A bicycle odometer (which measures distance traveled) is attacl)0otv v04n2xx9qt s uhed near the wheel hub and is designed for 27-inch wheels. What happens if you ovs42 lt0q)9x0v nu xtuse it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constp+k),lmtue sgf04u dc z:0e1bant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linearku0bz+dmt0 ec1 g e u,)sp4:lf acceleration change?

Could a nonrigid body be described by aze+lw9t 7 5v-4v w:lds2impm z single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a great5qhy tu rr t0sn 5k399gm-6imwer torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind yow:m vro:1lee4ur head than whe:wmel:o v41ren your arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets ata1,3l jr-0pupg:ptt u 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 wp0tt- pulur:g 3,p a1jhich gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs wv19kiaf- bmt4ith flesh and muscle concentrated high, close to the body (Fig. 8–34). On theai vk4m9fb-t1 basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beam?6j9t -3vlh8 qskqd l4c

If the net force on a system is zero, is the net torque also zero? If t/pe if5p0*jf,ir- jij n76hboooh 25 mhe net torque on a system is zero, is the net force zero?r06n5* mi efi7i ohjjp2- bh5oof/,jp

Two inclines have the same height but make different angles 6i zehdv9 c*u/with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Exi hu9z d*vc/e6plain.

Two solid spheres simultaneously start rolling (frh4avq*f t1s-i-)clkwy7+d fd om rest) down 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 speed there? Which has the greater total kinetic enwqi fs-d*ck at)1lhfv 7y-+4dergy at the bottom?

A sphere and a cylinder have95,jq(b9xb5x sau ,r6 jlwfy:jpvi t4 the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy ayx bwb ,fq9xt9ujis5jvpl65 ( :ajr,4t the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most mov +.0mla4;e5nvgfdvzf+8 u kjning or rotating objects eventually slow down and a+8 dzj knev+.gf;4 f nm5vul0stop. Explain.

If there were a great migration of pexltar+xxy -xk1s 65c)ople toward the Earth’s equator, how would t5+l r)tk-xxc1 xsy 6xahis affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having bui(2+ui6g yaany initial rotation when she leaves the b 6auy2u ib+g(ioard?

The moment of inertia of a rotating solid *-rf 8xfpv./t nw *isudisk about an axis through its center of mxfu-. p*iw n/rt* fs8vass 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/mnutnx 4s65r mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, o5m4tu/6 rxs nnr stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow anmd ;4(j- duoqy-d p9nqd the other is solid. Describe an experiment jd;9oupd(-m qd-n yq4 to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In whk5,6;aotoz0j 5qm:uxrbe k3oa ad g62at direction is the linear velocity of a point on the top of the wheel? If the angular acceleration point;aaqum3bgtx56 ,e:raokod5oj 60k z2 s east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotat8+m05ssr f+j lh txdm:ing turntable. What happens if you walk towa :dr f8+thl0xjs5smm +rd the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As he tfz8znz) *ml.28bwhk t+k qg8 chrows the ball, the upperbzwhg.mk q2)8 f*8nlt+z8k zc 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 conservation of angular momentum, discussd m 03u2:cmwan why a helicopter must have more than one rotor (or pr m0d3 c:nm2awuopeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in rasvtq l73 xk)u0dians: (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, using t;hi/e ,f+z 3.d ewyfqxhe information inside the Front Cover, the angular diamezwfx+. dfqi;3yh/e e, ters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moo2khkg-*ynzg 7 n, 380,000 km from Earth. The beam diverges at an an27-zg ngykhk *gle $\theta$ (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 rata1 vl 22sv5,ax9zu4( liejtzxe of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 9(z5l,tea xlj u2asvzi2v4 x1 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor gmv sl1pc adyjehd 2*d*;8p 1w6x9f0 m3.5 m to another child. If the ball makes 15.0sx86ghw0yml1c* ;df dp av1 p2*j dme9 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolution3 nd;p e.ivgwr*r5 : d:svpo40 s1sazfs do the wh ia5 d*pe :vds;npz14o f: sv3.s0rwrgeels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotaty0 apmty)7bg,(w hb,s jl7u 9e t:bba7es at 2500 rpm. Calculate its angular velo 0j:bmb7(9bgp t,y,a7ht b w)as7uylecity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 8–vgdb-b ye,03gqyr )v0 38). (a) What is the linear speed of a chv0-)gedq,y30 b gyvbrild 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,li.:xpx,b xyas( *t j (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 c(ohso.7oa/ hpoint
(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 i u73 0xr kf*q6v6vilhkf a particle 7.0 cm from the axis of rotation is to experience an acceleratixvhur 3l7 066*qkik vfon of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about ks1 /wt qqe .nj.at hd-(*u:ntt0y9lvits center from 130 rpm to 280 rpm invtqtwj9an tqd 0.l1thn-e/ (ky *:su. 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 radius (rbzb- 36;xakwg kqjn b 9-0yv$R_1$ 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 02j cut4f.gats2ostwb3 w kn)n9,n5mApollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the star c4nt2wbg jankw )u5os2t3mtf s9.,0n t 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 uniform+n sqrm ar hz* /4g(hf)e2xi9hly from rest to 15,000 rpm in 220 s. Through how many revolutions dig s*2+r hafhe hnmrqx9z/i)4( d it turn in this time?    $rev$

  An automobile engine slows down from 4500 :xehykd z)6 :thj+2 ksrpm 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 snb2a.pmwps p( -hd6 n4tresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 coh 4b psn6wd-( .pnap2mmplete 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 diameterm4(udh;ljy 0tr /.yac accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. 4(.haruc0tj/dyy lm; How 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:u5vyceyvf7c9ue 5 f4 1500 revolutions beforev4f5euuf:y79c 5yvc e it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces ih mmte99m-k k;ts speed uniformly from 99-9m t kkhm;em5km/h to 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

  The tires of a car make 65 revolutions as the cas xq esr ova9o7l4g409r reduces its speed uniformly from 95km/h to 45km/h The tires havar9s9ooevsl g40 xq4 7e 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 climbinsm xeu.)s yf*)g a hill. The pe sxf))m esu*y.dals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the ex3at 8 utft fn l9dp-4r2r-+(7vtgzo vnd of a door 74 cm wide. What is the magnitude of the torque if the fx--r dttzn 4o t7 rtl+9p(ffgv3av 82uorce is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. Assohrx3hy xo* c d7oea7:mt-e,2 ume thathx-,:oe ty ac72xm37ho o r*ed a friction 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 whig+kz2x28vm zml vi8o n ,1uft)2ukp 1 k6u5shsch pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this sf1s lv8zu6k k +5 2n8h12v)upus,zk mgio2xtmystem.

  The bolts on the cylinder head of axyr +6kyb11f ln engine require tightening to a torque of 381x1 lf6+y kybr $m \cdot N$ 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 whiy nkm4 b. c0b 81+j4osvitmz6en the axis of rotation is v.tij+0m84mzc ki1 bnoby 4s6 through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. Tnww-kk; fs)l6x su73phe rim and tire have a combined mass of 1.25 kg. The mass of the w-ls7f3 x nw6s;p)ukk hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light row8 a2yosf hd , vb(2*yjrn*hs6d is rotated in a horizontal circle of6w2y y* h(h bsf,osvj8d2rna* 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 wheel rotating at constant angulark6w9poa 9ccayl 47fe 7(1moqt speed (Fig. 8–42). The f9cofo qkwyt4p 69(al7a 17mec riction 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 momentvw j26bquh72v. u/gzl.p 3k zs of inertia of the array of point objects shown in Fig. 8–43 about wz3gv7k uz/ 2j busl6pvq2..h
(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 consi z gaa;s.v;x;ym k9nb sm+a2)xsts of 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,s):nba :nwej1r n3 lpjc ,mg2) 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 the req),j b nrwpm ng:3nc)s2 l1:jaeuired 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 uniformr2v )khi,tl(zsn.c -lmm:bx6(tc6 nw cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calcuc 6 -mw(nch t(bm)s6vil2n.t,lzrxk:late
(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 a4fl l n-okypq ep2/qr21e3wr8 bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a sml0f /d6fccm)u4ljb tj5d ;: nfall 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 rad m fnj4ld0 jc:;df5lf/u) t6bcius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually brou(s0ow5abahfi r4*i * +/usi maght unifob*aa* 5ia4srfiu(/0 +oiws hmrmly 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 3.6-kg ball at 7 c*(g hcnla8t+0 z8ymh d5u .ph$m/s^2$ 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 iqozp27r es ,:ub m7-dcs thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps m -o bq7 c2dm7uzrspe:,uscle, 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 considerevbl e+em5 j 2c;;d8zpad a long thin rod, as shown in Fig. 8–46.z8mecpe5dba ;;l +2v j
(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 twp gfx.o.a(eu. o masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turnsyp2vsi5g4*t2j zzn z2 (revolutions) and releases it a *s2tj zy2 pzivg5n42zt 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 hasc5fjvqi24 r /t96ncj l a moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develm7hk rptg y xb(ol5 waaf;:fc09 g83j.ops 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 radiu)sjt0pj1 e4gcn0 qi8ms 9.0 cm rolls without slipping down a lane0 q1 iegctp8jn4s mj)0 at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to:flhgh*tg x*gk5i f ;. the Sun as the sum of two*k:* ffi5 tl.ghhg;gx terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much net ;2csdl,1qe7q vgn(e e work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume qqns;2c(d1,g eev l7e it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts 12oslqy+kl -y0kk55c3zc mu - brnwj 8from rest and rolls without slip--csrk wz3jo0yk5k+2 yuml5b8 l qc1nping 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 itsgq/mx9 6: 2 era1uramf tip. It starts to fall and its lower end does notm 16eqr2xu/a9:m gr fa slip. What will be the 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 ball rotating 6ri e,kw3mz 1txy.q/n on the end of a thin string in a circle of radius 1.10 m at an angular si6zk/ .tyqwer3,mx n 1peed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angulm9ddjo8 bsa+/1t f )qxar momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rqfd9ad/smo)t b+ jx 81pm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on awkx.e +l.6v wt platform that is rotating at a rate of 1.3rev/s If he raises his arms to at+kv lx.w6ew. 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. 8–2l * b 74jd5ufdnyv)7-xwdnuz- 7ez:7wa9yn hm9) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the nuwl-xe7ud *n7d)w7zy 5ybjnz vmd a-9fh4 7:tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increaserkj *ur if:,9e her spin rotation rate from an initial rate of 1.0 rev every 2 ei9furj,:rk*.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center at a ur oieqy 6(,(pfrequency of 1.5rev/s The wheel can 6ue,o qi(y rp(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 after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a f4)8nll. e3pyp l7i od ns8ens9igure 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 jmda p3(( c.p2wstl 3s-g0 eqbmomentum 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 ofkn qr1e-sv4wnloqd-w1y5b 5w/ o.s7lrn7w6 z moment of inertia I is dropped onto an identical disk rotating4s.-1swq oe1q 75n6l vr-zb5nn wwow kdlry/7 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(g6qt;+(s cx i+p,*5 -vehv jhwvlo0:sd iibn $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-rocz9: r2 pxb(gcund platform of radius 3.0 m and momentpg9( x:cbzc2r 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 with an ang84y2k3sr5nl kxbz t/x)qwzg1ular velocity of 0 s2x 45kyw)n8tqzbz3x/l1 kg r.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 dwarf, losing about half itss4xgtd py2d :; mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mas4:ytd ;g dx2pss 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 .kze)jct .:itin 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 t) d3*94c b*l+h(bm ojjfwyny$ 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 freel l(mnwod5k;y 6: nglif do-51p qog.5ly without friction. The moment o5w fln:nd5g klpd6ym;ol5qi1o(o. -gf 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 the edge ofrzx3lj4 ztp -: a 6.5-m diameter merry-go-round turntable that is mounted on frictionlessj:l r3 tx-pzz4 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 lyk72xeu z g+dc0ing 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 from the spool? Howe+72dz0 u cgxk far does the spool’s center of mass move?

  The Moon orbits the Earth such that the (sb 9m:i.x6wrjml6r bsame side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axixmr(r69 bl s6.jbw m:is) 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 3r+wvg mjs c:0rate 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 ofik/b p5/l; lzr a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6 bkz 5il;//prl.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 solid cylindrical disks, each of massyznfk-z v ;pd6o6t-3(hg3zqb 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter (pn k b6z-v 3thgyfo3qd- ;6zz0.010 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 the angula- ;rn *brt vr7;opuq 4du oys,:9yer7br 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 ti9 +,5d1u3qv 3sxgb jceg2k+-kejg f rkmes as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass car2gr j besxq1k-k+gdg3vf,ucj3e 9+5k ries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution autoa 0mmnlbt.a57mobile is for it to use energy stored in a heavy rotating ltbaa0 mm. n75flywheel. 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 an i: ydok 14e91rqzx9 jj$H_2O$ 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 ro he-goo 9(3cb tmoby3-lling 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 length L can pivot freely (i.e., we(;zl,:-m;cghkj iymx ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceler;m,-(gcxh mzjy:k l i;ation 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.kdu1.dn17oa d It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which id.nd ou7kd1a1t rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling ,fejm mg.(i;j(h emh7 with speed v=4.2m/s on a flat road is making a turn with a radi7(mme .j ;mfi( j,ehghus The forces acting on the 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 intozru-645 4w :dp jteefs 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 f- uje4t4s 5erd wpz6f:eat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, ma)nnazkw vzx)ez ;97m0king reasonable estimates for the dimensions. Then calculate tez)vmx9 )0; zaw7k nznhe ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which covg60e u: j8uudnsists of two cylindrical plates, of mass 8:ujdvu6u0 ge$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alongv43wr)d zn6t dz8h)pq the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest por4 zvpd638h tdq))zw nint of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not az 5o u ns5*0cvq60-es+sjonb6mav;xbssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as t4t)e,fi b+bgk:vedfyqx1+1. ,gll gfhe car reduces its speed uniformly from 90km/h to gvey 4el+ bgd, f,f:.xt)g+q1bikfl160km/h The tires 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