A bicycle odometer (which measures distance traveled) is attached near the whe(ubtj7r/ps:)( ilxm tel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?r((7mt s :blip)jut/x

Suppose a disk rotates at constant angular velocity. Does a point on the rim hap2zf4v i buym4 l/6tgz-*ft ,cve radial and/or tangential accele,ucvg 6f *4fy - tp2izl4tmzb/ration? If the disk’s 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 describe-boqpq:+ -+ 0qq0tgfzp 7cfvbd by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater 8 /up13sscueqtee848 j8xzq ntorque 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 behyf jm. +s8sy21 eg/kkts6qz6xind your head than when your arms are stretched out in front.86z 6sgsky+eqtxm/yjs 1 2f k of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pedayddzg oz k2 d*fp74-9+t6i4c7np oos )ryzc-ml cranks. In which gearkz dif-pz rmt *o-g6pdzo) o4cn247y7 cd+9sy is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to r6q,6qc/ djh1rkwwv/i 1 yaa, nun fast have slender lower legs with flesh and muscle concentratec ,/r,1a qavnwkhyq w66dj/1id high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narro/r2 d8p2qij 1wktvp 0tw beam?

If the net force on a system is zerb3 )7exx(fh .nrvxhig6j. +pqj0c0u go, is the net torque also zero? If the net torque on a system is z x ibhj7nu.q(cefrhj+g xx)pv360 . g0ero, is the net force zero?

Two inclines have the same height but make dik lx3ct/w8u ,yfferent angles with the horizontal. The same steel ball i3xw ucl/ky, t8s rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) ak ) 3obcx )a2sy/-apddown an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bok)pcxbd /aa)3- oa ys2ttom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They stark obl+;l18bhc t from rest at the top of an incline. Which reaches the bottom first? Whichh8 b;l+k c1olb 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 cons dm5( jlcdu vf6,mxblj*:2zr0 erved. Yet most moving or rotating objjf02*v5z ,xdlumdb rc:j6 ( mlects eventually slow down and stop. Explain.

If there were a great migration of people toward the E0 jz/vacvw26earth’s equator, how would this affect the length of the da2e wcv6jvaz/ 0y?

Can the diver of Fig. 8–29 do a sommdu+x(xv 1j,tkky0*j ersault without having any initial rotation when she leaves the bojyx0 ,tk*k ux1mdj+( vard?

The moment of inertia of a rotating solid disk about an axis thrfsamjx;gep1 0.u4n wq54r) nhough its center ofps;4 n1gq5 x 0mnfrue) j4w.ha mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg massqd5k)i i4ipe6 in each outstretched hand. If you suddenly dr5)i k6depqi4i op the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass3 akg;dfn8*v(rr g* fk. However, one is hollow and the other is solid. Describe an experiment to determine wn rgdkvfa*g; k3(rf8*hich is which.

The angular velocity of a wheel rotating on 6zmt c xe(.uj,a horizontal 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 topmz,6(cxut ej . of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotatn,,w etpjd 1g/h/vs0eing turntable. What happens if you walk toj e //v,thpen0gwsd1,ward the center?

A shortstop may leap into the aii.,gbzod sopj24ky2 0 r to catch a ball and throw it quickly. As he throws the ball, the upper part, ysopikd2bz204jgo. 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 conserv)7z j qqzi+ sptz+af.,ation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways thq. q)i++jzp,7 a fztzse second propeller can operate to keep the helicopter stable.

  Express the following angles in r-g(wg prqk/zu,ufg*ra -/ah w3 2ao8dadians: (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, usingx-2jhq x5ausca 2l;t7 the information inside the Front Cover, qh2aa5 -xjuxs7 tc;2l the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam divergesw;8e*3/ac ybgzcz j1y at wzy8/cygc b1a;e*jz3 an 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. When the motor is t 7bopj9rh- g+eurned off during operation, the blades slow to rphr7-jg o+ 9ebest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on7cwmrk +3ne,i eh44wis 6gda; a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, w enhm4 ei dg3s;wwi,c4a +7rk6hat is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions do tyo1d jyy /a1i /moj70 x8maq 725ccsvxhe1s/q7iymcx x vojm02 5/ o1 ya7c8adjy wheels make?    $rev$

  (a) A grinding wheel j6jyb5(o avae9gb:g :1w 5 mpv r4bbo20.35 m in diameter rotates at 2500 rpm. Calculate its angular veloyg5: e4bbv r agjv6 b9a21mbo:5wp(j ocity 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 gp,pa 158 ox6fc k9zbjs (Fig. 8–38). (a) What9apjpg 8zx1ck o,5f6b is the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in it76f;p uo /eik lguhd99xd,tm+s orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speph7 ,brd:5gpss5e ln+ed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0t:9ou,wtb( l vgfq d38 cm from the axis of rotation is to experience an acceleration wt d:,(qou3v b98ftg lof 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its cen6k); nwm7fm : td/djdqa1 1dgster from 130 rpm to 280d d7sj1 /d mtfd:k;6w)n1m aqg rpm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiukce:xuq (hijqd8)7 8ms $R_1$ 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, 9 fq ,v+e bop2vzvaegb5+km; 0astronauts 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,2 ev+ o5m+pbf;a zvqk0 vbeg9 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 uniformly3/zp3u(u vm omsddvn :o.iomq;c7 68i from rest to 15,000 rpm in 220 s. Through how many qmu v67d;zmos383i uodvp:c (oni.m/ revolutions did it turn in this time?    $rev$

  An automobile engine slo+ ofkkc.a7-zc ws down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling 1ympz(x 2lba4 “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before ry2z 4m1p(bxal eaching 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 cq.g:).kn pcts. Howc: nkq t)p.cg. far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 150 3jxnf 4g(lgz90 revolutions before it g39 l zx4njf(gcomes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces et/jkd1f - mb9n.io+hg4sp+m3 7 oovqits speed uniformly from 95km/h to 45kinp.b7oo sm3 j4 +ktf9 g deom/-v1hq+m/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

  The tires of a car make 65 revolutions as the car reduces its speed unifo ,lx3.szkco0 i ot zjpk95: zv0wqqk op,3-or.rmly from 95km/h to 45kmxrktc ,oo 3q 0 ,kvwpz:-3.5q0izjo.z9kp ols/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 w , 0d+ wsn8bg(6 rdw: w-c iaeyp;skj,wq,lv3dhen climbing a hill. The pedals jdlap8b ; iw-w ,k dwrces3: ,nsg,+6qw0(dvyrotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on thwehg3ue-0ey( d3f. d j-qc3whe end of a door 74 cm wide. What is the magnitude of the torque if the force is exerteg ej3hwqy.0e-uh3d3c( w - defd
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. Assu .8+2 xoae44kk .yutu*v*)quabpdfiv me that a e*ux v+t . bu fkauq y*a)o.v8kdp2i44friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod which piv49jj2 m) zsndm58 aainr+; rrbots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude d8a n5 bmrjmazrs+;r2 jn4)9iand direction of the net torque on this system.

  The bolts on the cylinder head of an engine require ti17xf*ew t t:gtc*bfh2ghtening to a torque of 38gt :thf*txw1f7ceb 2* $m \cdot N$ 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 radius 0.648 m when tlb gznpk4y 9 s5jln.yk 8 ;,zys(q;e3phe axis ofkq4g l e;(zsy8.y yj5bz knnsp9;p,3l rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle hs053w j8 rjvswheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of thswr 03sj58h jve hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the endnqvi3 bxp883jc: 5zm g5) befo of a thin, light rod is rotated in a horizontal c)zj ve8f5:iqbbo8 x mgpc335nircle 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’sst-l8rje6 h8l wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clays- et8l r6hl8j 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 24utd1 1x3tmlbnay++u l7ei z of the array of point objects shown in Fig. 8–43 abollu ni 41dtbx1uz3a7mt+y +2eut
(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*-0lbmq,,* wbf xmm fq 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 at the correct rate, e-h0)v+z*c6ll oydm :y7to: gnd q(qjongineers fire four tamy)+o7d 6 q*zlt ohvdog:-qyljnc0(:ngential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass ofxwr*vq l;cueej. nl x or;(y8)i8k 2f:9fa1hh 0.580 kg.ox8l wrah1eyu j82rlk;vfhce(n)f:. ;q ix*9 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, ac8sbxwj)n65d s celerating 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 tangentibc/21zwhlle3mbv c-;ally 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 hasbc;l21mlezb3c -hv w/ 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 rxc: q qjpy;*2kue brvn0/ w0f(otating at 10,300 rpm is shut off and is eventually brought uniformx :;e(v 2nj *0kbpyrqq/ 0wucfly 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 a*w1ksmtq ;/k - -z xn,j7kgdsi+dtc s+ 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 tw( -ponr+z: aiex p(6bhe action of the forearm, which rotates about the el6 (pnrz epiao (-x:+bwbow 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 lon7vl:j mwg *zcb;b cu16nm9gb9g thin rod, as shown in Fig. 8–4 * 19b9gv mjb7z6;lubn:ccm wg6.
(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 masssbed)b+ xjof,(+,wktx f 4mb2es, $m_1$ 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 four8xbj cb.u19sai))1sricrg3 xp n 9bd. full turns (revolutions) and releasa8r)d.j)bnci9irbg 3cp us s 11b9xx. es 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 inertia lhj09 jwyp .p7 yhgakz7dd,7/ 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 devel9nn.x-v u s z-z5kimcz-d p:1lops 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 wi-4 h stkjml2j z;: /y:nojxr3dthout slipping down a lane a j nykx2m j dth:-js:r;/z4lo3t 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with renw(xxmwt 3tplo **0s(wmv :0 qspect to the Sun as the sum of two t* v :sln (3*twqwmxxp 0o0w(mterms,
(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 of 7.50 m. How much h. c31* optegehp 64ainet work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume1 hgc.eh*op64 tia3pe it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls wit2k; ,1wikiytzhout slipping down a 3yik1izt;k 2w,0.0 $^{\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 vdur1vbyi: 8 p c6 -xd/kau*5fcertically on its tip. It starts to fall and 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 obuc/v 1k5 fup8rid :*xy6-da cf energy.]    $m/s$

  What is the angular momentum ow9eaoxza roe ,--5y 6if a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at w9z oxa5ei-r 6- e,yoaan angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylzt-0 0-rone *z.my yc7nzlgdap9(uz;indrical grinding wheel of radi- n (0p7e zz9;-.lgzc0utyan yz* rdomus 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, 7gx+r xtb*qc:1j7 qlion a platform that is rotating at a rate of 1.3rev/sj1+g77lxx: qqt*ci rb If he raises 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 in Fig. 8–29) can reduc l,.)ri(t zhtm.ptb,0zz1d ine her moment of inertia by a factor of about 3.5 when changing from the m.pzz)t.nbti ( dz1l0iht, r,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:l42o 3zs kcegur4n 3y4z9uju rate from an initial rate of 1.0 rev every :ku4yr u 4 z9scoejln23z4g3u2.0 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 ptb(*wq,iuj5ru 5rey0 0cvb6at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel afti*q0(05,ev6cw jurr b bpy5uter the clay sticks to it?    $rev/s$

  (a) What is the angul in1*xwdp4m ftoz2, :v*bep0 g*bd*+k pfvyw0ar momentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular m 3od mlc;by3(93p epjc.eyb8komentum 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 onto pyi;mxxfd,a*h :gx *- an identical disk rotating at angular ;ga:-yx*xpdxhimf*, speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.z1b9z5mm l6: m pay.ux,u:imn4 $rev/s$ 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 kg8 i vnu*,(mxlm stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inerv*(un,8 im xlmtia 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 with9-symd/zjefc s3 : x6i an angular velocity of 0 yf9 6csz/ijd3sme-x:.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 white dwarfiqm/s0- 0ewu+(91khpnq dmhh, losing about half its mass in the process, and winding up with a radius 1.e9w hs-di k0+1 qpmnq/0hh(um0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in zer77up3eakq 2e-88i obj2fd 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 al v(+7ayxo 1b$ 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 dshubs.77/kbyjmt, ( rotate freely without friction. The moment of inertia of the person plus tht,s .s/kh b(b 7y7ujmde 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 ofv-alf1: qm zs. a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a mo mvs .a-z1:qlfment 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 groyv -j f b:7- c(xmlv*:fscg*ltund with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds -cysj vcm:**f 7t (gx:- blvflfrom the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth suc;d nz/(vggxt85i +u plh that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular m/(gt ;+vz ixgdu8p5nlomentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate tj i7.5f:i mpvof 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 -x,p-pv zsog+0.20 m acquires a rotational rate of fromp,+szv- p ogx- rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two soldiv ;jzj(h;m2c a b(:pid 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.b h2ijmdc(j; v(:z a;p 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 the angular speed of thewt*u bhgo6x2 6 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 wie 1) wcli7ymud.a:x7c;kb/wgth mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to ukmw :; gl1ebdw.xyc7a ci7)u/ndergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it turig t2e4xh-rb w3x 19o use energy stored in a h49e 3ug-r1 rtxxwhib 2eavy 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 a7rn mus:49szv ous /8vn $H_2O$ 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 a1qz (-u+ ,y0x cytt x4gulelj5 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 length L can pivot freely (i.e., we ign huv2*u r(av(bore friction) about a hinge attached to a wall, as ih(u*ubv2a(v rn Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, anmo.zn5z. l b cg5 a4bn51gm(gtd we wa. 1a b5nob5t g(mn.4cmg5zl zgnt to exert a 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 tuig cx,w5lc y/5mg91tq1r*z lg rn with a radius The forces acting on the cyclist and cycle are the norl1im5rty gz*g5wl1 9 gxcc q/,mal 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;61 3e ma7emjpasn(ke:;on pm-uos h2 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 where does the torque; 2(m s-6sp7o ao pnamhe 1uekn;mj3:e come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms lndm +i :89-cdd. :-rz pihmlzas thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms he-dc pn.r8d+-d mh9m:zliz: i lld tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrq+zt n zmou;)dr:a,7vical plates, of matnromq 7)a:,d v;z+z uss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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. *(yqtu53uxu nx di(6o 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without le xuy3x(*n6u d(oqit u5aving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but wqb -t2n.kdywy(dhp 0d75 ok6 q1(g wvdo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces ,mdly l61i,xmits speed uniformly from 90km/h to 60km/h The tiresmdxl, ly61, mi have 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