A bicycle odometer (which measures distance traveled) is attached neard)0)rxdhh v5js6:6 1eucru ws the wheel hub and is designed for 27-inch wheels. What happens ijrdhh16: udxvu)crss)605w e f you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a pointfnjvm* 4r 6b)+xy* 9tg pryom-:s;kcu on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component og6r+)mop:*rxk f y-bscv9u*4 n; myjtf linear acceleration change?

Could a nonrigid body be describ1kzd d(-y;fd xed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than abm)f q 381dvof.w b-ii8 :ffgpaf.0wh 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 withua.t n8 kyvg*4 your hands behind your head than when your arms are stretchev ygn8k.*a t4ud out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and thg, t.2xnl0-z- r3 8mm(wq8yymh3wnrx p (autzree at the pedal cranks. In which gear is it harder to pedal, ah8ytlxm-q zmy,rw t(g.(r0 pwn3nu3z2mx -8a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to runbam4 2v j;rq84a9com n fast have slender lower legs with flesh and muscle concentrated high, close to4 aa9qmjm;r82 noc4bv the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Figpcxp+oti8m (l ,tf 5dhk4x k fpcf*74,. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? 2dshjtm 3-:qwIf the net torq-:t qd2 mhjsw3ue on a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the horidq9yt:x ezfb ,9 f9d;ozontal. The same steel ball is rolled down ey f9,d qe9txb9zf ;d:oach incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres sim k zk)d4,+ecepultaneously start 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 greater kp4d,e +ce kz)total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They staryn(6ptmth gu 9qg(:g;t from rest at the top of an incline. Which reaches the bottom mygt: (6qgh9(n;tg p ufirst? 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 momeu 3s): /z )asb;vahe2gb nb)ynntum are conserved. Yet most moving or rotating objects eventually slow down and stop. Explainu ):3b /h svbbans ;gzney))a2.

If there were a great migration of people toward the Earc 20yx4e nq+l.qffu3 dth’s equator, how would this affect ly.xeqd 3nff u2+0 cq4the length of the day?

Can the diver of Fig. 8–29 do a somersault without ha5f;0nun(9tg9p yga msving any initial rotation when she leaves the b;g g9nptm9 0sy(5uafn oard?

The moment of inertia of a rotating solid disk abouthn0yyw8 x4i -s an axis through its center of m sih wn8xyy04-ass 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 av9:fpch i8oiu w:k.o-0fvd,w 2-kg mass in each outstretched handi-o08 9 :wcof .kwvip:u,dfhv. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have t2 ftl:qrsn 3x ,sqa91okhckw, xo8c-4he same mass. However, one is hollow and the other is solid. Describe an experiment to determine whlas83t h,q9 2wxxcq ,4 kcn:okfr-1 soich is which.

The angular velocity of a wheel rotatina(,n1w ,u+vl/p evjeu puxb7h x.u9c+ g on a horizontal axle points west. In what directi 1,b7np/uel+xvja,euhxu9p v.wcu+( on 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 the edge of a large freely rotating turntab5a rj ykp;d/.gyw+ zn.le. What happens if you walk toward the c; zg/j a.yn5y.rpkd+ wenter?

A shortstop may leap into the air to catch a balc ,gc1z l(yi5/di0 rtll and throw it quickly. As he throws the ball, the upper part of his bgirc (zlytd,1/0 5cil ody rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of cqs43c,9 w/r(eslh dqronservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller cd3/(er qh s,l94qrw csan operate to keep the helicopter stable.

  Express the followingz u5v4ilv;c 3g angles 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 because of an amazing coincidence. Calculate, usinx 0 azh5lf 121auen, 9rysnp5jg the information inside the Front Cover, the angu ,5e u90 h2lf1nzayajp51 snxrlar 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, 380,000 km from Ear z8f+,rgcmn: ith. The beam diverges at an angle rm i8 :z+ngfc,$\theta$ (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 motor0ks).spx q- / w(qhgbg is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down? pk bq./(xwgh0-qs s)g    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to xk+ jg1qddkj.go 6r 8)xwp(-p another child. If the ball makes 15.0 revolutions, what i gp6 j w(1x8d-d +orgj)q.kxkps its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How manykcu ..a bqi ,(+pjj+ ceaahh+( revolutions do the wheels mak+ ,((aubk.p i+jqehcaja h.c+e?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calr8)-gx hyhbn *culate its angularhb)n8r*-x ghy 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 (Fig. 8–31kmv2cf(yy *;l0rms b,xc+ze8). (a) What is the linear speed of a child0bvcl2c*rx+ky f,myz1 (m; se 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 q/eu 8kp j xg-(v0z2ivvelocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spee .mey* 8mmofca8:oljjw.t .;u 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 cm from thd*zk;snw -df4e axis of rotation is to experience an acceleration of 100 d-wzn d4k*s;f,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel a1/x(l4f z2;zcj.t tjt ewvfyx3l53t cccelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 23l1 ccyttf; z4t e/f.jz (x vwxt3j5ls. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius m :7 tqz.ygss:atjf/g o9/ gp4$R_1$ 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 v:h*.vr+ -a;xlg2phygi /mj y Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy a yvjg2 *vhh+x/: g-pmi;y.lrevenly. 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 unifor, 4ul s(y/rgdmo h2v/jmly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this time?/ mgrh/,42l(dvu ys oj    $rev$

  An automobile engine slows dow+k;y)m 3lq /d1wrgvjd ,nigc b jhk(0;n 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 whi8*6 rtit 4,be,nh dp8z 6jhrolrling “human centrifuge,” which takes 1.0 min to turn thro8,8tnl46z rbhpe jor h,6tdi *ugh 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 un f6p/e3rv(l ,9lr elgo zt)zr.iformly from 240 rpm to 360 rpm in 6.5 s. Ho l.f/r(rt rzz),9le63eol vg pw far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running a x sb7qg5c8mfw2)gc i-t 850rev/min It turns 1500 revolutioig2 xgb- 8swc 5)c7mqfns before 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 revolutions as the car reduces its speed uniformly froy u -v7;b.j.nzdny*.dk1 qws om 95km/h to 45kmzkb .j;qnnu-wyd.dv7*1so.y/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 redu0ej.utb 0+hgoces its speed uniformly fro0u j+oe ht0g.bm 95km/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

  A 55-kg person riding a bike puts all her weight on each pedal when climbing.xlsowl-: /rr j7cc.n a hill. The pedals rotate in a circle of radiuxr cs7o nr-.c: lw./jls 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 o/b fex,hvun3: n the end of a door 74 cm wide. What is the magnitude of the torque if the force is exfbex/ :vh, 3unerted
(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–tb.e4d io2 ;uv,xdcr* ,p2czw8 ,o fmo39. Assume that*ew pbf ,cdcr oi24zvt 2duo,.ox,8m; a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends y8+ul*b 1a+sta0qa ciof 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 s0acui y1++q tal8b* amagnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a to szv3yy/d+4cbh tdhr11 sm581tushh* rque of 38 y cu5vhz1 dhhh*s8s1td/m+ 34r1 ytbs $m \cdot N$ 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 7. 6heanij3xh et(:o;vh(ye a..iguxd,yw a: of radius 0.648 m when the axis of rotation is through its cyv i x 73d.:w(n6;eaja ae:,e hhth..oyi (guxenter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The ria7(d 6rj .thp3d6wm dqm and tire have a combined mass of 1.25p6mrj (d.q a67dh3d tw kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is r a z/i.f,uf*lxid:db 1otated in a horizontal circi.ffuz d1:*/ixlb ,da le 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; /zpr jc2mv3a wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and t3/r;v2zmjc a phe 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 t)j+e;ni, 3l6d h dapjnhe array of point objects shown in Fig. 8–43 aboujj+n i,ae n;h36dp)dl 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 oxygenvj5t o yn 4u6y6vuvq+5muhopw06 n; a1 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 spinningw2bffin/8;9iqzxk;heu,p8 g xqx -i5sp)o)p at 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 force of e5-h;qbqsfpzx8;x)/n98 iioiup k gp 2f)w xe,ach rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 0.xs/ 983p :o.orte5dd8vvxj zc580 kg. Calculatev . dtjzpoc so9/rdv8:x3e85 x
(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, acce 9q3s8l 2xfha(hm/jmv lerating 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 merry-go-round afm3r szu 4k+v/;oraprdc x.;* 18cda-aw v3zand 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 othera; ar urz+wxz.vcdac/-3o;f*4mas p8 k d31vr 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 shjjs ;8q/vv0 gs r:fjd(ut off and is eventually brought uniformly to re0jvs/ qvg(f j;:s8rjdst by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accm4q,6 7qxie22k 9qwifxzl z7qelerates 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 actiz sdc7c,yy4+ h4o qf4hon of the forearm, which rotates about the elbow joint under the actio 74chz,y+ 4hosdy fqc4n 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 shown:/f4j2u lwvczpv*nq 9 in Fig. 8–4lv/q wjvp:u42c*f 9zn 6.
(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 obc 41, ewx(fhsf 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 swu9m .tc .yb6within four full turns (revolutions) and releastc.9 bw u6.symes it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of3 j*vi2h9dlloe0col 1 inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 2e(znuee,e-l9 6 qxdr480 $m \cdot N$ 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 la .cqcfme77x0et l o8:vf0 5hctne at 3m :eqv ht70xc07 fc8.c elfo5t.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with re0p/byy u d-nj,.xtleog :50xqqmdw 9 4spect to the Sun as the sum of two ter /y- p ddte.o 095mq,ybj:w4xgl qn0uxms,
(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 v98f cp+;ls rw8nj*kva radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it 9r+fvj;8 klv 8*pcwnsis a solid cylinder.    J

  A sphere of radius 20.0 cm and masi-fg 65pcykj2 o0tlb. s 1.80 kg starts from rest and rolls without slipping dowck 60j-gpi .y5otlf b2n 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 i7epv 1rk52ob5xkb y/m uqs.5kts tip. It starts to fall and its u or 5pes1kkx /v2yb5.bk5qm7lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating -e(vgahc* l*fk; h5ug l18hw pon the end of a thin string in a circle of radius 1.10 m at an angular spekh;c -g l8 lhfuh*p a5ewg*1v(ed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angularz4u.g tj..rg f,vt9wc momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating atgc. wt9ft ,4vz.ujr.g 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a rat.c7o.mbz9b: / ge -kmv ouw4 wkwkk(-ke of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–49(okebm-. 7kkwwwmu/-c k bk4.go :vz8, 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 reduce8ns 4t7rqj1 wy her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If shents yj4w71r q8 makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an init)h: m;ib ku5swro/: jg07b 7rwiwz/ps ial rate of 1.0 rev every 2.0 s to a final r/hruz:r/5:p) jgsb70 b k7mwwsiw;o iate 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 ueyz/8w - (dgtkq3bs1its 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(g qey-wsd13bk utz8/ wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a fi 9hj lwt.8w9v7olptv/ gure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Ea9t/d8v .lfj qtrth
(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 cylindricalg yjl1pvi.vqle9:r 4tks3i3( disk of moment of inertia I is dropped onto an identical disk rotating at angula:g4 s31l.vpi ( ekvyjilrqt9 3r speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atok;hw2m *db 8t 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 centerxa.wdw ,qw /i5 of a rotating merry-go-round platform of radius 3.0 m and moment of inertiadwq. aw/w ,x5i 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 velocity 6+msu et14el l*-2jvw ie+ vhhof 0.8 16hs iwe+ehjvl mt-vel2u4 +*$rad/s$ 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, losing about f(o u)/ .x1oxpkut lev8si 9g8half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming thxu9)/xo lv(if8.gsp o 18e utke lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess n )xd/(*( ujay7ijcfdko 60qaof 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 -/q mfol4.l nw$ 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, in1 voepkw7t /bd :ruxfw vc896be 2n5)ditially at rest, that can rotate freely without friction. The moment of inertiot8n 7bu 69xd 2kvcv5we)fp1be/rd:wa 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 s7v4mu bf(r i6hn;n-bvtands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted (4br vv-nbum7 fn6hi ;on frictionless bearings and has a moment of 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 t+guvh 65ne2poyojq 6,he ground with the end of the rope lying on the top edge of the spool. A person ojopuv,6 +eqygh56n2 grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Eartha o4t e x8sm; 7q-5(sw(qhzk qph)6p zll(uqk; such that the same side always faces the Earth. Determine the ratio of h4qxksl 6q5 -k; t qplo;w8p(u (h7zq(em)sazthe Moon’s spin angular momentum (about its own axis) 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 of 1 ho9l2 .r)mquz .t 5nkgm/$s^2$ 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 0.20 m 8 75gn)sv6i k amsr+hiacquires a rotational rate of from rest over a 6.6ikn hvm8s+7i s)rg5a0-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 crq6en0*v7x b disks, each of mass 0.050 kg and diameter 0.0q6*e7 xbr nvc075 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 tle2*8ffrcgoq -)i+ y-o. fbox he angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 iu5b2)hj e/uj0u kz*mtimes as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries offku)z2u5j h u*j me/ib0 no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energf t*jryt (z+ :;5ahabsle/vkq +0i bw8y stored in a heavy rotating flywheel. Suppose such a car has a total mass of 14bq(a/zl sk5yteiwvaf 0+br* +t:; hj 800 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 al:j2uqb g v rn; afo6ox86x+b3n $H_2O$ 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 speep ;u:mo l*g/mgd 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 fricti/cr(;up-dnzvl j 0z;,hnq 8bhon) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mas n0d8 h, hjb c;qlpv(-;/uzrzns of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is kl np8uhxmr.jhlupq: 98,6 t+standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step agaiumll n hp9+u 88k,rx :t.p6hjqnst which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed /5p h/quc/m*ypfps g( v=4.2m/s on a flat road is making a turn with a radius The forces act (p5/ppyc*/h usmfg q/ing on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.5 g77w v 1di -jg ;zkr(ux0qb:;eyrfpb(0-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 i077ufv ge;y;r x(z bgb-j1pk: dr q(ws. 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 solidi+ykt;u9 . t9ko mucz* cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calcuk;m u*+o.9k czitt9 uylate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which qolvwd:*g nv,5nhw6: consists of two cylindrical plates, of mnl hdvo nw 6w*5gq:,:vass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 track of Fig. 8–5;lq 6pwehl pi +ia4cc i8-+y+owli7a78. 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 without leaving the track? Assumeli-a8il+7hy 7ialp6c+qiw+ 4w eocp; $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not anyqc) oule. ceq8wi0 9v:qsx . 2g:+lessume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutig urmk0p 8t81sons as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) 8 t0u8 sr1kgmpWhat was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s