A bicycle odometer (whic3*w2fr0 r+uqmz s nci*h measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. z c m0w3+su f*rrqin2*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 9 v2g,0dr(ey hgkuvi)zx: .ylthe rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/oe0ygvi) (rl,vxgh: .9 d 2yzukr tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a sin3cw2ss l:nwn9emi- x 1gle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque tx, tr/x2c,om ahan 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 jjlm;-t, va*wyour hands behind your head than when your arms are stretched out in fr- ;t*vwlmj aj,ont of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets vee)pgn l :opjc:0t z 6q8z3h2at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which glgze :cvn thpz6280p:e)q3 joear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to runloc+3g1vq b8 koa y))f fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8kcg81q lf yb)v)3ooa+–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beam?) j2zflua 1wp37-kv w; w,vosk

If the net force on a system is zero, ixrl3 4s)*wk*ix2tq uwjna*q. / d fruzo9f+;cs the net torque also zero? If the net torque on a system is zero, is the net forwclj orx9*u 3kuw rdznt sfq*4xi2+;. f/q )a*ce zero?

Two inclines have the samz q0og1-hetnct0g.: de height but make different angles with the horizontal. The same steel ball is rolled down each incling:z 0toegt1hq ndc-.0e. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) clsie4 4 (;8/u,2hl yrgopahedown an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater sp ao/8ei4 ch,hp4lsr2y lue( g;eed 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 sta nqj5k2xx10airt from rest at th05x1xjan2 iqk e 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. Yet most moving or r*3ebh6 zw2agc otating objects eventually slow dozca6b e w*2g3hwn and stop. Explain.

If there were a great migration of people tqb z)7cyps .y4oward the Earth’s equator, how would this affect the le)spy.b 74czyqngth of the day?

Can the diver of Fig. 8–29 do le q ai,:tn1j9 z ikg 5c9+5km8as;uswdk2-y ja somersault without having any initial rotation when she leaves :2e5aklsiwks5-y a998 jij+cz , g;1kt qdmn uthe board?

The moment of inertia of a rotating so,linf or4ni2s o37 x1vlid disk about an axis through its center of massf,l73 oi2 rsoin1xvn4 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 rotatint /rvbdo4 jo5,g stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular veloj5d/orvob4t ,city increase, decrease, or stay the same? Explain.

Two spheres look identical and ha4yvd ut q e.w)p85f6v./f vws 7t7tnkmve the same mass. However, one is hollow and the other is solid. Deskutw) 7tpnysve/.57f.dq6 v8 t v fm4wcribe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In w( ugevv- +bp, elh5-hy9n9cxny g/ 0rzhat 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 the wheel. Is the angular speed iv5-cznrg9hbeyy-he ,x+9 upl /(v 0ng ncreasing or decreasing?

Suppose you are standing on the edge of a large freely .yo znbj /6o5gd6rv0 protating turntable. What happen6yovd /b5nzo p6jrg0. s if you walk toward the center?

A shortstop may leap into the air to cat k:p4(ua:(vx trwt t2kch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite tt p r:(k42wvxu t(ka:direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angujjh + ;h6hlh,elar momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or j,e;lh hh6hj+more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 1f/jz 5zhqn,1m x d0dg30 $^{\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 Earth9jp xws xwl6pa( 3b(887qj 4a www)phk because of an amazing coincidence. Calculate, using the8akj w s984jh6 3((w apbwpw qxp7)wxl information 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, 380,000 km f rbz:oh,t*ak/rom Earth. The beam diverges at a a/ohtk*b:,zr n angle $\theta$ (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. n 4hq)rz/z3qrfc dr5:q bo /,zWhen the motor is turned off during operation, the blades fnorqc)zr z:/4h d rq/b,5 3qzslow to rest 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 3.5d a)v gpi6d)6b m to another child. If the ball makes 15.0 revolutions, whaadbg6) d)vi6pt is its diameter?    m

  A bicycle with tires 68 cm i g y/sgcj,uh4,n diameter travels 8.0 km. How many revolutions do the wheels mak gs/,c, huy4gje?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotlqzh8+ k g3mh12hwhg(ates at 2500 rpm. Calculate its angular ve (81lkqhg3+2wz hmg hhlocity 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 makesj *dd5si(jh )c one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m fro(*di5sd jchj)m 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 nr x44td+hd+s3rc r8o the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poin0(s8leg/ h eh-xr.*lxi x:q rsp)a-tnt
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the axsi0bkep- ehpv3y 3n0j bdy 9h ,;hb0,iis of rotation is to experience an acceleratvbhk0sb pj0y,3hneyidi 3h0 ,be9-; pion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 yh9mic 8 emg99rpm to 280 rpm in 4.ge9m9ch y9mi8 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 radius xpa2:)e8a16)d f7rnkh zrtew$R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apoll9n7fg.*dh0dgcmj 9 imzh/0 rfo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At thif*h gf/ 0.mhdgd7cmr n0jz99e start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Through ja,4dydg5b8eawu; vc-6 4acshow many revolutions did it turn in thiua-5 ad64ajv 8gwbcc ;e4sdy ,s time?    $rev$

  An automobile engine slows down from 4500 rpm tb y/wx19tct4ceit- le ym:(d6o 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flia dbqjf1)n eg1 wt ww +;r4y4hkl:o66ying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn throught1fbl6w1o qkad)jr +4; 6w:nhgyei4w 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 mv041 m22j7ag 8rcmcoeotvc 34;xtok 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of kc1m2cj4o xo tt;24 7 vo0m gecvr3am8the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rr0l-mc2zngnuhqll + q g+h5z :+((idaev/min It turns 1500 revolutions before it comes to a silhazl l+-q0qrm+nu(2czg dn hg5 +(:top.
(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 revczp. ,h8u l hs vntu) /:km24pdk/2yrjolutions as the car reduces its speed uniformly from 95km/h to 45km/h The t2ucd,u/mlhh :2jtp skryzv.n pk84 )/ires 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 carz0ijnnntkgmc/ 5b /.1 reduces its speed uniformly from 95km/h to 45km/h The tires have a diam gn/k05jnctinm z/.b 1eter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbing ptddv89l,85v7 mu w rda hill. The pedals rotate ind9l7p8td d5 r,u wm8vv 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 N on the end of a door 745vq27 6mhschanj,u: mj 3eva, cm wide. What is the magnitude of the torque if the force is e:cvmnm63jehj 2, ,7 a5qah vusxerted
(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 wlss ;t8vx4+xtheel shown in Fig. 8–39. Assume that a fri8s tl ;tsvx+4xction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are9 f3jpsyun*slep p+q) yk2)db 4-wjo , attached to the ends of a massless rod which pivots as show9s jpq fj4eyp))p l ok,nbu-+2*y3dswn in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque 2v0 x8 kgu8:hdhbsrs8 of 38kgxs b0:8vh8 uhsd r28 $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radk w7k1ivo-lxs lhki5 a euyx 3.n 26*jz2qf)s+ius 0.648 m when the axis of rotation is through its ckkslz 2owhsxl)3i n q57jxa+2 e.-yiv6f k1u*enter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm.w qgx m*e3,uad 4wg1k in diameter. The rim and tire g.xqg,4wek 3md 1* wuahave a combined 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 i/,gig ut-t+mz s rotated in a horizontal circle/,gtm+- u zigt of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s whee bq ld-/5u6tjj d1fynb-62gwbl rotating at constant angular speed (Fig. 8–42). The friction force between her hands and tljq6td b bbg6u2w-/-dfy jn15he 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 shown in Fivx6mie9 +xv r7hn+ ny4g. 8–43 about h m 6vnye47x+rxn9i+v
(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 cv:q8i r/.s+upr)z avtwo 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, unifo263k bx ezph3g k/pmzk02;pberm cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is ge 32b0z h p k;/p2xzkkm6b3pethe 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 rad5,ip,sum* g hyius of 8.50 cm and a mass of 0.580 kg. Calculate g*uy5hp m,s, i
(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 from ij5c6ebx 9 bn 1*ztv y,3kr:ss,ga.rvrest 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-rou;b((js o7fqpb nd and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torquojf q;7bps(( be. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is en *,xan 8a2r s26se t4firc ;uzjbln.6ventually brought unif6n zaa,;bn6 r4 xjnf 2e.tus il28csr*ormly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates *qwztt(v,( vh;o9hne /kd ji4a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of tu-;gh -rwb bd-he forearm, which rotates about the elbow joint under the action of the u g -;-wb-rdbhtriceps 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 cakhrs 07za s x*t-oag73n be considered a long thin rod, as shown in Fig. 8–46z0rso*xa-gst3 7 kha7.
(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 two ma- 58tdcr hb-ljmq*iw/i z ph71sses, $m_1$ 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 acceleratesd qn1(*vs kwi+ the hammer from rest within four full turns (revolutions) and releases itwq+nv1kid s( * 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 mou d h,cx88/wm;plv 0rmc 2-typk;e/iw ment 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 engine0gv,/4 e3zs hpfstq s8m vq0z/ develops 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 wi6/pg dis67ap2imr ,muthout slipping down a lane aa i ,m2/ur7dgis pm66pt 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kineticbcs7.w fi( 6ic 52xwau energy of the Earth with respect to the Sun as the sum of two termswc72sxfi .b6ai(u5 wc,
(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 2w)*8aweapyr mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? 8e*)2yw awapr Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from restjx /gn8lh lwj)0td3cojt1/s 4 and rolls without sl8jd4)3t1 ox gjl /0w ht/jncslipping 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 ft wwmk 3v9p iz.qiv(fz 7*z,z-all and its lower end does not slip. What will be the speed of the upper end of tv*wz ,-93p zzi.ft vw(i 7qzmkhe 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 oqwm:m(0 u* eqhw+ t4boe95gaqf a thin string in a circle of radius 1.10 m at an angular speed of 10.w:q(tqoq5awb9e+m0 *emg uh 44 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uni*xs4ghwx): w 7x6 bppzform cylindrical grinding wheel of radius 18 cm when rop6 :g4wpxx7bs)*z wh xtating 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 platfoz0z dw:-y08(lbpsgsxcd . (sh rm that is rotating at a rate of 1.3rev/s If he raisesd.(b:z c-hp 8wysx dsg(0s0 zl his arms to 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 ini(b(aipc h7 ii9e -b3n Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position toi 73i(cnhi-e abi(9p b 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 rate xaz9;sh-8pzoj 1th(.msw +cmof 1.0 rev every 2.0 s to a fina 1(ch8oz+ mz x9ja. hts-;mswpl 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 frroh f36bvoh6 )equency 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 disho v6)3hr fbo6k 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 momendfv2*ws5vx 6ka x55 petum 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 momento616n hx.vp ecum 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 inoaq3x :2n-lmwo,wfq2mb,ch- .i9tz yertia I is dropped onto an identical disk rotating at anty wom-o,xq,2-i 2n azqc:flw3hb 9.mgular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4iu9u(nn+1+q8kmp 5wt . gomn1z8xyg4js3 yfq $rev/s$ 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 a bnp7 p5 by;g oz*,1)a)ttfokthe center of a rotating merry-go-round platform of ra 71p;y,*b )oa gpkon5zbtt)fadius 3.0 m 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 rotatiniqnug2:a8fk u7v l81 ug freely with an angular velocity of 0 81ki:qfv 2ung8lua7 u.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 collapses into a whsrf::;t1fz fd)l *rql82x ri r/i /jrwite dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carrieslw)fdqrrx:1*r/j/ifr l f28i;rz :t s away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 120+obd p2(ep1jd2tvm* / bym m7r5knsn( $km/h$ 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 1js- ov5agfwcj)8l+ eoy kv11$ 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, tha)8i1 *omhstb n v6s)w0htbz:ct can rotate freely without friction. The mome m*b1 hw)8tno6iszhs)c t0v:b nt of inertia 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 t-er gg/x,bs oc1r;(j ehe edge of a 6.5-m diameter merry-go-round turgx,/;c rsg-(breoje 1ntable that is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying on th0f5ox z ek2p0le top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. Thpx5ko fl0ez 02e 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 s4ma1m c;sn-)rby gcq; k7fo9wame 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 l7n akb;gy sr q;cmc19f ow)m4-atter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates fweb 3x u( 23uog fn0 zw9b3sr5*he8envrom 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 cylinder of radius 0.20 m acw cb2: e77vdnpo9rs ga9*0eklquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Ca2ov :7a9ekpe 70cgw9*lnd srb lculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two v 64xwt yj(l5esolid 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 an tlw6v5y4jx(ed 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 1pw+- cy +k)fjlk-y s5/jfkelthe 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, wemufk mfni( 8z*rn2 88dre 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 sp *kmn f88 (2frzmdu8nieed 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 automobile is for it to useq.ut tmhsth3 4e4rhrz 4qbjmf;3a+:x(m, fd ) energy stored in a hea 4q, thtfh 33 d z).smebjrqmfmtha;4r4:ux +(vy 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 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 0iq,s wy4 *owp;ya1kban $H_2O$ 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 rollinw7nnf t4 p j:chl:,3- vimbnr+nk:5c xg on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and lengm9b((-zplm b mth L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is -b( lmbz(m9pmheld horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is sudtki(r 0 ;o)standing vertically on the floor, and we want to exert a;ri(0 uo sdk)t horizontal force F at its axle so that 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 a flat road is making a turn wit v2+2znt 0rmlmh a radius The forces acting on the cyclist and cycle are the nrtl+zmm02 nv2ormal 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.g:j*mbpuo y/ 450-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and wher4gj:buo *m/p ye does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a 2pkbc jmy : k ntob2-+t9-goj3solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds foryokkjg- oj:tc tb3p9nm -b+22 a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, +n 77qwq nhn )dvz/ jbz/x-tq/of masqqn/zntn+h-d j/x/z) 7b7qv ws $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fig. 8–5uil r4dr.l6p2x hn+f08. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without l2+6 rlld.p iruf0h nx4eaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do5qukf 8qy+7v q not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed ,oil)g asbu4 *; uvp4;9skxsglqf1+nuniformly from 90km/h to 60km/h The tires h o;a4,bp)q uv9+sunl 4;gl1s k *ifsgxave a diameter 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