A bicycle odometer (which measures distancea*9ht ufpu,e6 traveled) is attached near the wheel hub a9tuef, *hup6a nd is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rlfr,2 ggfw,, sim have radial and/or tangential acceleration? If the disk’s ,ffsg,g2rl ,w angular velocity 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 descpj0f-0 smeojo y) 5d(vribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? E3vgc *a)hj3u +wldwnx n7r 6e3xplain.

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 tha m;6jsebszm5;f k4apq*q, ib w.tt18vn when your armm w;mjqpb k*qsz5 .4,b6vitaf 1t8es;s are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three ntftc:t:g8+6:r9be0,gxowb py p5 w l at the pedal cranks. In which gear isr08 twn,p twg6b x:::tf p+lyoecg59b 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 slender5jzvrpd6i(ky0- wy 0 a lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why thwy-0kz(ra5 6iyp j d0vis distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow ta6f uep1 sftr95a,uz:8cn 8h beam?

If the net force on a sgm b/(ztk )2 9h-z-pfkal ai*yystem is zero, is the net torque also zero? If the net torque on a system is zero, is the net force ( ytligz -k a*h)fk9m/p2 -bazzero?

Two inclines have the same height but make different angles with the horizonx7 x o2;jt,rzhtal. The same steel ball is rolled down each incline. On whrxx 27ho;j, ztich incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incli *)i0mszt.cx zh3rz 4hne. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the xztrhz*s 3.z4 im)0chgreater 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 start fr7ftx/ bzhd;dute98 dk :9 hfa8om rest at the top of an ia7d8u: tf9xk/dtf e8 d;bhhz9ncline. 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. Yet )zum+-ror/1ztx-*q iy)u : t+k b gmwmmost moving or rotating objects ev gix+q/-+1t -y *w)u:umrbmrzo )tzkmentually slow down and stop. Explain.

If there were a great migration of people toward the Eagt jg6vn7c *6arth’s equator, how would this affect the length of the 6nc7gt *gv ja6day?

Can the diver of Fig. 8–29 do a somersault without )e tcb7dq3.kl xti+2lkwh 5.t having any initial rotation when she leaves l. kb5+qdct ewt h7kl3t. 2ix)the board?

The moment of inertia of a rotating solid diska7j/ vh odss.0 about an axis through its center of mass issa.7 do /0hsjv $\frac{1}{2}WR^2$ (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 sitt zmqg qfw;)6qts/*w v8jpo 04 x0apjm7ing on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Exva*8qz7 0mxofm q6; gswqp wt/0)jjp4plain.

Two spheres look identical and have the same mass. However, one ixorx6h0ec k,z nj3anhm)a9xd -3ti:0s hollow and the other is solid. Describe an experiment to ded3,xa ax 0tz)3r9 -xcj nh m0nh:k6eiotermine which is which.

The angular velocity of a w57x uxj9z.dwj7 2afr :;khk ozheel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheelz7z xjkf r axoj;5u7w9:.d2hk? 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 phxj b+a0 bk4e-94;i btsxv f6the edge of a large freely rotating turntable. What happens if you walk toward the c44tv k6ef+bb9 axs x bijph0-;enter?

A shortstop may leap into the air to catch a ball and throw it quickly. Asckt127c ;po kn he throws the bapk c7;2nkoc1tll, the upper part of his body 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 conservac,;zf- i xo4nx3rvb(ytion of angular momentum, discuss why a helicopter must have more than one rotor (or propelle b( n,xy;34ci -xvzorfr). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles .7 texz(hk-+zwp0dhl in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate, upogc bm)o1jt f 8h3-d2v48cbu sing the information inside the Front Cover, the angular diameter c-f83vpjh4obto8dmu)2gc1 bs (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,wp9sd5(p zi zd .g.yy4000 km from Earth. The beam diverges at an anglyy4i. 5gzd(.pzdp9 w se $\theta$ (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. Whend ga;qq g/18dz the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angul z8qgaq/; d1dgar 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 makw4 pzj2od 51hew.tc g4es 15.0 revolutions, what is i1p ch45dowjzet.w24 g ts diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How m+0em91 5 nk fuzr.yteiany revolutions do the wheels maknz5r0m+9e u.y1 tekife?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2m8n9u1 gk30i2bm kacl4c (ajrd:s x5p500 rpm. Calculate its angular velocity 1s:p3u l x9k mrj20c8kgc(d abam54i nin $rad/s$ $\omega$ =    $rad/sec$
(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 makezwi*y /34loaoqj yj6/s one complete revolution in 4.0 s (Fig. 8–38). (a) What is the lineaoilz y/*qayo 463jj /wr 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 mko:sj ; n:2ahEarth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ofzvngj btxbo(2, a9kb 15ube+: 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 pawc o:2vkpn(i,l2h89 wncv , cgrticle 7.0 cm from the axis of rotati2gln( 2, k:vvcicpcww,9n8 hoon is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel ac)q9w/ jzfpvgyw8hmq0zr v5. 0 celerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s.v85 9rw v)zq0/gh0yfzmqw.p j 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 radium6-aqd+1dmr x s $R_1$ 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, astrlazgb(14hi ,zb3rn z;onauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder withbh a1zn lgzr3zb,4(i; 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 uniforml(2id9h ppdg,vy from rest to 15,000 rpm in 220 s. Through how ,dig2pd h9v( pmany revolutions did it turn in this time?    $rev$

  An automobile engine slow*4kf)i gn0crhj qc *,hu3cc. bs 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 tested06dqhg:u xn7cciet.u3m,bw 9 for the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0nu0gh, e9tc 7mbx i.c: 3uwqd6 min to turn through 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 diametern mcyrx9u8,5 d gag4,hpyj 2j1 accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in th92gc81ru gma p5j d,njy4xy ,his time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 r ls nkodg;8a;f:v4 *vrevolutions before it comes to a stop4;:8rfnlko ;* dgsvva .
(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 redm0* ebz/fn4h w 7dgm/euces its speed uniformly from 95km/h to 45km/h The *4gm/efb/hednz m0w7 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 eol;w dkhj67mnv2e /yuy9;)w as the car reduces its speed uniformly from 95km/h y;2ly;k w/96wen ehvd)j7u omto 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when ccxfb7xbomu8/psq xs l-9);jrw 8i 0.b limbing a hill. The pedals rotate in a circle of radixluosfwi8;b/xj8c)r .spb m-07b 9qxus 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 the end of a door 74 cm wide. b+y,dg+x81uca 1 l -zki*e(i l ma/igoWhat is the magnitude of the torque i1 bd u1z*8+-iliiaoaeg/,m(+gk yclx f the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about thlj hjbm,r/we4 jt+pnixce .0.5cfg9 6e axle of the wheel shown in Fig. 8–39. Assume that a friction torque of/,6tjh+ 0jn5l pem rwei.fbgxc94j c. 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, k+zpl.m883m2 ju cevf are attached 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 relea pklumcm82j8ev 3f.z +sed. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine req ognhg0fv 99/nuire tightening to a torque of 38n gfghn09/9vo $m \cdot N$ 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 inertmjdjg+0 2( wc+uoxg d4ia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its center.(co4dj 0gjm2w+g+ x du    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in dia wvgub2yb/d64; znwatt9 9, mrmeter. The rim and tire have a combined mass of 1.25 kg. The mass of the humtz b/vy9uw; nbawr , 946dt2gb can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotv j9fia /y.w*cn+0huvt h(x4 xated in a horizontal circle of radius 1.2 m. Cav./0uv(cx 9jyhhnxt4if * w+alculate
(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 angulai1nh/da7 fzzlktt:wf k9 d67.r speed (Fig. 8–42). The frict7l:wfitkdz f 9zn 7dthk/61a. ion 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 objects showgjb byjuu+(d7h. hv ew18sfxc-1s30p n in Fig. 8–43 +dp0s3 w .x1j8s7jcuhbh1yge(ubvf -about
(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 atoms wgq)q7tyt.h, is1 z t;.e )losghose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at thzs r5war1wzq (98 k8bgg55 wxxe correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a r5(zag s1xb9k5gz8 5w wxwr q8mass 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 8.50 cm )mi-2uzc bl)b and a mass of 0.5-bu m2 )cl)bzi80 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, accelerating it 3knilns4 q)kqbw8n 6q2vv0 8x7)prrofrom 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 tang,bbdmr *:xf1 eentially 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 mr,debm* x1 fb:ass 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 rpm is shut off and is ever, s6. uuwm8vmrc/ gxy9tv+5dntually brought uniformly to rest by a fru,wu 9t5rmrx .vm/v cd6+ysg 8ictional 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-kov.e u:g7e 2lhg 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 l* u*n)mvv :q (sfho8tp/(hy.(d nd czforearm, which rotates about the elbow fhy *( zc/tm lq(v d:8 n(u.opsdh)*nvjoint 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 kt6z r8x8u( n1fx 4ztu1;2cewthyvg0 long thin rod, as shown in Fig. 8–46u ;xtwvh 4 rtn0xgk zz12uy868c(1eft .
(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 ua:ems6ckq6qka 61 ;nva d0f (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 acceleb)hq4f0*pef;; 3egd gbfq:9jnt raj0 rates the hammer from rest within four full turns (revolutnqb0d0f4 *jpahgq3 gb jt) f;;ef9re: ions) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of ifzj; kur1.z0b3 /xmzy nertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 5ffzntvj1+tp3/q8*k zf wvz. 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 rlqz;;r18(x(q0 z ptume2dwal olls without slipping down a lane at 8xl12a(qm 0 u z(dqz;;erpwtl 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Ea35 yhufqn9 8ipq ky6a.lhri;6 rth with respect to the Sun as the sum of two terms,ih.n 6; yfk q9hu53q6 8ryilap
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius//h 9ymjv0zhj of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution permzhj09h/y/ vj 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and r+ 9.crdri0a fpolls without slipping down a 30.ia0p+r.cf dr 90 $^{\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 s gw;7j.ylwyhuw 0kpf j-7ln0-tarts to fall and its lower end does not slip. What will be thelpj 0-juykw.0fwnh77lw; -gy speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg o v rge1 -*c;z8k4yuyuball rotating on the end of a thin string in a circle of radiy u-z rv4;cueo 1gk*8yus 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 cylindrica9 / ku*lj10iafm+ot uml grinding wheel of radius 18 cm when rotkt9ufa 01oj+l mm/*u iating 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, han5dlta3ym;oy v 1l7e, dds at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48,d 1;ldyoa37eymvt l,5 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 inerti0k0acqg7 waz 3aepw ;-a by a factor of about 3.5 when changing from the strak7a00pecga-z;w 3wqaight 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 rotat7 nq4zkl0ct 6ac:tqt.3 xqf h,ion rate from an initial rate of 1.0 rev every 2.0 s to a final l3a nf :tq cqqh 7k0xt4zc6t,.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 apdjg;6o s.o :fround a vertical axis 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 c .;fo djgsp6o:lay, 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 momentum of a figure skater spinning at 3yo23 m) a4r+dk dmpy4b.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 m v(ck-44y+xk,dhnl9h jn-gf zomentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped on 0ha: (d ls*gly6mthe+to an identical diskylh(t*h 0s6a :e ldgm+ 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 d /t*;yjewfg; pp5x4.rdnj3p $rev/s$ 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 a7f7vp +v*ljvot the center of a rotating merry-go-round platform of radius 3.0 ml+o f*7 pvvj7v and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely witffy0p z/t5z,,p. ubt ii2uzocu,oh5;h an angular velocity of 0.8fi0y, o/p,zip5f bhz u z5utt2u.oc, ; $rad/s$ 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 abo8apb4y c mu:geo417fput 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 momentum, what would the Sun’s new rotation rate be?(round pp eumo7 : 8fgayb41c4to 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 inhbq-2aedyk:fi;2kij lt8 .a0 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 t2v5 bd6oq8j bso3fw .$ 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 lenp j 2 1vzwdyti17o67 .3ewu/hwf)e without friction. The moment of inertia of the person plus th e6njeiof p e/dv7uw1t wwh2 3)y1.7zle 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 6.5-m diameter merry-:vrjp- w/dw-l go-round turntable that is mounted on/j:ldpvr w--w frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope6c:kjf76rlaje 6m*hi8 co ij( 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 ihe66c :(licrm6k7 jf8 j a*jowithout 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 tha m-d,n mlhiu:wcc6*t4t the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, t 6,ccmud t*wmni :4l-hreat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates frs) 128p,ye(eghj jca9e-ht *kn 6eulq om 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 of a uniform cylindw 5uoxqpz.1:d(0srw eer 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 the mwr1(dues5 .w 0z:p xoqotor.    $m \cdot N$

  (a) A yo-yo is made e3f1 xj)wgh:p of two solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches thwx: )e1fg3j hpe 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 r kxk x3+8+rqz1 smpxe6ptf65 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 8u h;ov zf,9oiw0n q+ywith mass 8.0 times as great, were rotating at a speed of 1.0 revolution ev0w o+yoz qiuvfh8 ;9,nery 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a lowds 4cd3d5p) ui-pollution automobile 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 unifordip3 duc ds54)m 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 0/90sulgrb7cemw 4 an;i 9azhan $H_2O$ 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 surfac )vohj zzbg 7n4r9g9 x7o1ybq,e at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we :.(a f jds)s0n)h:ipn 0q2ra x j;lkqyignore 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 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 t idj2q )a:nnp ;.0(q:s0 rxfhay jlk)she rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and 78j3j( pz+lawysz gd.we want to exert a horizontal force F at its axle so thata+j 8zpy zd7ls3( jw.g it will 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 4hl(s nwc/1ceq gs9i 8a flat road is making a turn with a radius The forces acting on thn w8s/hg(slcic 1q 9e4e cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begins 4o2p-0yu( q6xzfsfc y whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate 6p ofxf0qs-c(4uyy 2zof 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as t7kwzq1uyk 6x, hin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretw,k zk17 ux6yqched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cyh.uxph-) )l)izg ,emllindrical plates, of massi ).xuhph-l )l,mg)ze $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track 5 blb37 uesxn9uo-r4u of Fig. 8–58. What is the minimum value of the vertical height h that the marble x57ubos-3eu nrulb94 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 aocvsgt t, 9;e968w7 r hxyzdl0bqn(, not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speeol1rne g- rza0*fl:q8)t7k) h hx1:ef* wxufhd uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. hrtl7l)*a eg* fruzxh xwqe1k)-f:o1 f hn:80(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