A bicycle odometer (which measures distance traveled) is attached nr9gd9v9dc8uca1 b 9l sear the wheel hub and is designed for 27-inch wheels. What hapc99 9g1lrau9sdv b8 dcpens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity-r vs((q:sy,sx xf icyir-, (u. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does f:i vyr-sc,s(riyx,(u s(xq- 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 value of the angular velocity j858kckk0:t 0eaq y sy$\omega$ Explain.

Can a small force ever exert a greater torque than a larger twdp*srw//tv q,wg45 zg*5ii 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 bul0co3.tikp 3 7iojj 4kfb8*7+8nqwep2yl zto do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you k7wtk7z3q 8pc4 yupoei lf+0j3oln*b2b i .8jto answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three +sk8d)cdaw 0cat the pedal crankck)0d dac+ w8ss. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with f qb 8v7yc;*qnylesh and muscle concentrated high, clb cq;*y8qyn7vose to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) yk4 o8p5qr7a3h lv vxs e7/kl6carry a long, narrow beam?

If the net force on a system is zero, is the 51fu3qk4x)mobpl0 gr net torque also zero? If the net torque on a g0ofm3q54)xbk1r ulp system is zero, is the net force zero?

Two inclines have the samon2ph,jz3cl: e height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at tn3 p lj:cz2h,ohe bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) do8yv wva/h-m:f5 d a4fkp;5h nawn an incline. One sphere has twice the radius and twice the mass of the othhaadpffn- vh 5 48 amk5wy;:v/er. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They -w. 0zrei vzqtp,pu7o l3kwc*+eo4g9start from r p0zqe e9u7vi,zrw c+ t-*kpo34. wgloest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. bt(e+sh.nk12k fnu/ qYet most moving or rotating objects eventually slow down and stop. knb/hnk1 +(2qu . tefsExplain.

If there were a great migration od oogs8.cs8fjxf0 dz0ec96 r3f people toward the Earth’s equator, how would this affect the length of the dayc8o6 xe89d.c0rfsgf0sd 3 joz?

Can the diver of Fig. 8–29 do a somersault without having any initial rotatio5(,: jzawvj*m o fb0eeczam(8n when sh8veam(zz 0w5cfj:* aom, jbe(e leaves the board?

The moment of inertia of a rotating solid disk about an axis th ln6d gr/l 1*o(b8bxegrough its center of man 8gbb*6d/rlox1e(l gss 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 mass in eacuvolnwmg 2e (/t2ch*2 ctzn;*h outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrecwo/ t(;2* tm2 nzlnuhg 2v*cease, or stay the same? Explain.

Two spheres look identical pyk9w,jdubbq ;;+x/cand have the same mass. However, one is hollow and the other is solid. Describe an experiment to d ;ypw+9kub/jc;d x, bqetermine which is which.

The angular velocity of a wheel rotae3wa59og kjelx k2y;d3 * jb8dting on a horizontal axle points west. In what direction is the linear velocity of a point onk;3db8dwoy egj3xl*ka 5j2e9 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 rotat)wjdcgff1tokt+xl9**8 )l v yh d2v(ring turntable. What h*t9+ hw1 d 8)xcg*yffto(r l)kvv2dlj appens if you walk toward the center?

A shortstop may leap into the air to catch a ball3/za ldwsb4:- iyf2qfij;ig ( and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notic g-3;/2 4b sqw(d:yijfflaiize 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, disc./idp 2xvj7h uuss why a helicopter must have more than one rotor (or propeller)i27px .vu/hdj. Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radiww- )wd5vgpf*) s16apv9 yprtans: (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 Eam9d4wt db .mrh:ds/m/rth because of an amazing coincidence. Calculate, using the information inside th//mstmr.w94 : mdbhdde Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. Th jn n)utj:)n)lwpn4 ;u1.uprj gcd+ t4e beam diverges at an angle c+j n4;)l: 4 jptunjund)n pwtr)g.1 u$\theta$ (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 ta94fo2xwsci:m)ucd : he motor is turned off during operation, the blades slow to r:do9wfx4cm) usa2ic :est 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 another child. If the ball make5xsbqhlb)* 1 ys 15.0 revolutions, what is its diamete ysx1*b lq)h5br?    m

  A bicycle with tires 68(p/wsannn7jr.f ,. 9zzv;rlx6ls po2 cm in diameter travels 8.0 km. How many revolutions do the wheels make? jn rrw.nll,9xppznz.s/627;v ao(fs    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calqxu: 5h lh:)(wy;kkuqculate its angular velocity5: kyxh)lh uq:wu(q;k 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 comz58 fw.l- v 6yitdrt8kplete revolution in 4.0 s (Fig. 8–38). (a) What is th86z8fr-5tt . vwyk dlie linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a)m 8k;pgmucf;di1 rr1/ in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speenaqw4l(p ntq6/d 4j8id 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 cenwo b 1q o 51r5nl2w+,6emijieq3vgie4trifuge rotate if a particle 7.0 cm from the axis of 3wl2+gi4o vo5e5ei6jwrnbqm 1 , e1qi rotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm twnic;duc e3. .o 280 rpm i3c.ue.w; cnid n 4.0 s. 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 radiu 5 2j1ujnc2szgpr p1j7s $R_1$ 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 ke al/00ikpl c6ty 4t5the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they acceleratee i 0ly 654pt/tckkal0d from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from res8wipufak9 4 *et to 15,000 rpm in 220 s. Through how many revolutions did it turn in this t4* pew8f aui9kime?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.v*4s+ ohgvg; .k)guxo5 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 h9yxj fpq1vqyu2/ j.7 1j/q yluighspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachin1/2v./yy7l9uqyuj1x qf p jqj g 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 acceleratesd/rw48 qei : 9vn6qguv uniformly from 240 rpm to 360 rpm in 6.5 s. How far wi gure6qv /9w48qi:dnvll a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 8 phza(lueshty0i 9*;7d/w tc1500 revolutionse0 ttl9usp/;w i( hcz7*8yd ha 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 revo0jauy;)aoar hqay2fh9 . 2nf m.o8 d(blutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires h 0hom) 2.b orjy(q n892.ydauhfaf;aaave 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 0o *v8woavjt/p a*f5kk2q eg -its speed uniformly from 95km/h to 45km/h The tires have a diamete/ a0ovo2w kjgq8*f - t*a5pkver 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 bikk- +do7r ioz4ve puts all her weight on each pedal when climbing a hill. The z- i+o4vd7ok rpedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 obl:52bakq ic31rmt pj*.l 2fN on the end of a door 74 cm wide. What is the magnitude of the torque if 2i l.3 mf2j5pab c:*qkro1 tlbthe 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 ogn + 2r)yu36wb/eaeu*,hbnjef the wheel shown in Fig. 8–39. Assume that a fuy* +r3/e abje ne n26,w)hugbriction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attacheg:8k9 io w1b*5r )ycn6 mlwjshd to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net to8 ihwol65ng w 9k*sj:1bcry)mrque on this system.

  The bolts on the cylinder head of an engineu4sfnlqz(2a; 2-s i:mzvg-ff7 h/mcu require tightening to a torque of 38 7vmn( 2 ;g-uilm4 zsqafsf : h2-u/zfc$m \cdot N$ 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 inet qgi)t p k(qkwobshvc-a. :h 6n+-4-grtia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation isct.: -)k baqshpiq- 4g6n h-+ gvkwo(t through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheu3/+v w92qbf7r 8o,p xjeuysmel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ig 7jq ep+syw9x u2 3r/bfmuvo8,nored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rota+/. pkxbxs1mf ted in a horizontal circle of radius 1.2 m. xsk1/. mpxb +fCalculate
(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 onnsarx1 6 dxz1d8 g4e8e a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her handse161r gxx8 dzsd4 ea8n 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 poiwve v:p r*3iz)dup60h nt objects shown in Fig. 8–43 abouupw0 p3 hzev*dr v:6i)t
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxyg/7-iiemh zvp7w 2(97ljuqzqz j )z-f ki7dn1ven 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 satella2d ru*ysm hoh 8o7o-h4w1e4lite 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 4.0muhyh4lr- 48* sde 21a 7howoo m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass o z1+j9(ec ncsl3 6czmcw*qp 1kf 0.580 ms1(p61z cw ck+zqc9 nlcj e*3kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, acceler8l9tg: maami2ating 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 and isl 6tfchf:y//7 yofi sm+x +, yodurf5: 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, neglect7uf,/fxlyo tyf+s::5h o y6 fi+dc /mring 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 eventually brought m2:xwncj6*roe); nar 41lmkuuniformly to rest by a frictiono;r1cerx:m )m6*a4j2nu ln wkal 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 accelerates a 3.6-kg ball at npp9v8dr6 3 kr3w+mpi5 ,,qpguagpi2 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 bacxo / n(.bp ,wye3.qtgll is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly t(3xbe .gwc n/oq,y.pfrom 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 bq74o u8bxy-g in Fig. 8–46.-ox ygu7q8bb4
(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 cons/b (:2y+7 /x6neriy ol fkkxreists 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 th(yi 5 xdghnbf;o0iux5u) .ee9 e hammer from rest within four full turns (revolutions) and releasesunx xydiu.9o( 55hegie) bf;0 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 2w thi:j;q4xia 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 devec 0+ocs;x,k wjsac x(5lops 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 kg and radius 9.0 cm rolls without slipping down a -r6nacagyz 52h:favfoba ng:,bd(l-m7 wo/. lane mf ga.o cad6n 7w-rlnfaba :5/(,z2:o- by vghat 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of ddgmd5lw.7/i+ +l(oluyk ,np two terms /7wmli (ly.,gn ++pdouldkd5 ,
(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 md068fj pqz;y8r am-nof 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 revol f8m0a;-y ndpq6jrz8 mution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cmnq: z385ji gqxq-t2tl and mass 1.80 kg starts from rest and rolls without slipping down t5 zq ilqt32j8xqg n-: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 it * hotkn,o9d2c 2)+1wdrjzyjf s tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of yk+nzwto)dho *c2fj,1dj 2r 9the 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 on the end od4hwbt3 g b4p qq(k+:i 5lgs6of a thin strin+qp( 6:gib4wtg34sk5qhdol b g in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular8gcv(izxn xcs38 /v8x momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 1nvz/c( 88vxsc3i 8gxx8 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platfh+ n2eyf 1pcs*7(t zszzjrh52h/ taz 8orm that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal positiohh2p+j s*zn(1er 7czz /8 zs2fthy5atn, 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 redug1hf6j3ni53 ja bheh 5ce her 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 is her angular 165hjf5e gbhj33h ian speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an itfi y iqum-8w.g3;zmw7*5 iuxnitial rate of 1.0 rev every 2.0 s to a fyquf7- ; i*ti 385z. mxwwmuiginal rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its centede 8u1 b)sv1lrr 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 wheeelr s8 1b)v1dul. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a fig k0irfrm7ls;t* -tw0uure 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 thet s+zc i;r6ts; 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 onto1 -2j5xfwanw gs4a)so an identicas45wnw agxo2- a )f1sjl disk 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 b x93s::fr;kcuur y.r2,c)uq 9xow ha 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 t.6,w*yhaokv she center of a rotating merry-go-round platform of radius 3.0 m and moment of inertiws* yo6h. k,vaa 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-roundpd*n9b2 rbqa s.1 b6cl is rotating freely with an angular velocity of 0 .2*bpdr96lnqb1 s bca.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 col:jv;t-xoh4 wplapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assu x;phvtwo:j-4ming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in; fh7ea ha b9rkx5/ dr;dn cy,1ai y7b5*bpr)j 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 +h.+x k kzuk(q$ 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 platfo2mhihf9+hn 2c(9 vo lcznk2* drm, initially at rest, that can rotate freely without friction. The moment of inertiaz2hln2+chokd mh(*fv92 cn 9 i of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at thy+ f0nsu4w 9;,m ) caub+rzcble edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a momecb9 4lnr+w s,)f+u0myabu;zcnt 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 the ground with the end of the dnn2)s5oft +t 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 slipp+)2nt n5ofts ding. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Eartxm t+6rpc, c*ph such that the same side always faces the Earth. Determine the ratio xmpccp r,*+6tof the 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-hto ;/uwo i24iwdm6p a rate 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 0.20 m acqui9orqg1 r5b f3wres a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the5b wrg31foqr9 motor.    $m \cdot N$

  (a) A yo-yo is made of two solid v7srxf a66sp; cylindrical disks, each of mass 0.050 kg and diameter 07;6sav 6 pxfrs.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is d1.i sq 3x(vn;ciouqc cf73 5a/qyjb6the 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 times as great, were rota b2tiuo8sm))q84nv bz o)s*1xaa c,bating at a speed of 1.0 revolution every 12 days. *iav8 ) o8 1s, bt)ncbaa2b xq4)omszuIf it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobik8giq k*y:+yf:i tr 1qle is for it to use energy stored in a heavy rotatin:iqykiyrq +g :18ftk *g flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and 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 tv2du ./rt -etmr 67sjj1af x0an $H_2O$ 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 hori fgtqp1q ;z5j.if/u p4zontal 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:q1 itr,cep/y L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The roc 1i trp:,/qeyd 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 radiq5 uqrw4g4qvj /us2v +us R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it reqw qu+v4 r5 g2vju/sq4sts (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road isn3.a b/ay3hng4 u5g7epnv7q dx,l q;r making a turn with a radius The forces acting on the cyclist and cyclee7u4a3qn bdv y7r/ g5,ah l 3;.nnqgxp are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of leng3ta4y83f c tz ifu+0idth 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 s. What is the uiydc8 40 f3t3z +faittorque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solj:q/v; w e+mtxid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against m+ te/x;w:vjq her body.   

  You are designing a clutch assembly which cons)py:x bw6s5z cists of two cylindrical plates, of cw)5xypsb :6zmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ro0n; ,c.ljr mk,0 fvzvkp6ipi0 ugh track of Fig. 8–58. Whnizrj ki ,vm;k0f6p,.pcvl 00at 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? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not asdb)cx9z 0q-xxe)w i8):t xh aik, 5vhzsume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutionshfq63 5k:l ua)tmd.1 bdrjn3h as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a di.h h6j)k f 1md5aut n3rbql3:dameter of 0.90 m. (a) What 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