A bicycle odometer (which 9zus-rz /nwh*measures distance traveled) is attached near the wheel hub and is designed for 27-inch wsr-nuw*zz 9h/ heels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant k-0u7kkcf n k/angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular vel n/0-k7kcf kukocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single y83,l 0; bp3fe7 mrrhqd ,tolsvalue of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a la*ayz/n.eg */n -nvyy4d4vyv,+ bxvtbf r)s p.rger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behind your head thd95ih0kp*x r-q luex (an when your arms are stretched out in front of you? A diagram (x0xu id9 *qpr5-lke hmay help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pedal sa)45c obrybp*3;ld m88(oya xhm t1gcranks. In which gear is it harder to pedal, a smop)h; cr 15 ydmm aolba(x84sy8b t*g3all 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 run fast have slender lof,b8*vu c1 qljl6ryf+wer legs with flesh and muscle concentrated higfl jv8 y+,lcf*r1bu6qh, 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 a 9qx,lpet/u2wq0c n-is(:r b–35) carry a long, narrow beam?

If the net force on a system ax.fvi,7dbjsv*ki , )is zero, is the net torque also zero? If the net torque on a system is zero, is the net forcakxvi,*.)jb,s7f i vd e zero?

Two inclines have the same height buzlhi:b c25 wo4n 8zam1t make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of tlmh45 ca182bwn: o zzihe ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incumevdl)q y 6 t razd8b*0:y1m(line. 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 total kinetic energy at the botua1 ( my :0* )ltdbd8yzerq6vmtom?

A sphere and a cylinder have the same radpyd 1:alipd*8/djgr -ius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kg- id/y8:*pald1dpjr inetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are cowu69,i3 zu8kwvc(b nd nserved. Yet most moving or rotating objects eventually slow downiwn38c, 6uu b(kzw d9v and stop. Explain.

If there were a great migo .l2*tqjh73o o ftzc5ration of people toward the Earth’s equator, how would this affect the jf2oh5tl*3zo.q7 octlength of the day?

Can the diver of Fig. 8–29 do a 0ts, g ub qhi)+x;t5hhsomersault without having any initial rotation whenh ,5q +0t st)hubigx;h she leaves the board?

The moment of inertia of a rotating solid disk about an axis through its centerqn -a *s/5wexf of massa/* nqxwfe5s - 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 holding96/fu qv yix;)pmrik+/febu 5 a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, o e iuifbfr/y6m;v )+9kpxuq5/ r stay the same? Explain.

Two spheres look identicalywb/nc-vg ju;g5j c/: and have the same mass. However, one is hollow and the other ;bwjjcg:5uv/n-c/ g yis solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axlerr) vexn(iiuz/ 5 g a/lj81(of points 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 ofzoul/8i ixnj gr(/1 re()5vfa the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntxsrsfm )s4+ zv4c4k1 tj+r skia*m)b8 able. What happens if you walk toward the ce) ackm1f+s*k84bjrrs )v+sm stx i4z4nter?

A shortstop may leap intog :7 sqf81gzre 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 71s 8ergz: fgqyou 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 momentum, discuss why a heli79j ,gp/fuvk0 - upvgs/xlpc-copt7/ gsju-xfvu0pclp,/vp - 9 gker must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) nk nbmgp9.g*) 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 Eh;7r p;orsh uw s-/cc+0ngc(tarth because of an amazing coincidence. Calculate, using the information inside the ctohn; s g0- rrs/phcc;+ wu(7Front 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, 380,000 kmufqvew /ul+8e7qu; c 0 from Earth. The beam diverges at an anglc+qq uwf7/0e ;vulu 8ee $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rota0h-( hk+rbnl 7gl s9jrte at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as7gh hnlk-srl( jbr 9+0 the blades slow down?    $rad/s^2$

  A child rolls a ball on ajtafk y(xxr/ 1a s5m *7ugn(g.bf23ia level floor 3.5 m to another child. If the ball makes 15.0 revolutions,iab((2/sryk gaf1uf 5n7tx* 3mjx.ag what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolu:tpa 4um*f 7wutions do the whe*uf:t wua7p4m els make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate it h7c*vpl6 );n7gxpjqo h+ ri,ts angular velocity inp),c;jh *qg o i6hxlr7v7+tpn $rad/s$ $\omega$ =    $rad/sec$
(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 revnvv* jfxlr) ah/6e10xolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from tx6n a *vvh) frjl/01xehe 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 (d)ixzsy 3q)5 ga) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sp6ty,1sm 5v,zh m ,kxcgn*vaa/ eed 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.sxm(p))3juq9s a74hlfj h3cz0 cm from the axis of rota 3p93 sxj(lmh) sz7ucj ah4f)qtion is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformlk t,rna m;.9ke- 4tieqy about its center from 130 rpm to 280 rpm in 4.0 s. Det9q-.emk4ni k r,taet; ermine
(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 radiuh37rge8 efap7s $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo space*8 eru1jmy/92d vd qzdcraft put themselves into a slow rotation to distribute the Sun’s energy euej*mdvdrd82z19/ q y venly. 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 6rt7p y0j9,3m s axcr(axmc5l)i: ylufrom rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this95,i3uapxyxcm 0yslr 7 ) ljtmac(6:r time?    $rev$

  An automobile engine slowg 4xeerj w45q)tm-c pa7h4 3ixs down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying hi dys 6it)edgj.69c 7f ;;kftah1 x;nsaghspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revol1;6ifaa f6y. 7)c; dxetj k9tg hsd;nsutions 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. 6 iz o kzuuwcp7(-s3l4i-kvm9 5fzuk rpm to 360 rpm in 6.5 s. How far will a point on the ed -oi.fkk7u3k4 wuv(zpz -s65cli9mz uge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/mi6/hl yn)2 waj;ubzvu2 n It turns 1500 revolutions before it comes to)v yz;a26nwb2 ujluh / 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 rejysms ,j4 c0)vduces its speed uniformly from 95km/h to 45km/h The tire0 smjvys, 4c)js 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 itsvg r99d 6h+jpf2vt,p/8o 1brlfmh 4 xx speed uniformly from 95km/h to 45km/h The tires have a diameter of g b+,mhtjo2h6vr49dfxlp 9r18vx/f p0.80 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 bi+:9kk fnn6fihucr(w:h ,y ay2ke puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 cc:whnh+:n,(riuyfk2a k 6 9yfm.
(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 vox;5i:ie -rf7xz e9zthe end of a door 74 cm wide. What is the magnitude of the torque if the foo;i e:e 9zr-xi x7fz5vrce 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 Figtzq8 emoq k,tk4a/5,m nk3n(c. 8–39. Assume that a friction torque kc(ktmakqqe8, ,tz4 on3/ 5mnof 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 of a massless rod whid tfh-2;wq 8qpch pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and;-p2q8fd qt wh direction of the net torque on this system.

  The bolts on the cylinder hea i4ow7 q-p;9nn(9 ptdqaznp -m x9neh.d of an engine require tightening to a torque of 38( .7hpapp q99mxz n;q9tnn- -4eiwnod $m \cdot N$ 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-k :+yz-pt qh8lwg sphere of radius 0.648 m when the axis of rotation is t+8tyh:q wz-lphrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of ejdr:aaf xg/ b+i 91qsanma5n8q) 0r; a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hj 5 fb:nxa 9dqqs8/ m1;aer) +ir0anagub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on thy.5 k u/jkrdy2e end of a thin, light rod is rotated in a horizontal uyk/j5. ry2kdcircle 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 wheel rotating at constant angularrb/i542;cch ujpyoq l,e6aud 7.f gr6b dr1e5 speed (Fig. 6p .,db yaqc4e5lb2cr edru ifj/ug5;h1o7 6 r8–42). The friction force between her 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 objecwbg-d;d oas9r4pcw b5+ q,l u7ts shown in Fig. 8–43 aboutuo9dwqb sd5lg +-,7cp a;w4rb
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atomp1zxvu .( di+u+r r1sgs 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 satelliteytp rjx :l9l1+zhje(: koabvu2ho7 *6 spinning 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 each rocket if the satellite is tot hz y a9lb: j2ruex+hkvoo*l(: 71jp6 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 k;rvccq )d/9od9be s9:e- xzm 0.580 kg. Calculatdk : o9bq9rc emex)vd/;s -9cze
(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, accex-+-jq;jx oq( 3 yupts2p/pcblerating 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 tangeny+*r9ipeqz/vdix + v 0tially 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 other on the edge. Calculate the torque required to produce the acceleration, neglee+*ix pvq9z0vi/+ drycting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is snl i )eim8.a3vhut off and is eventually brought uniformly to rest by a fnal8 )3i.e vmirictional 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. 8q8ca/ ;.g5kmtx ;yk o vyz6lc*–45 accelerates 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 action of the forearm,c3.dyb75dmc9c q x+iu0dy d6r which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly fromdc9c3 d.bi 6duy5 r7 qm0cyx+d 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 coxqxa: d*rl30unsidered a long thin rod, as shown in Fig. 8–46 *qd0x:ralx3u.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of zql*u1vn5w h.z /2t tptwo 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 tu4 o;9z8n09o+kg2v 1a it s*qoify rovxrns (revolutions) and releases ityfqon*o ork4it g90xi 8asvz9 +v2o1 ; 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 of inertia9f 4xdnjd 57gm 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 develor n0ic a zm:k-5*qh1cgps 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 kgtd9tw 02vmws7ty39/ 8 q ze .n*fn.yj/ygr brq and radius 9.0 cm rolls without slipping down a lane .q298z ny3jersvy0mw.tg 7fy*rqbt n/9/d wt at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Eart-o4u:jmfo 6fq h with respect to the Sun as the sum of tqo f m-f6j4o:uwo terms,
(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 owax4 l2am2* yff 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it iaxl2m w4*af 2ys a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts frubncesg:rf;,exdtr 7;q4r; pno .) wh8 .db. qom rest and rolls without slipping down d ;ncs .wr gbqru .f ),7e4dp;neo: qxrhbt8.;a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall and its any* )cxz :;,zkytt1n lower end does not slip. What will be the speed of nz ,tz1:a ct)nx y*;kythe upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum l-na(uk-,rh8ruk 80oby d5p vof a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at 8yk8v r(u0,-rl ka u5hbopn-dan angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular 4twarw )( 8hrimomentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm?ah84writ() w r    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at hi4 o 1b xsjs6(gtsa2p6ds side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position,a6jxo2 dsg1ps tsb64( 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 heracpy t ql:+3b:3szb :moka3a9j2p qh/ 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 in 1.5 s when in the tuck position, what 39j3plzt/bchqky+ :3q:amp2 ob : aasis her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initiavs8mj er9* agarh*f ,1b (+qdh g+aa)ul rate of 1.0 rev every 2.0 s to a final rate of 91a*m+eu h )d8a,a*s+av qbhgf(gj r r3 $rev/s$ 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 axnqn+ *ylsi-m its6; e4egl; 3jis 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 afteim3ee s6t+l4ylnis-q;j;*gn r the clay sticks to it?    $rev/s$

  (a) What is the angula t3m(-49ibmpp by 1kuow9u9e lvw5d.pr momentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular mom,31qp -2cmidkzv1qpz xgeb) : a;-u;lu h2rbbentum 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 mom;q;6tx glpod xb5avhv2 +zi )/ent of inertia I is dropped onto an identical disk rotatit;iop;dvb/5x a lxzq 6g+)h2v ng at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atqdc qvgmhb0mi/ v c, 5jt8v3,+ 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 centmq4h55b xs3b xt: b0oslwr b0u,i+ y0ner of a rotating merry-go-round platform of radius 3.0 m and moment of inlubx ws n3sobtxm 0:,rhb0+ by0554i qertia 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 :zp)5 da d72 c9kuvhbnof 0.8 bhz7c :pd nkdu5 92)va$rad/s$ 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 rb(se;s 2tp3cdwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existings b2(tc;p ers3 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 win qped xamau9;n )92z5eds 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 x/:k pi+4 5jtegbar97y cby-xt6h d-b$ 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 wuevl* 2wi b1-mithout friction. The moment of inertia of the person pluw2liume v *b-1s the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6 k+( 2lrjy*ilyi typ-j,4g4eb.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of jg ( yjly,p-4l 2y *e4rit+kib 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground ws g5x+fvdz5 2gith the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of m +52xvfgdg 5zsass move?

  The Moon orbits the Earth such that the sam 0/* zyy6pp*fzs b+z3hp9q99vkkosime side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (Izfps m9p kihy3 +bky v6q *p0/9z*9zosn the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ratju7 xzm:g d4c)e 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 1s *isnd1(j2 otu;hfx the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque deliveredd;(sfj1 ot*ix 1sn 2uh by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of ma)6s4; m2lr2 qfhy diciijau( (ss 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 calculath sml2;yi(urq i6jd(2)4fcai e the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wh)c d g.qz8sqh;rd-c(ieel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were r/rg vqoqf;u v+41f kb/otating 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 lost4go1;r/ vuvk /qfbq+f mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to u3f r)juvobpmn 32c 0g72 z+hwcse energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m andm2c0wpfur23 cvj ng 3o7)+bhz 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 aitlxb0k1)y8,w*w k3 jn /wqlqd tk1,kn $H_2O$ 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 rollingk--k+w y;hy06 jnh jd+dbhfp; 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 pg ) j7.)7:uffpzygl qfe4r l,M and length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall,77lzffr)4ey uj, fp)q:g. glp 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 mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It i,/ bbwums dc.d37+ga bs standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it wilb cbgds7 bm u+3a.w,d/l climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on axkl -k,c *+v5:pauffynv7o ;g --doyg flat road is making a turn with a radius The forces acting on the cyclg-+u7lfyo : ovx-cn,vay *g kk-f5dp;ist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sl1w8a6)*yon /p hr6-zllhlm 2 nlw iw-qing of length 1.5 m and begins whirling the ronzy 6l1 oqmaw8l/h)rni*2 pwll 6wh- -ck in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body c mh1i5 w+bw yth.:f1u:v m8akas a solid cylinder and her arms as thin rods, makinga 8.u1 +w1vm :wh5mtfyicb k:h 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 against her body.   

  You are designing a clutch assembly which consists of twvrlz ojg38z0/ o cylindrical plates, of /0o8z3z vglrj mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ro+n9qi1sjw jeje0t-/tugh 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 without leaving thewn9-jjt e0qi/esj 1+t track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assu y(w sepymha(pi8fi//)9+c bnme $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolut dt-v4ln() m5(8eqsh- b .o7rkd; guvm notxe6ions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular accelereoh;-)ge 54 dolbqm6tk (xnsv n u(rdv-8t. m7ation 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