A bicycle odometer (which measures disr 38ziemr zpj8):qu0etance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if youj 0iq r8zr)uz:3 eepm8 use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poou2 6 193r, w+pl g*qdlk2pcll qovxt/int on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of eit2l ptglvo ,r6okq +ul9/3dp2lq c*1xwher component of linear acceleration change?

Could a nonrigid body bamje4m615:0( e42fvmgfezhqhw8s-*ar x xe s e described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a gre )c:ko:4zd *zfffm u0jater 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 silom 6vndgg;,,6wm ;6i stwkr*t-up with your hands behind your head than when your arms are stretched out inm6g,gr ;l di,; ks o6tmvw6wn* front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and threr : 9psa,v 66r lc+rtfuex05bce at the pedal cranks. In which gear is it harder to pedal, a small r 0fre5x p:b asrc6vl,6 uc+t9rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender 3.3,x 2aipm+ je orjewlower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribut +omp3ajw3j,xe2 i e.rion of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow baupgzy+g0pk cd: 8-b 1eam?

If the net force on a system is zero, is t r:gtuirh -+rl d94k3ohe net torque also zero? If the net torque on a sysg4tk9ruh3r +:-lo r idtem is zero, is the net force zero?

Two inclines have the same height but make d u.i:z 5ktkgm+ifferent angles with the horizontal. The same steel ball is rolled down each incline. On which iuk+t:g5mzk. incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously sta/l d62eez4)s aj 2nnmfrt rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the great22e 4sa6fle /jdnm) nzer total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the sk*g9lln/j k:e ame mass. They start from rest at the top of an incline. Which reaches the jl9kl/e ng:*kbottom 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 momentum are conserved. Yet most moving bk l vzwn 7cfa,i35m27or rotating objects evenf v7 c5lka3zbm2nw ,i7tually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how.qrh byx vf2e3* y+*c 3zmchu c,zz6uhe-63bo would this affect the length of the 2*.ux ohy+he6 vbbzc cqf *33c 6zzmr3 he,-uyday?

Can the diver of Fig. 8–29 do a somersault wqi7( 0f z;be,tw kecg1ithout having any initial rotation when she leav7g1(zew q;tk0cifeb, es the board?

The moment of inertia of a rotating solid disk *7on avg hjzh)kk:6.htpv . x7about an axis through its center o ohx7)j *7:tkganhvh. .6 zvkpf 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 holding a 2-kg massiv5 m* sq4w:2ndp+gru.cwg;s in each outstretched hand. If you suddenly drop the masses, will your angu4;pg:5musc qs iv+gdw2r.w* nlar velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and rq 7k-1-hifpuoek- xbyoa+ 0:have the same mass. However, one is hollow and the other is solid. Describe an experimen-h bpe-k0rxooq1u y-:+f iak7 t to determine which is which.

The angular velocity of a wheel rotat pxa595b:5i/ubx)v wzoo6 ntming on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angul/anb9: o)x 5px oimuzbvwt556ar acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of ,3 zqsk( (x/;okch ugzf0 j0fja large freely rotating turntable. What happens if j zkf/ ,0(gk o0j;3zxhsuqfc( you walk toward the center?

A shortstop may leap into 9 ih+,:sfipy-p 6qf38 esb2d1t meshs 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,6 8eshs1:tisp39fh2m-pyf i+bqd se his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservatrpkt r 4xz1tv*k( +zb0 q28hwoion of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the se1wporzt(tz+h* 2 k4qkxvb08 rcond propeller can operate to keep the helicopter stable.

  Express the following angles in ra*s v-eh os7e:y9kglnc g49; whj7hwv+dians: (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 because of an amazing coincbk9 mhp /spk k7c(.qu0idence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen ocup 07 khp /k9mk(qsb.n Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam divep(t9i:s pag8mc-lh/r9c t k2+xws du 3rges at s/a phtpkcs-3:2xtugd9 rm w9(8+ ic 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 rotat7rn( -27gd.igi d xsvj( cap1re at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to r2ix.7(g(aids-dj7 g n1 rcvp rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to an kr*joqn0k, mj7akt+ ,z cpegg 18c1h*other child. If the ball makes jogqm8 ke1n01tc7*z+,kpa g*hrk, jc15.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions do c 1hzjj9 /s:kithe w zjk/1:ih c9jsheels make?    $rev$

  (a) A grinding wheel 0.35 m in d ywb2d.+f 7uctiameter rotates at 2500 rpm. Calculate its angular 2w+7uct d.yfbvelocity 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 (o*1hxn 4yp/a kFig. 8–38). (a) W*/o nka4hy 1pxhat 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 t suupew43k( mi;kztpc06+v +nhe Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speeasyo5c1*mlv 1kvn, t0 d 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 if a particle 7.0 +e,) 5 pvab7 l-mtt,du2vgiwqo rm 4l)cm from the axis of rota+t 5vltamd7ie4uvo-l ),m gbpw, 2r)qtion is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to 284w 30 gqt yrhbz(1ks5v2te9pj0 rpm in 4.0 s. Detewgj t1sphz4 t30q5kr 9vb(2 yermine
(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 nxzz(m8 6zdx;q)ff( a$R_1$ 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 abo3bjd; cl yk z m/6+v9fl)v+vkkard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minc6lvfvy+;3kv z/ mk+)jbk9ld ute 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 unifor 0:696pja opx hy )fpjz(26xfqfw n2aamly from rest to 15,000 rpm in 220 s. Through how ma j:6wo2a(ffhyn)6z 6x j a9pa2 0xfppqny revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculatjvimnd8s6 -:/nmyq9tyn2 l-7bow* b ee
(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 sto 3ie fw882lkdresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its finaoei3f 2wld8 k8l 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 accelerv(viq+ m3v ot /yzr o.g8df(c4ates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of to(v i q(czymrvt .g+of34d/8vhe wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turnqo98oaacbkpn6:zl ey4o7j;1sw5+j0r b de)ws 1500 revolutions before it comes to a st 4:jb w6n y9ko )qeb; pjc+zs87 eowoa1l05radop.
(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 revobf7m348g6,eccs v 4sn e u-wwxlutions as the car reduces its speed uniformly from 95km/,bms4 -3 x7e8fw 4sew cuvcg6nh 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 revol3k(:nw3v(rb v umee3nutions as the car reduces its speed uniformly from 95km/h tov (bru 3m( vw:3ekne3n 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

  A 55-kg person riding a bike puts all her weight on each pedal whenk2. 97sxa s;ukxu+cht climbing a hill. The pedals rotath;.xk+t u2x9 sau ksc7e 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 t*xhn7tkdgwqe *c + r.1he end of a door 74 cm wide. What is the magnitur1+.t gk*h ncx* w7edqde 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. A* eoj8xq,gbjciv4zo3e* .f/ tssume that a friction torque of 0.z oj*et ./f ,cxe*8jbio qg43v4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached *y6;e lvbcz;wpv x;)l5f7h xdto the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the r;;y65 fvlp7b ;)c l *zevhdxwxod 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 upvr,6mfs*, 0) ssrew require tightening to a torque of 38e,vf0s *,su6wr)rs p m $m \cdot N$ 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 radius j rp9d84kc2p 4 *:,,mokskzfr 3w haqf0.648 m when the axis of rotation is throk4qr a,chdw4spp m *f:z krk8,9 32ojfugh its center.    $kg \cdot m^2$

  Calculate the moment of inert oye ru4.xsr/2ia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can bees/ x.y2rr4 uo ignored (why?).    $kg \cdot m^2$

  A small 650-gram balr/vp2bro+l z 8l on the end of a thin, light rod is rotated in a horizontalvro pb r+/l28z circle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheelx(nbaz) .oz. 7 b5czo iytc8/u rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N total. /uz(o7bx oza.iny b .c8t5zc)
(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. g up9dt7jjh4mhkj2(2 8–43 ab 27jgtm2h9p jkh(ujd4 out
(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 oxyge f .oxc bcr;e 08)3u+kt:b6 bxl4xemlvn 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 /2 rbw)nr rjl,the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady br)jrln2wr ,/ 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 wi:7pni ap2()0alboor:cbi.h9 x jd0ty th a radius of 8.50 cm and a mass of 0.580 kg. Calculateo b.id(ht2p09 x )o :prlj cna07i:ayb
(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 tl(if p aj)t2deq17go3 8o0 eoeo 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 tav4a93 jby9 j6 or wb4nduk/jof5 yo4 gb/:h+swngentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each o:r3joyb6 944bv ahf ogw/usjkwndy4j +bo9/5ther 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 eventu8iic0p:o ma;cally brought uniformly to rest by a frictionalia m p8c;:ic0o torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accel jpa0u(e nsbuu (5cv5)erates 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 bal4.h,og( qncly it (f;dyk:) ual is thrown solely by the action of the forearm, which rotates about the elbow joint under the actiond. qh(agcf tu,o) l4i;k: n(yy of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as s+ d 7qf99fesjphown in Fig. 8–46.997fp sqe+jfd
(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 2+ui r pzscef kerx0pv v9x*.1ux 5f7,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 from rest within four full turns y4wqm5 lce4,gcz 5 (ia(revolutions) and releases it at a speed mlyi ceq544w ga(5, zcof 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 .54bdah p15ni:-hkwqi /utbd 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 devesrac7yh(7 0uvhipd2e,ja,) ,hawj8z03o wd q lops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 jou .q:phbt)(kg and radius 9.0 cm rolls without slipping down a lane at 3oh.q( p:utb )j.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to/nd3ccljjgh * :eob-gnl 7d*3 the Sun as the sum of two tjl n g3gchb jd 3/n:co*7*e-lderms,
(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 workfuwa:7is;e* v is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cyl;a: wi*sv7uefinder.    J

  A sphere of radius 20.0 cm and+19f mc ku7gu. xnaxcr 1,i)sc mass 1.80 kg starts from rest and rolls without slipping 1x c .fu), +7mgncakc x1urs9idown 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 vebjj( w ))bqv9hrtically 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 justjb)v9(jqb h) w before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of gp7 *dzkqx-,* h d1ocrxaq-l7a thin string in a circle of radius 1.10 m at an angular speed kh7,cdl o *dz7q1gaqpx-x* -r of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-6 u90 6kjnd5rebm,kzszx5,i m kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm? 9jzkk6i e5,un 6z0rmb,5 x mds    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his siysdd7+p 7pxm3ok 7p3 cde, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed y7d 3p+s pco3m77d xkpof 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 momkd9 (qz,g b8f6ppkh 4xent 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 in 1.5 s when in t p hg,(6qxd8zp k9bfk4he 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 ra,d .jw,su/+. odyzpd mte of 1.0 rev every 2.0 s to a final rate ,oyj d,m.z+psuwd/.d 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 a(od ,1*-q* fk gbnwgcjmy/ 6pg frequency of 1.5rev/s The wheel can be considered a u,/ym(djpg 1 bwngqc* -k gfo6*niform 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 to it?    $rev/s$

  (a) What is the angular momentut/3( qk2tw.tu.hb lqum 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 lob rb3nu.u 1 b5b3gy,z 7;vbemomentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$

(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto an identic i1c+ri;vz2a lal disl va1i2 +ricz;k rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2761wz5b crpsh .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 7qcq.1 p+d3u9mthij++ of u d1qrki)tat the center of a rotating merry-go-round platforjq3 fqr.1hod9+t71i ti uqku c+dmp+)m of radius 3.0 m and moment of inertia 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 angul vub5mj0 c**rtar velocity of 0uc*mt5*j b vr0.8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, lo.;h,p*qgr;yn:fe r ts .t9lsv2ja) h w72ilzmsing about half its mass in the process, and winding up with a r :pst 9.mwej;il.2yta f7lvg ;h,*rn)qs 2zhradius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds4 .m2adp x1mw. xughu/ 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 + (:fen3lvl uj$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freely witho eqlv q66l52rmut friction. The moment of inertia of vleq6r65m 2ql 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 7o yymu/jcg +2j3(ynm of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 1700 omymjgu3 /y(y+ j2c n7$kg \cdot m^2$ 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 roan rn f,zb..)d2/,q . wopxnyik6d9 aope lying on the top edge of the spool. A person gra6nofrinzo,b k a aw)q29.d p. nxy/,d.bs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the samjdwfgkn-57:6 + ukt gke side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In thk:gt kg+kw- d7f6u5nj e latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a 5ueybvxq je2* sf0a1:n fw 28nznfy3eo8. /ynrate 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 cylinder of radius cg+c805 jtodi3pwc8e 0.20 m acquires a djc8w o 3tic0gc5+e8p rotational rate of 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 massjchq1 9 yf;+co (po3kp 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end(h; op1 3jp cfkcqyo+9 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 angvw3xox/ zwd,k x x)0l ao*c*d0ular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with massx15q-pbln :(g +zq ing 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 + 1qbzp:gnlin- g(x5qstar 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 t +f v6x(vnb7r/8mviw 72 wdfeyo use energy stored in a heavy rotating flywheel. Suppose such a car has a tota2ef7wv6 7ixb +(/v f8 mdwvnryl mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an n)v6-kqoy6uc- lds j- $H_2O$ 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 rolj5zr(s3)v:e f57, nf yzzhqawling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore friction)42wspsf lfesz1ep07:z. -bt v3gk su 0 about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then .u 3s g1e2 ssp4:kzwf 7z0fls0-petvbreleased. 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 standing vertically on the flkp yoi+n0g:t,xpkm9/egu 4e (e :5qksoor, and we want to exert a horizontal force F at its axle so that it will climb a step against whichp,tq 5gnxs:9yg k omi/e ke pek4:0u+( it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn wi2k-:wwbgg,o9 (ps./fsu so 89uyv edyth a radius The forces acting on the cyclist and cycle are the normal fos9 -y bwufv(gk,p.w 8 2:sdoso9e/ygurce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 slinpxo*fzji 1+*on i *j(dg of length 1.5 m and begins whirling the rock in a nearly horizontal cid*ix(jifoj 1o*p+nz * rcle 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, makin pa n1i2ir4y xo)4ew8ng reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly r)p iny8i124wao4xe nagainst her body.   

  You are designing a clutch assembly which consists o ozk;k 5pit17vf two cylindrical plates, of mast ; ov75z1pikks $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 qmxl tw:,,- nzm w:p(yalong the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop wit w,x z(m:ny,ptl-w:m qhout leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but87u ,ttd qq/sv do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces ikodp,z . c)ob)ic k s8oy7ak65r6* ngsts speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire?*k, c6kz)i7 6 sks8) aydocg.p5bonro $\approx$    $rad/s^2$(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