: (cke6 gjbo4t a/cd)z5volutions as the car reduces its speed uniformly from 95km/bjck dgdmo:j54ace)6 yz (t5k0/(zsx h to 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 revolutions as the car reduces itj fq-x* okk;a+s speed uniformly from 95km/h to 45km/h The tires ha;kk+a*ojxq -f ve a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each peda/d tzzd 6okcn1;)ct7sn 3/j bql when climbing a hill. The pedals rotatd3/ ; tq)nkn o/ct61jczs bdz7e 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 of a door 74 cm wide.g2*gdhils 6:oi87gga .dm:my What is the magnitude of the torque if the force is exertgg galgdh.i dyi8o6 27m *::msed
(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 k*dcf51ok db)about the axle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0.41c*)kb5dk d of $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the .l zifcc1l5 3cends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net t1c fl. li5cc3zorque on this system.

  The bolts on the cylinder head of an engine require tightenid,bd. x yr34rv /z9e)gf p8jhdng to a torque of 38 v.dbz4hdy ,x3d/err9) g 8jfp $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of ra qlovfbv2pl t*m8,m5.dius 0.648 m when the axis of rotation is through its center. t . bmpm25l8oqv,*vfl    $kg \cdot m^2$

  Calculate the moment of inertia of a 458;*pod nrp a p )bw.b*px72iqrjhaj bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of ;*p5i4 87wbrara*b. dpnqoxp j p2)jh1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball ,:g vml gjrz.flv rgpb9m,k6yysf3x :;lv 7:0 on the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculaz3.brlms rgf0g76px9,vg vvy:lkmj : y,:l; fte
(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 potteoc( v,( nn6ebg9jfce0 r’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between h c jv9f0n 6geceon(b,(er hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fig. 8–43k2 v0+c yen /zoa-s)fed5ibv.f2z8oi,a ;zmc about bo.02zniioea m )8dv+k,c;a5 fz vf2c yzes/-
(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 oxydm,krgob9*w ) gen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the corre4ibw1. -mh, kb aqpsf:a7,rw nfd- z2rct rate, engineers fire four tangential rockets as sp7:mwf1wi2qs,4rbz af ad,n.b- -k hr hown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady 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 uniformzii) 3danf 26*u 3rhfy cylinder with a radius of 8.50 cm and a mass of 0.580d) 2un3f yz*3iifh 6ar kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest v/4*c v+sq g 22qqsmadto 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 merry-go-ro11hbi+bjs;:juwk8r1v4we6 idfz 9h myaf ) j7 und 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) ;f +h 6hdw41uia jye8f7s 1 1jbvkwb)zr9ji:msit 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 evoxvv( dd *pz0(entually brought uniformly to rest by a frictional torque o(*(dopv0dvz x f 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 accelerateso xi6vxwt d 7)0gsiu-1 a 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 act*5ful:b iv k/zu7)pgq ion of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The bavfq:kp*/iu7z ) gub5lll 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. luhi6p ;:+,mpoxk w ;d8–46.k6x,pl:u+owi;m h dp;
(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 cf b4sz15gtt 8oonsists 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 dx0+qfxv+cz o; +-bhv from rest within four full turns (revolutions) and relxx fhzo;+dvc-0 v +qb+eases 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 al*iznr6 rlgv(l 6- cb- moment 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 tov 2eerzbh8 e--rque 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 cm rolls without slipping down a *p8 ;jfzck:rolanj;fp* :r8ok cze at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic eny *qtbvo28- tbergy of the Earth with respect to the Sun as the sum of two t t-b*yo bvqt28erms,
(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 rad-p v6d 4j htdkmb; ng7m(b8:ayius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rated6vmjp8ygdab;(:4h7ntm - b k of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from re-doi u :*cz3,:h tmtuest and rolls without slipping,: t-:mceuhutoi3 d*z down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balaf o+q iat8znz *c+j.w*nced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation 8zn fzc* i+towqj+a* .of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball roto8fp, ulgig2d1+hl; pating on the end of a thin string inhl;1ug do8 ,2p+pl fig a circle 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;g0yf 9 wx,,tnz0wo)wxor-mi 2.8-kg uniform cylindrical grinding wheel of radi;nmw0w) ft ow-,9iog0xyxr,z us 18 cm 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 h2 3t mbak67zf2cpr *)u9vrnutis side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontalzfu t72c3mn ruv629t a* )bpkr 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 4lgeag,f6n szzqz165r u m7p1her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations 5 gnzzz1e,6 sufr7lgm1pq46ain 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate ocbi s4ikz 5)m6f 1.0 rev every 2.0 s to ai b )6iczs45km 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 around)eif74- vxz0rc5i-7wft kahm a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 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 t7k74fcrvx-5mw e -iazfi)h0 to it?    $rev/s$

  (a) What is the angular momentu/5z1( ml.wl o emp0kqdm 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 td .flnsz:dv 4 ;y,1b n6vqgm5lhe 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 +et ce7f)cc* nx2oxq:inertia I is dropped onto an identical disk rotatix f+c *x7qce e:notc2)ng at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a dsd;+eak 0 oahmh1ob-39 ;tf2o0tzhgt 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-q9a5/ bvgl+5tudj w n3round platform of radius 3.0 m and moment of inn/b5j9 v 5+d3lqwtugaertia 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 0 k) f i;y)rdvl7i+mfb giflw o5d3:s+with an angular velocity of 0.8l m70dg )yvl 3o)ridff; ki+s+5biw:f $rad/s$ 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 collihz 9 o1 v imafym+(1213modklapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% o2zmy1v d 1lh+mi9 fkmo(o13a if 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 windscfpr.fx4k 3uy47- ls t n1t5zt 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 w8hi6hux6 3o;v +g9undl 1t ix$ 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,ggm0;- mye -zi zy*z:q,nga(w that can rotate freely without frictii *ag-y-gw(, z;zmz: 0gm qnyeon. 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 persoab/8a9 h)xq*alku ke5n stands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of ha9aue ab8k )xlqk/5 *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 v4poonvw45u 5 ,1 u ;mcyxeoa9rolls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walkamo94u u,xoo cv 51n5 v4pw;yes 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 sameg 3mgee9mew uu4:jka 8td)x2 k3y2+fv side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis ) kw:3mvdgf9+gxykt 8a3eje2eum2 u 4) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate owz bm+lu;0w+dj) )go g i0ou+l2lhn5k f 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 uniforma:j- xh55) n/myoi+ex 1:b*gdavf twn cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleratmvhn fbaxi /eygx o1+)*: dj5t-a:5wnion. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each2 ,*x 2hi 0f-+bqizaivirkd2s 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 as+2ih*fid0v,2 ib - i2kqzxrspeed 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 ol:nu3i0d8 2idjw dzt2tjf16e f 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 ofs be69b6bl9*bkm 2/ hfvuf 8qf our Sun, 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 kbm sk8b * 9ef/v6b96 qfbu2fhlm, 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 automl-pihotjwmfk1m8)29 6u gh 4s obile 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 diame8o1lpjski )2-m94 thh gmufw 6ter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustratei)(-+ghsqqwk+ 4tqavcq lx , 5s 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 horizontal4mn1ozl*vq et+zm+ /wmmt3 j u .d94z8t;z oti 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 zam pun)40 t7ywqx8(m length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod a (y7 qxwntzmm)0u4p8 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. 8–21g.]

A wheel of mass M has radius R. It is stan(ffiyvv9;vz 8ding vertically 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.y9; v8zv(fv if 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn with a7ue;n 9b5fhzmy3qhkx h 2*uu8 radius The forces acting on the cyclist and cyclkuu598u*ne mzx yh 3bq ;h2fh7e 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 mpw0 0dlg41gi msq3y y. and begins whirling the rock in a nearly horizontal circlep.ismyl10g w40d y3qg above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, mxi:mr fv4(ht ,aking reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with out:fit x,h4 v(mrstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which cons)hafntny+ j ,7cqu kr6y.bq+:/yvb5gists of two cylindrical plates, of masuqfa)kh+g6rt 5 /.n 7v:qyy c+jbnyb,s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 roukj.uzmt(j7 h5scp5z67 wmxu )gh track of Fig. 8–58. What ispc(mzmu7j5 w7szt5h6 xk .j)u the minimum value 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 notqf:0mxz x3xyc/q5k+3 zvi3 sl assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its sp s x t6fson1u.e3toz+ s)y-p-peed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acs)foxse.s-p 6oyt p+-t1 un z3celeration 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