A bicycle odometer (which measures distance traveled) is attached near 53s:s 7y2twnr f8iqsd the wheel hub and is designed for 27-inch wheq stnr wsd23i 8yf5:7sels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does24hl/w 8 s/0af;nmy i;rhgwak a point on the rim have radial and/or tangential acceleration? If the h /lf ah42 im kr;n0ga;w8ysw/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 described by a single va 95 8dnxkvyxd,lue of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a largerq8/dna r xmps0xf t/i-4is8t nmf0,j; force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head tha s f6py/tscg(ro*x:y2n when your arms are stretched out in front of you? A diagram may help you to ansg/p*tx2rc:6y s s (yfower this.

A 21-speed bicycle has seven sprockets a3 dfkz /p14doyfh g2fplgg46 ,t the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or 4g /4,o6pkz 1dgflf 3dghfpy2 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 lks+6zu (cif:able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution oz6lsiu+:fk ( cf mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a lonygfqbjd,06bd);j:u z9gnd5 t g, narrow beam?

If the net force on a system is zero, is the net torque3wl21j bl tkhow(.(tzpwm6-q also zero? If the net torque on a.whwk wjo(6tmqbpl 13 z- tl2( system is zero, is the net force zero?

Two inclines have the same height but make different angles with the dihb1jz4 n/729f l 8ql*h lntzhorizontal. The same qfz2l49hlt*l jn zhb 17nd8/isteel ball is 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) down an incline. Onsp3o ft4;*-sw zf3wvp e 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 energy 433 f psvt*;opfz-wwsat the bottom?

A sphere and a cylinder havefmy-- ez/a 8ge 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-ee8 /yza -fmg 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 mome+ l5 - i23zb. zcynq,lc;iikbyntum are conserved. Yet most moving or rotating obj.l ;c, 3-zizb i 25yli+ykncqbects eventually slow down and stop. Explain.

If there were a great migration of people toward thku 2gw1(;ufsce Earth’s equator, how would this affect the length of the day fgcuks;1 u2w(?

Can the diver of Fig. 8–29 do a somersault witho ,yanar2.v( uoqjv, zu ,-u, w-u.wszout having any initial rotation when she leaves the ruw-juuoz u, o.,., , -w aanzqvy2vs(board?

The moment of inertia of a rotating solid disufqp5nb, v( :rk about an axis through its center o qf5r( b,:vupnf 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 mass in each outstret /t(rc0jr7pf1pd( vuoched hand. If you suddenly drop the masses, will uf 7v0pp (1jo /cd(rtryour angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the samy m84uk 0jh1ore mass. However, one is hollow and the other is solid. Describe an ex14 r0myujh8k operiment to determine which is which.

The angular velocity of a wheel rotatingig6 3hz64.6pmhcsm zjpr;:clyi/9f s on a horizontal axle points west. In what di f. 6i6lpr9/:sh 3;scgz6cm4ip hmjyzrection 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 increasing or decreasing?

Suppose you are standing on the edge of a large 2nu(u1*8i u)cjy svcn freely rotating turntable. What happens if you walk toward t1su( c jn*nu) uyc82ivhe center?

A shortstop may leap into the air to catch a ball anu7* nt.b8 qwbt1b+ch 1dp t2mkd throw it quickly. As he throws the ball, the upper part of his body rotates. If 1w7pt hb1mq.+d8ttbb *ucnk2 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, discuss why a yatf: ,2 pg+cb7r q l2)tejf:ehelicopter must have more than o ,glqj::ftfba2ree c+7 2p) ytne rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 30 5,moui9ba3.++h kda *v ynsdl$^{\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 coincidoc+ zuhht:iv9yb, n1 yd3pw/; ence. Calculate, using the information insu y 3p;cydbh,1n9zh o/i vw+:tide 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 from b5 bymaf+/.pl,d t lxb40 m6buEarth. The beam diverges at an ab+ludyxbm ,4fmpb0/ tb .la 56ngle $\theta$ (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 i ;/e+p/1bm2q ktm cvx7wi gf9ns turned off during operatiow c1 /m9x pq7;kt/ nfmgb2ive+n, the blades slow 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 3.5 m to another child. If the bhys3if g-c slv:k01bp -l7mfo u94 f-fall makes 15.0 revolutil-c 14f i0f93s: 7fublkv-og- hpyfm sons, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutionnvya(i h,hj ,;s do th(nvyh ij ;a,h,e wheels make?    $rev$

  (a) A grinding wheel 0.35 m in j1b+z( pzi(1s6 9h5uos:dkkd hwb a0 tdiameter rotates at 2500 rpm. Calculate its angular velocity in i91j:+ ub6s0okk 1at pdhbsz(h(zd w5$rad/s$ $\omega$ =    $rad/sec$
(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 revkakow(3 v4 lrc; o.+msolution in 4.0 s (Fig. 8–38). (a) What is the linear speed ofs4.c mo kl+kv;owr3(a 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 i)rhrp0 j*m*;vnlgs4its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed mu x lym4nst+r4wgdn+5u2zb.7 pkg1*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 i xaak):b 6rar1cm7,bbf a particle 7.0 cm from the axis of rotabaam:b7 bc1x) k6a ,rrtion is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to 28lk j )mrkks6(:ywzcqi)e ,7 u80 rpm in 4.0 s. De)m8 k:7s,ikqke 6y zwl(rj cu)termine
(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 tb * z3g(t: qt),ndr,e1bnypl$R_1$ 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 Mooh 671.t5kk zl jhsfsv)cx;yf6 n, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of theif7x1fs t lhy ;j5vsh zc)6k.6kr 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 15,0005r*za n j;,ibi16ejd r rpm in 220 s. Through how many revolutions did it turn in this tr1 ;6jd,i5ib*zr jnaeime?    $rev$

  An automobile engine slows d/opfk y)px7n 1)fs9 kn)8 itrmown 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 q/ pr5sl z(pz3stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn pslrz 3 /5(zqpthrough 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 fr8zcm7 fao-(n:uk rg8 com 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the whee rc8kfn87c z- o:mgau(l have traveled in this time?    m

  A cooling fan is turned ofs8 r)be3 9a mt/dkns0r*qr/iaf when it is running at 850rev/min It turns 1500 revolutionsr 8/aqs*s teb0 /9 mrdrin3)ak before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as tk j1s15isege(x r t+i2gh.l)b he car reduces its speed uniformly from 95km/h to 45km/h The tires have a dgkg.h1)tsijbi1 ee +5(x rsl2iameter 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 ca:x7kuo.xsyr-z/jg r n* ade 3ybtk1 5.r reduces its speed uniformly from 9dnukby -o:t y7rgxx135 es..a rkzj /*5km/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

  A 55-kg person riding a bike puts all her wil .;jg0(b :ut ukc,hseight on each pedal when climbing a hill. The pedals rotate in a circle of radiubj.s(,gkiulh ct:0 u;s 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is the mmw0sj9o. qqj cad4y0 /agnitude of the 09qwojc/jsd.0qmay 4 torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the: m6ufzvs8r3t axle of the wheel shown in Fig. 8–39. Assume that a friction torque of 0.4f8r3uvs z:tm6 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m,r t;gx9w k1) u(kvne0p are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position pvrwgk (u ;k0nt ex19)and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylindtmkn, i 8(ear,6+yt /xqiabh0er head of an engine require tightening to a torque of 38 h6ayteqxk/m nr +,t,i ai8 0(b$m \cdot N$ 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 thea:v-4iq9l 4hnttzzp( axis of rotation is through its ceqh4zt4p :9-z n tl(vainter.    $kg \cdot m^2$

  Calculate the moment of ineroa-oygo;. ;3or /rhw atia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. They-.; rh g/o oao3ra;wo mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin,t- vwac+e q bpx 51afqi525ocd/;fwu0 (3aa ip light rod is rotated in a horizontal;qpwv/-fp5da wii t0 ccab5 q13+auo25xfe (a circle 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 ai7 g*8bmohc 6q bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). Th8*c6q7mgi b ohe friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the a1vc6fpu. x vqj/jpu 63rray of point objects shown in Fig. 8–43 .vu6qfuj6 /p j vpc13xabout
(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 tw;fx m0v 5xq ,6k*kxegno 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 + +n0 )h6fzyj7)apvapw 9r fabrate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg a)va6+ h7ppbfjn az9 fa0r+)wynd 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 8.50k yqp3k,*t7wj cm and a mass of 0.580 kg. Ca y,37k*jpqkt wlculate
(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 ygcr1n;t pa e )+wtz5m(1ze2na 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 small hand-dro2 *p-b7r0. qdyhfzamiven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry2.rp-hb*mo 7zdaq 0yf-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut ofwzv5jc+2h3 bdf and is eventually brought uniformly to rest by a frictionac +v jb2hwzd53l 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 tq9 /vh,2hiqr9j,nvsfv 0k7m 8ik8a a $m/s^2$ 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 pu*w2 u4-i udrthe action of the forearm, which rotates about the elbow joint under the action of the triceps m4-du i r2uu*pwuscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in dse21f. (ym c zf5wx/qFig. 8–46.xd ysfe1q2zc.( m5/ fw
(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 mas;ql4mv)3o 8-lpklx prses, $m_1$ 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 fourb;/ yx-;zg q gd,riyo5 full turns (revolutions) and releases i;y-q bzxgg 5o d,;/iyrt 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 o hxxf18 ,z87 f6qcdpwtf $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develosy:w+ dfcl5)sjg/kxw+x;f n/ps 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 radiz g smthu2kub3 i96z40us 9.0 cm rolls without slipping down a lane at 3.hbik2 6z3tz49gsum 0u 3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to th sxgxhbv e18226bwzw5hd 26xye Sun as the sum of tw2whegsd2xb5bxhy8 1v26w6 z xo 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 164p5rmsi;fu/; (utgn 7g0 kg and a radius of 7.50 m. How much net work is requis7/frnguig5;t;p m (ured to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 k-:v poxc/ 9el8ij j rvu+a0up2g starts from rest and rolls without slipp9 x0jc8l/ prv:2uejuia+- o vping 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 tipr i,;2ttf z sbw3 0g94y,rcvcm. 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 of,4v 3,zrb 2r f;cty9mtgwc0s i energy.]    $m/s$

  What is the angular momentum of a 8u8m lu22biv+6r sps x0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed s+p82r8b2s ivu6xm ulof 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheely7 cbon:x7in3i-zl3w of radius 18 cm when rotating az77c-wyin3ibo 3xl: nt 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 platform that is rotating at a rate ocrs vu0xh0(j 8iiz(d5w.u6ixf 1.3rev/s If he raises his arms to a 08xjdc6riz(.ixuh iuv5( ws0horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her m f ,de dy*fk)/:la(ayioment of inertia by a factor of about 3.5 when changing from thedfi*d ),ka le:y/a(fy straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from a/n kq3dqko9xqt f;, q*n initial rate of 1.0 rev every 2.0 s to a final rateqqno3/f ,xtqk;kq*9d 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 4hdhwc,0av *;y /5wcomlsj; k(b+garat 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-k*rj5 hbkodcs,l/4+aym h(av 0gwcw;;g 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 angula3+13ghzfq k x0a/zan or 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 momentum ofbs)ha;*griwz t55(tg 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 x/pgqrv8 n*shs v skaul3n8c),qw5) : moment of inertia I is dropped onto an identical disk rotating ),v8/ 8cvk)sn3qpsa5 *nglsx qrw u:h at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsx/6q w i m go+sazyb86s+*j;by at 2.4 $rev/s$ 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 centqrv0q.ms) )f7 cur9 xder of a rotating merry-go-round platfor7fr)qd) u9rm. sxqc0v m of radius 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 rotating freely with an angular ve)m l/x. lmov:jlocity of 0jv):x ll/mm.o .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 65o ( lonsj:nwits mass in the proc 5:nolosj6(nw ess, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round 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 exou u. r-vfw7g1cess 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 lvjw2y3:-+xf5 py4kg:/bw tfq a k si.$ 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, initi- ml)f:wh3-vh e .itixally at rest, that can rotate freely without friction. The moment of inertia of the person plus thf :eixl.h3wv -ti-)mhe platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of m7quiey7 ut3)a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia u uqe7)m37it yof 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 theur2jo/2f;/ 2d *xs (hdnnykle 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 off2kn*;2udlrey hsn2 (x //doj rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same sis4 xz; unp)n xp/98znbde always faces the Earth. Determ;xs8nz px/zb9n u)4npine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 m 6zw-g :5rimyqi/:kez 0es3x q/$s^2$ 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 of4z 35j8aexnmx a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest3 zxajmnx4e 58 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 solid cylindrical hcth w1 u)v5+ma 3irc;disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub i51a rumc;h c )h3+wvtof mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches 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 pb,o h 1(w): f)gdhsw(cduq5cthe 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 blph*,94wd ce f1le8wwith mass 8.0 times 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 procesc*h9w 8 ebe41dl,wlfp s, 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 automo c6m,6oqoy,xwl8 pk vqbqa,v 09x f2-rbile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel oqrv8vqq -wba,fl m90,pk oc yx,o6 2x6f 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 illustrated2fk, qnl 4n9gs an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surfad-kce (6r0vrbce 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 ignore fricor 3ae78z qx*ztion) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then relezrz * qeox38a7ased. 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 famd sy zzc5s8kh42) v*ba r)68; ytxohloor, and we want to exert a horizontal force Fho )zks8y8 z); samrtyav6 hx45*dbc 2 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 isq.f :ppwc)q: n making a turn with a radius The forces acting on the cyclist and cycle are the normal f.wn p )c:fpq:qorce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 6 orb6.6g sqmsm 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 torquss b 666oqrg.me come from?    $m \cdot N$

  Model a figure skater’s body as8.h fcv c1qjt8 a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstrfjqhvc 8t1. 8cetched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly .2 sw5c oe*-nt rmz,mgax k74ewhich consists of two cylindrical plates, of mass ae,c.*meo54s - mtnrgkxz2 7w$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 tl lr0 lg i-snmphl8adx)8 gz-ws14 /l5rack 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 lplh1 mw48l l5xz0/asg)lsgir8d- - nhighest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but d;;h,umb ys-*)acl: fjz c *ljio not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car . o3kwk*u n1vareduces its speed uniformly from 90km/h to 60km/h The tires have a di v3 1akn*.okwuameter 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