A bicycle odometer (which measures distance traveled) is attached near the wheelidb7h,c ,-f (t,ls(xp a,pk bs hub and is designed for 27-inch wheels. What happens if you use it on a bicycle kb(dph,x(7 f,p t is-,slabc, with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on th d ,,,n*-fym81lf lvrgzjv;wje rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the poin ,,lv8f w;l-1,*vfgmdnyjrzj t 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 yg +-u,o kei-yby a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expla lwe;zlyo16y1in.

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 withtom/ul /ve0 g; your hands behind your head than when your arms are stretched out in front of you? A digto e;mv/ ul0/agram may help you to answer this.

A 21-speed bicycle has seven sprockets at thu w gpd07; q-mn,x+haet9vx /je rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocw; m-gv eht9x/q,dj+7x u apn0ket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fe ,)eqj-x 8, -kswc2xty, pjxnast have slender lower legs with flesh and musclej- w xs, 2j,-nexycep tk8)q,x concentrated 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) carrybu (39g,qh ml 9:tes)fz tiz4n.6 bwtz a long, narrow beam?

If the net force on a system is zero, is the net torquedn2)wyu/v ks dnq 806t*zj gm5 also zero? If the net tor*nk t5j n/u80s2)vmq dzd yg6wque on a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizontal.5g +a ya4jrhgao0 j(mr+e. ,fl The.4gea +a o fl(jjy,+ 5hgr0ram same steel 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 rosf(n256 +xro a2gm))n xugihci-ff4l lling (from 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 en 5mox fia)s2ug(4-ixnc)r 26hflfn+ gergy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start fr .cl-v8ee;v1sr2k wdlom rest at the top of an incline. Which reaches tvekcv 12er8 s.ll dw-;he bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved./8 +ihcpj1 qiv Yet most moving or rotativqi /1cp +j8hing objects eventually slow down and stop. Explain.

If there were a great migration of people toward thet - 7e-28 ud;xxslsrpj Earth’s equator, how would this affectsr upx728 d-jelx ;ts- the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any ifg.p+ -wiqsyc: h46w tnitial rotation when she lei:q 4c +pw yhs6ftw-.gaves the board?

The moment of inertia of a rotating solid rr838ou8j38:itm dvvrm +rnr+dpn c*disk about an axis through its center of massut 8r*jr8c3md8v : p3 +r nr8ndovr+im 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 agmg,6u-2e8ybht ;go j 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the sam,2b6 ugemoh gj-ty 8;ge? Explain.

Two spheres look identical and have the same mass. Hi i*( l3mphw(bowever, one is hollow and the other pli(* mib3h (wis solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horiz 1-j +:la)y9b wxn,0swiq ifcxontal 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, descrf0w ws:xnx-9, +cjiab 1 liyq)ibe 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 rotating tuq jsc hrpde8:5/ z,hr6rntable. What happens if you walhhd/:,c5ep8 j6srz qrk toward the center?

A shortstop may leap into the air to catch a h9rn7a3a k:hvei ,3-3 veowwn+(phayball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notichaw3,no 9e wnavh 3y3pvh:(ark+- 7eie that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of ank .bqg6sz/ 5c:7qq, oo: ojlfrgular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propelleroq:6qgf.5osclz brjq: ,7o /k can operate to keep the helicopter stable.

  Express the following angles in rrk,e6adu : ihf(.+ xzwadians: (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 becauso3kxqbg ttq+ y(b bz41 2+ 3ilh2bk/rne of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radib 2i 42ybx+q +g l1knt k(tzqob/b3r3hans) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 i 6s,oaxqr4ot+e7omdvb(lv0 k:n/ bu; w)2 fh km from Earth. The beam diverges at an aixf)al0v,tev6n;: b 7w/h ood2r(sum kbo4+qngle $\theta$ (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. Wheg6 4 8xk16enh vq59bxkq(wdckn the motor is turned off during opera9n6kvd56k14bc(w8 eg hkxxqqtion, 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 floora k:+is;3 uqoo4vlru/ 3.5 m to another child. If the ball makes 15.0/s3+ qu4:uaoko;vr li revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolu134c4-o;ud7 dqfa/ yzss :.aoyx pyk ytions do the wheels make qap.z; f :y4-xda7okc /1su4yyyod3 s?    $rev$

  (a) A grinding wheel 0.35 m in: ,q;gqrgnx.qmm 9how2jt7e8 diameter rotates at 2500 rpm. Calculate its angular vel8ogqq7m;wq er tj2 mh9n:g x.,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 4.0qmg b5cas(oo ;rm v1203k wn*f s (Fig. 8–38). (a) What is tmg2smk (51r0fow; cba *onv q3he 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 its orbit around theqc5 vc29s2 q.7h1e6chwqov sl Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a ( ekcj5;lu dv3point
(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 ro8zfncq xz.xwxhx;j4 bk1nf l)r//; i6tate if a particle 7.0 cm from the axis of rotatio6; ;)xx41jbwf/n kfzzq8xrhn.cl/ xi n is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center fr j:xpm37 *vek2ea;qan.rxk;fwn* 7 plom 130 rpm to 280 rpm in 4.0 s. Dn2x*wk*pf lk p:7x ave;r7m; .n3eja qetermine
(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+w:xnbv zgk1 0b*6iw e $R_1$ 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, astronauul-d j9pg+ad b4v1w3u ts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought owg4a1 3vbuuj- +dldp9f 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 tnn(qlaxl *q;fs 4z3+s. xi4hy2sar. do 15,000 rpm in 220 s. Through how many revolutions did it turn in al4i4ld shqxzn.* q3nsfa.(r+ x2sy; this time?    $rev$

  An automobile engine slows downpbd; s+:h;meda6ki7,,p*iwcr e+lbk 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 ino 1u nen sk2wg4aelz15p)+hn w tt-.0q a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before r+l 1ekqun.2hwesw 4tt0 z -na o1)5gpneaching 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 diam-hgq4yyjb .u4 e 0csvjs8xf6 (eter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of 6(.jx04-gvsc ehb4j ufy 8syqthe wheel have traveled in this time?    m

  A cooling fan is turned off whj,ne /h(ls kn+en it is running at 850rev/min It turns 1500 revolutions before it comes to a se nls (/hj+,nktop.
(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 ca;iga zbj:6m y+r reduces its speed uniformly from 95km/h toiz+ 6yg;ma:bj 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 rev sa vk4d/c9)dxolutions as the car reduces its speed uniformly fr va/dx)k9cd4s om 95km/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 weight on each pedal when climbing ln+ 9 -nqpml2va hill. The pedals rotate in a circle of radiun -m v+n9qpl2ls 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 ofp byi,bc74w0-wu gwu- 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is0ww7 -b4gwcupib,u -y 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 ta1b0 hb-y l2a(ve.xg whe axle of the wheel shown in Fig. 8–39. Assume twb1x( hv- .a20glbae yhat 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 whicapm5dlz3tu 3gvw21q7sgt + 8 mh pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate8t5+qd7smuatg3zl w v 13p2mg the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque k)sls4 t tbv a-:vshh69-pfg/ of 38 tk p4-va6 vs-lh:hb/ )ssgft9$m \cdot N$ 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 amg.7u3 a 5tuji 10.8-kg sphere of radius 0.648 m when the axis o miat75u 3u.gjf rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicyclkq;x7d 7igckxxlg, r;6e+5qq e wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (whc;7rq qi 5x6le xk7xq kd;,+ggy?).    $kg \cdot m^2$

  A small 650-gram balcox4ej0 l k3(xmd g32al on the end of a thin, light rod is rotated in a horizontal circle of radius 1.2xgjde33axo42lkc ( m0 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 plb.*r d9y/ib*dk 4dwiotter’s wheel rotating at constant angular speed (Fig. 8–42). The friction forcel/w*r4ibk9 dibd d .y* 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 of1ic+8+pnz2* vne w nmv the array of point objects shown in Fig. 8–43 about2i+1mnzvvnwe8c * pn+
(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 o:tddjnfe 3b/f9y;p- bf 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 m9x x:mo3n gq3rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellitmq3o9 nm:g 3xxe 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 of 0bnx9 /s69 krho.580 kg. Calculatekr6s b h9o9x/n
(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 k m )/cq46nkb94gm0ot :pbnfya 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 t6z( 3 kjp)jtuon a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, negltj63j) (zku ptecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating a.3uk 4m vpddka.9tgb9t 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictionalgkdbm ua9..vk9t4 3dp 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 accelers7z)a8 k we uh+gg+s:rates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of thefck 62vi/v*xg sp+e 0v forearm, which rotates about the elbo*kicvpe0gvfxs2v /6 + w 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 consiy k5 aj6xbk. ;ndr*n.fdered a long thin rod, as shown in Fig. 8–4.;yb kjr5a *xdnfn6.k 6.
(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 c,p+jzw iht y:(r4mf/c onsists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from restm.(f)/ urt :tvuc v5vs,w uo kq4/xyu; within four full turns (revolutions) and releases it at a speed o5uyum rox v.q ;,)utt( k/f/4: vuscwvf 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 ini)+i5f4e u cngfa/ ql nrk7-2certia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a 2 gsk.kv 4o o.e-6lrqvtorque 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 ay91le 7 wb 7-ijwivp8end radius 9.0 cm rolls without slipping down a lane at 3.3i pwby 7eje1l97i8v-w $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Suz. x(bmpdn.( nn as the sum of t(nd.b zmxp( .nwo 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 aqpun4/c7i htuchp r,0f /tpt6ygn4,( r.u /wjnd a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume i/,nc/q iufp0r /4h wgu ytc,pju(p.7 4hrn6ttt is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1 ,-uxp9iuh t:a.80 kg starts from rest and rolls without slipping doa, ip-u9x: tuhwn 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 tiz+a )bmfxic;cl 7 vo0,p. It starts to fall and its lower end does not slip. What will be the spivccx)+l ; bo07zfm,aeed 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 t(0x dml+j;ksjlt )op+r;s) dof a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m d+ 0xs;orljs (ktd m))+jlp ;tat an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angularnn7zr6o( s 3qx momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm whrnqz67n3o xs(en 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, on a platform that9/qwoi gtp-)s udm 5(y is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to -)dyiu (9tqm5p /owsg0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can rb zpfp3 + ljn;sq;6xlfg 9)af)educe 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 tuck position, what is henz 3f)l pbf9+pj ;6;asqxg )flr angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increapdf*w2t,bvr)xnl4 * ;b rf-v cse her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate ofvd v c fb;nrl4*,)wbr2pt*f-x 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.k /ferptqn i;(8de d0 axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The pott8/0d perdqnke(fit. ; er 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 angulae w(8mh,e,a pwr 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 ofpplf3tt0( p /m 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 momena6p1; ngx)wtp+ j vq*2:xi bjjt of inertia I is dropped onto an identical disk rotating ag q;*i1tv26xjwpj n)xpb:a +jt angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns6sq sl;k*ph/kt;9k d;j -cmeh 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 satwq 5+ega9k-8 dfg 5plcfdb/og: 9.vtands at the center of a rotating merry-go-round platform p b/ o8ga ff.g al:5vt5 +9qeg-ddc9wkof 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 q;(awhcz)v5xm m. b5 2-lpcourotating freely with an angular velocity of 0.8 u5 lp zwm5voxa(mb- .cqc2h);$rad/s$ 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 whb2 xdmfgyu (j 7;vpb 5qck/ evl))(j;iite dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to thfy2g )j j5/ ( ivk;m7ev;pcx )bqb(lude nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of vzq1s7: s j)jz120 $km/h$ 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 dlm8) ef;l l r6- k9ode6+igcj$ 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, initi7fxo l7v5jv;y.itn- sally at rest, that can rotate freely without friction. The moment of inertia onv-7x fo7j lit5s; .vyf 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 of a 6.5-m diameter mefc8a4qdt nj35 nm6ic (rry-go-round turntable that is mounted on frictionless bearings86m ni3facj5 d4(cnq t 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 rofa1n qq+ c6 uc0k,m:xrpe lying on the top edge of the spool. A perso0q+r:k1 aqccf xm6u ,nn 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? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same s +m hfizc q70+.pjl(eeide always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (abol+0ep zqeh+m(icj7f .ut 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(w 6ohs;jbpv7jc sh+0 j/ 5zgp a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylindergan jq*ha2/elc bye))sb8l 15 of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivera hel5qs /8blgna2))jc ey*b1ed by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kgtnk+2*4 w lqbugq upv n9)s+,r and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conn, ) sw*q4+gbuv tl2 runkq9+pservation 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 iw)a *smeyw )b1s the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass xcaei 5u2qt 4 s5/6gye8.0 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 t/eegs564uq t cy5 ia2xhe 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 automob1r 5fyf1 fhjwvh. 7a)zile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, usf vwr.7yah5)f jzf1h1es 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 to*ymlsg,,lkfx qv0+u08ha1an $H_2O$ 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 surfas3 y gc dvdau;*g; t*m;zxp7qwyf r cz+4wt;2)ce 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 igngj h6g0fm1: ecore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontefc1 gh:m6g0 jally 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 vertica f7jet8(fr53:ondi dd3xeo x .lly on the floor, and we want to exert a horizontal force F at its axle so that it will climb. 7tx3x d:n5eo(r dj doif3fe8 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 wexym01k yxh,8zt/v ; on a flat road is making a turn with a radius The forces acting on the cyclist e hm8xz,xy1 w0/ ktvy;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-(io b0s q d9vq++wx)gdkg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 1dvgsoxd ()qw+iq9 b+0 20 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a sol;/ ;qw(ezha *p6kgm fuid 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 outstretched arms, and with arms held tightly against her bodzp(u/;m6*kq e ;ahgwfy.   

  You are designing a clutch assembly which consists of two cylindrical y vzj 8k4d6;dv*z.vp l;aefx 2a+(mavplates, of massxdmd(j2 a pvale+4ka;vfvzyzv. 68; * $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rouf)4ayek 8 i0psgh 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 point of the loop8s4p)0ykiafe without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assumee(i,a0 jhpt9mls z8y irp5 ;5y $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car rehgq;36-e t helduces its speed uniformly from 90km/h to 60km/h The tires have a3;6glq- teh eh 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