A bicycle odometer (which measures distance traveled) 7u*/;xl 0 infssll i2jis attached near the wheel hub and is designed for 27-inch wheels. What happens if you use itl fli2i0 *x ns7/us;lj on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does,-s3 vk9redn)w rd0ox a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of ,vn0rxwr-d)od 9e3ks either component of linear acceleration change?

Could a nonrigid body b*hd29s ehk.d .ndqf8p0nv- ive described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever +p.1 vh4nxd7g.v : ucdl1tkrq)be d1jexert a greater torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head than 6+gnry1/v tuc vc51vk when your arms are stretched out in front of you? A diagram may help you to ansyvcvg1u1n / c +6v5rtkwer this.

A 21-speed bicycle has seven sprockets at the rear wheel and threev/ sdu 1elaknt22zb*2 at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Whvlan sb1 ezd2*/t 22kuy?

Mammals that depend on being able to run fast have slender lowervpx ,3 cte.tur (xt-,v legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution t-,tvrx 3ep (vx t,.ucof mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, na8 wagi9eifo uwj(.,x1 4cq0xp rrow beam?

If the net force on a3:js pq*8r ttg system is zero, is the net torque also zero? If the net torque on a system is zero, is the net force zpr:q3 8t*j sgtero?

Two inclines have the same height but make different angles with t - 1z xnce;hra:zi(k)jhe horizontal. The same steel bal er:(-hkzcz n)1aixj;l is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres sim3+eh c,uzo . cg/eriu)ultaneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bo +e)z c.r e3uhougc,i/ttom 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 jfz-9v 5czp30wym; xtthe same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the m p3590z- fytczx;wvjgreater 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. Yetrs4(qn6mbu a2onsfz 3-ul(/e most moving or rotating objects eventually slow down and stoezuab-qs(4r(smu 3 nl/n26ofp. Explain.

If there were a great migration of people toward the Earth’s equator, how woubpsi.3oo 7z2l s;agb6ld this affect th 7l2zg;.o p 6siob3base length of the day?

Can the diver of Fig. 8–29 do a somersauoxl ,/ lv xv ed6:mlwpv6.* rv,n8mgv2lt without having any initial rotation when she lg:mmv6vvv ,l2 /l6,rnv8 xxwlo.* ed peaves the board?

The moment of inertia ;;hqoc;v un 0pof a rotating solid disk about an axis through its center of mass i;h0pcn;ouv q;s $\frac{1}{2}WR^2$ (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 s0gz7ev0xd k 2*im; 2gimze 9o*h.r wnktool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the9vm2z n mgkix*7hko erg w;z0.d0i 2*e same? Explain.

Two spheres look identical and have the same mass. However, a6j,zx-d :zqe6/z zscone is hollow and the o6e:j/, dzsc 6xzaq-zzther is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a hor91*6aa5p0 nbn vm hxf( r-bpwxizontal axle 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 of the95r-a pp61 ab 0mfhnxw(v*b xn wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large p6/;uiu8o 2jfp;pw1mc av; qbfreely rotating turntable. What happens if you walk toward the ceb;pf 8;q u2po/ mvu1jw;p6aicnter?

A shortstop may leap ieox2skl9 +(q 2qt 5ym xpn3d4mnto the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his bs3o42yn(xt2lqmdqp emk9 5x+ 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 conservation of angular4 mjah6*tg*) cewsl0d momentum, discuss why a helicopter must have more than one rotor (or prods h)j*6m*a4tw gecl 0peller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the followingw ng 6zf m6i,498 kx*n/l dw +xm0qfh.caknnm( 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 becauslw ri7)k d24kqg+ gj.de of an amazing coincidence. Calculate, using the irk47gw2 l g. qdidk+j)nformation inside the 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, 4im3 ayg :s6ukydk.) jm0*7x2 jmiui t380,000 km from Earth. The beam diverges at an ayik: 0sm img *jj642m.yi )3uatxuk7dngle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate8xp s.ut4wdn 0 at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to 8nd0 sx 4twpu.rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball oeyikd 3p amvcus;-x.ei;w wj a02 ;7k0n a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, 2u.wj m0 i ekacv;wek0;axid3ps 7;y-what is its diameter?    m

  A bicycle with tires 68 cm in diametez56ij9 mx0w7 mr kuh;/ fekf.lr travels 8.0 km. How many revolutions do the wheels lmzi9hk056 7er w. /;mkfjfxumake?    $rev$

  (a) A grinding wheel 0. yo56kk;; hafpg,okn135 m in diameter rotates at 2500 rpm. Calculate its angular velocit; 5 ohyn,kp g1ofk6;aky 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 (Fi wjwb7eo50 a6rg. 8–38). (a) What is the linear sajr6w0e 75ob wpeed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around c+btt n*k:vv(r3+jj oce-a 4cthe Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speedjz9mo.sd d9c;f 6 lpja9*ook* 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 vgk6/y ow *sek*w o xm2zka .34+ve0plparticle 7.0 cm from the axis of rotation is to experie *vwo +2x6 /*zvoa0em.ey3pg4 wklsk knce an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly abou m-;xlj12bxujo af5/ovrpr3 99un7wut its center from 130 rpm to 280 rpm in 4.0 s. Determ1j -9 fv2 wrbxoxumunorljua 9/ ;57p3ine
(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 ))*gk+ ov,q5o :g pixj heb5js$R_1$ 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, astroky am gu.xl esy)u-ph6 g7(d )bf9vw,4nauts aboard the Apollo spacecraft put themselves intk) x. 9buywhps6avle ), g-4fyugdm( 7o a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerkl; n:.;fwkj e6 sc5pvates uniformly from rest to 15,000 rpm in 220 s. Through how many revolutiskkl jn6efpc:;v;w. 5 ons did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rp -;-jpw;e pxwki*6my gm 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 yop bwd jkr8da72an0ai-n mp7 br+*2,highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn throu0dpp72rnmad*a -riabwyn782j k ,b o+ gh 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6.5.x p/3z6 -7 purqguypn s. How far will a point on the edge of the wheel have traveled in thig6uz 3n -ppu 7xrypq./s time?    m

  A cooling fan is turned off whe;4wlq 2)dd9dptk-4 efkr;lb qn it is running at 850rev/min It turns 1500 revolutitfrd-2p ql lwkb9e4 ;;qkdd)4ons 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 65t gd 6pjvtz +ey7m0(5mw h;o;j revolutions as the car reduces its speed uniformly from 95km/h to 45km/h Thgj5+vt 0y;; (wzm6 pjdmh7eot e tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed un xpqvskpj *k80hj+cb)0hs4+miformly from 95km/h to 45km/h The tires hakh*4jk0 h) sj+ 8q0pxsb+ vmcpve 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 climbinfk1*nxu 2bu;c g a hill. The pedals rotate in a circle of radiusbkfu *cu;x12 n 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on t2* gi3dwptm9.z 6 4wp:xhrtld he end of a door 74 cm wide. What is the magnitude of the torque if the forcermg23 ld*hwt6wxt 4pz .id9:p 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 oz8mjv sl: 4.ew++ox fwheel shown in Fig. 8–39. Assume that a friction torque of 0+4fezwlvx:.m+o j 8os.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached t4d. rt9aji,cf8at; setpz+ 6o o 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 magnitudeot.r 9pata+z4id e;t6sfc8 ,j and direction of the net torque on this system.

  The bolts on the cylinder head of an engine requir6)qer va- n;.zgjqo8be tightening to a torque of 38 env;8qbg jorz )q .-6a$m \cdot N$ 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 5k;hfxo*1s; a.jy w1hfss ee.inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is througok 15eh xjs.safse h;;w1fy. *h its center.    $kg \cdot m^2$

  Calculate the moment of inertia clapq1j zde.9(rpa* + of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combin9ezcq. a j1p+(adlrp*ed mass of 1.25 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 rotate4,;fsz h0tnm lsg s/p:d in a horizontal circle of radius 0sg4s; pmhzn/ts f:,l 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 rotatingz 1p2w id3aq4m at constant angular speed (Fig. 8–42). The friction force be243mdzapqi 1wtween 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 + vofx 3-;i 8t;b kwb9osd4kxsekk,e*of point objects shown in Fig. 8–43 ab9+we,e x d-; b34sok *8tibkv xkko;fsout
(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 fxmjk5a0 -8e4d 5k kmcof two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning ax9 y)7: 8upglc:tjv(u aa8cy vt the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellit l:8vpa8)v: c(9a yj tgyux7cue has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8 t 429ng6ut0hg,ncr qj.50 cm and a mass of 0.58n 9 uqg4h0,rgtcnj26t 0 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerc+, 4y049 4xvjys/+r yqca gq9gebgpzating 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 s4 tf gv(qjx(;xmall hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assumx4 q(t vfx;(gje 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, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rp5ug);lkseuwq 89,ap/t) qoi z 2iaip9m is shut off and is eventually brought uniformly to rest by a frictiona qagi i, ik2/;u op989wqlpaste))5zul 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 azlciq762me0qusr 5l 1t 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 z)yee9m ao5u1-z blr ;solely by the action of the forearm, which rotates about tho1rz -le5 b z;e9m)uaye elbow joint under the action 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 ov;0cb8*cink gn.l0 lrod, as shown in Fig. 8–46.8 o0ln b;kvi*0ncclg.
(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 m+fs z0g9 l/zgconsists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full tu4 (1tm*im5(uj qedifk s.8ijf rns (revolutions) and releases it at a 5tufi .j(dsiqm(*k4 mf1e8ijspeed 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 momet03w:zfq1cfvb6-k ope)afx+ nt 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 develo9rp1 m6bpmo *cps 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 h)2gsx,n8kky/j)b rqf sn 7p )kcb9t,and radius 9.0 cm rolls without slipping down a lane agkj,bn92k7yft) s)nr b q),p / s8kcxht 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun qbg a5tjzed/2rfg)0xcw( / 3 nas the sum of tw0(czagnfwj3qx/r/ dgt 2) b5eo 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 of 1640 kg and a rqd czmr1q a+u.uz+25wadius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.0zcr a. 1++uuqmdqw25z 0 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mas8 heq;j+*8ji kx f*f o4snd,ins 1.80 kg starts from rest and rolls without slippi+ iji**48,fne x dn8f;ksqh jong down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall z d6hxm:xpkmvvb3m1;b e;*;(sh aw( uand its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.] vsz;x*vb 6ha : k(pbu1;hm;d3exm w( m   $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of xem2rvw-p0*pnz vj+5 6:knvp a thin strikr*6p-nvpzn 25pm:ev w +0vjxng 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 angular momentum of a 2.8-kg uniform jv2az,uz4ubo2a* 3cz*d6ovz cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpmzd cuuoojavza2,bz3*4v6 *2z?    $kg \cdot m^2$
(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 rreplx2a)jldai 3. 68 jh,p7p ajhmg:0otating at a rate of 1.3rev/s If he raises his arms ,aiex g0hlpaj8)6j r3l7. d2hj p:mapto a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of y ytcd*xgfd trb3 7;:+j9 y6jhfy+ty/inertia by a factor of about 3.5 when changing btc hy+x*tfy3:d9j y+d7 ytgf ;rj6/yfrom 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 speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial ra p:sge1imv41mg0.yl,;v bh pate of 1.0 rev evypmp4g :lv s,mgi .h;1e0a1bvery 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center at a t5n7ze7m:7o )s 7syop q,9 lyfyd 0xvufrequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameotqfpdxy m5790o, yuyns s:ze77v) l7ter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momenzt+7 (uox) -(ks2xp0dxkacs mtum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum ofgozj-yyy9co 47z.6cm8f q7 pp 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 ofbtf cxbo9 a;4 2/plu- tlfsk0: moment of inertia I is dropped onto an identicapt2ub:lkbof-4 9satl; /xfc 0l 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 2.4 aci tys; ,u4n8$rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merrfe9kea1etgb7 ,u d;.ny-go-round platform of radius 3.0 m and moment uneetd 1,7kef .;ab 9gof inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an aneosv5bk /+v7 hj0 *kpngular velocity of 0.8 ks vvjo+*p57 k0 nebh/$rad/s$ 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 abo2*negj *sc(iout half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentig* osc 2nj*e(um, 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 of 1)cxl h-yx7 p.f20 $km/h$ 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 ( 29 xpnv pxsl3zs9 *0ods/ztl$ 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 platfdb(omzu 6iy * 7gkj8a-orm, initially at rest, that can rotate freely without friction. The moment of inertia of the per-u(i g6mj b*ko yz7d8ason plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge o8;pylwmcl1hwc6nq 0. u)x qc .f a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment 1 ccl.6h8p0;wnl.uw )xqmqcy 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 groundc9a-lp.tpc h2gm 01 oqq8y6wq with the end of the rope lying on the top edge of the spool. A person grabs the enh8cy.1aqp92 m6 tq-lp0ogq cwd of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always ejw2l1b 5v0 0wckzw 3sl w(ui+faces the Earth. Determine the ratio ofkw2e50s3(vb0 ulw iwz+w c1lj 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)epi1fymn . ,v (lbqf58s)i gx from rest at 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 of9vp0y g2:s fbf 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 delivered by thef0fb ps:2v9gy motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050wy7)-8cytk7in1n dm w kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo whe )t7c1iy7y- kdwmw8nnn 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 z +p,w2syu ra1the 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 ye4ei46dsgv :w;2yo a 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 s4v2yaeyi6wesdg:o; 4 phere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution auton+of7 7q jmlt.mobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheeltq + mn7.loj7f “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 a (p5k,+ h-kj wgz:vtetn $H_2O$ 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 speed v7p-j- 8xsf cst)4 krlm=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 masscqk )(fvav3m7:m;y)yv eo *vx M and length L can pivot freely (i.e., we ignore friction) 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 x evvvc:*qa o 3kfvy))7ymm;(acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and we fa xxwx/h6)ug5dn 3/owant to exert a horizontal force F at its axle so that it will climb a step again/awd/x)xf5hxugn 3o 6 st which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with s *4jie,ec2nt):z3ya /nzype x peed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cycp e c3e)yx/ne4, jz:nia2*tzylist 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 sling of length 1.5 m and bym58n mdn;zf 5)9rk gslzq09 zegins whirling the rock in a nearly horizontal circle abo mzyq;n )rg5l m9z fs058dn9kzve his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her a.o+ug p(0h tfarms 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 wiufohag(+tp. 0 th arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindricalp50-6jc lgtml plates, of mass 6tlg 0j pl5-cm$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 radiufw ttk gw*i1lg/4n -5fs r rolls along the looped rough track of Fig. 8–58. What is the minimut 1/glw4gkw 5iftf- *nm 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 norq be1q -iwq,0t assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car red ,ov t/wf)kqcmqa;0:plg 3 s,cuces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of qcp0 )t/m3olf w;,,k scqva:g 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