A bicycle odometer (which mea nbmqgku-.:yxptp 0 e0*/-;:tcig bgo sures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-itp -* qcx;g/gntgup boeby-:.m:k00inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on g,,wt -9jxemdthe rim have radial and/or tangential accdwg,x9tmje- , eleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by atxr *fse. -/fb single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forcecp qh1;7g/5w8pi uays ? 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)nug 1hr,7* xdaitd-d -svlv law6h-4 than when your arms are stretched out in front of you? A diagram4l,naw-i*dxdd v u7)hv1 r 6ls-g a-ht may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear w3jfhi +2i u 7b+2tpbt1ijpf1rheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small2 +if1+j t3p7t b1if j2huibpr front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with fleshtn-fk/cw wcj6yd5c :tv-e ,sy0. d(r v and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why0 /wnv 5c6dejfs- kdrw vt(ycc-y .t,: this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–3e(to ) r0j8i88vjijgt5) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero?pddb4;6vi/t -jl f:lov(wri:wa/ +t e If the net torque on a system is zero, is the nwvai(w d :tb t6dplj:/e4ro v;i-/lf+et force zero?

Two inclines have the same height but make differe:r 8 wbi4j4uyrnt angles with the horizontal. The same steel ball is rolled down each incline. On wh yu4wb4rr8ji:ich incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneouslr84k0ie( 5m/rloyu lhgx416 ty8awtfy start rolling (from rest) down an incline. One sphe y88 4l05mu(a6lr1xi 4tr et yokfwh/gre 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 at the bottom?

A sphere and a cylinder have the same raj-w9vi0q ds*ke d5a ;zdius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greatwzqdij-*d e k 5;0v9aser speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet mog6cwa )bex j7nzwr74 7st moving or rotating objects eventuallyxn 7 awcwj7)7g4e r6zb slow down and stop. Explain.

If there were a great migration of people toward theh r4ut6:s92iyvoe:9 rmpy l(c Earth’s equator, how would this affect the : prh o:rys6(c9ymi2t4 l9uevlength of the day?

Can the diver of Fig. 8–29 do a 4z57/fyhma uv94 ln eosomersault without having any initial rotation when she lhl7env9za4 y4om/5f ueaves the board?

The moment of inertia of a rotating solid disk about an axis througck .mt tcklc3+;4gv8i1raz1 gh its center of mass i3ga 8cr1.tkzvtm g;i 4+lc ck1s $\frac{1}{2}WR^2$ (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 ;k23vtv(ztg gp es/ud j 7le1.holding a 2-kg mass in each outstretched hand. Izkd se1/ept(uv3lg27t.v; gj f you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow and th ze:q,a lmt(1dp vjfu)iinx, (63,byqe other is solid. Describe an experiment to determine which is whicvfj uy1 mi6,b,qqzni)p (ed,t :3 (laxh.

The angular velocity of a wscx -ep1y ecdkpg6 ff oyk 6)/ae.,;.theel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this popgy/ ,coxe.feyk.6 td -f)1a;kcp 6e sint at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge ofqqy+thj+z.4 t a large freely rotating turntable. What hat+.+hqtj yzq4ppens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throwq+9kc*ph4h5tu5z: yy i /qslo it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Exp*ych5+oq9iq/: py uthl4 sk5 zlain.

On the basis of the law of conservation of angular momentum, discuss why a hels+kry3s+ft w lk 4mmnj (x c/g9z/u.-oicopter must have more than onw 4l-j smf+yur.kc x9n /kz/ o3+gm(tse rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in rr: i/wn /37gm 8ytgjgqadians: (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, v-x hk)9h3chrnqg l*.pq: k,nusing the information inside the Front Cover, the angulaqnq.3h-kvcpn9)hg xh, k* r:lr diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Mof +dj74l.sn;v cp on;snei)*yon, 380,000 km from Earth. The beam diverges at an angle ncdv p*7)n. o;njl4; eyssi+f$\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor is turnedfta-s26 j: owb off during operation, the blades slow to rest in 3.0 s. What is th-6:bft wos2j ae angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level fgd/l*0b r6qa) i lk.pz :zogq3loor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its dia*:k o)qdp.zqb06 igr /gzal3l meter?    m

  A bicycle with tires 68 cm in die kj)*,nfuh-xle; 0hj ameter travels 8.0 km. How many revolutions do the whee0 ;f nek*lexjh -),hujls make?    $rev$

  (a) A grinding wheel 0.35 m in diameter romy+s8- h w 71egrzd1ml/6,gnlr2pu bmtates at 2500 rpm. Calculate its angular mg86mzg m7 e2ub/ hdrl1y- +srn,pl1w velocity 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 couto/:i w zv7*ymplete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m frozwv 7uyi*/t:om 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 orbit8bfottp vyp kp667:6w around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed6 ngs bs,jx-.c)sm+op 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 censj+s.cv4 +ivc c3e4m wtrifuge rotate if a particle 7.0 cm from the axis of rotati4c4+3wi c+ jsmv.s vecon is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelbtjabwc 0xcu9e-9 y5;fwe /f) erates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Detera5/bew ejxt fu9c-w)ycb90f; mine
(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 radiunt 9ipyl1/c8 qs $R_1$ 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, astron7k tmq,brzgq4 a,7q-p auts 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 inap rzgq,4bm k7-q7t,q terval. 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 1( ahu ht1*px) r7wfakuniformly from rest to 15,000 rpm in 220 s. Through how m7u*a(wh rfa11p t k)xhany revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in zhax0 hgo;s te(2dxa 3qm)3 y: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 mi0)nx: ;j:v0bcym htid- 3aj the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0j;jbiydm: ithmn0- x 3v a):c0 min to turn through 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 unifoa1lwn,d +, tmjrmly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in th wn,1, jtlam+dis time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns zgk20qvy 9inho(k3j 31500 revolutions before it c3onz39j2hk(q yg0kv iomes 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 i/vf20.6 un kudpq0mtits speed uniformly from 95km/h to 45km/h The tires mdk00qtvu 6p/in fu2. 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*hhjefs;5 i7i 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.807if;i5 hjs he* 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 q-- ocg1tcmf (when climbing a hill. The pedals rotate in a circle of radqm c-tcog-1( fius 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 widxmbk3,zpj ;3e9wpi3 2k gj,d xe. What is the magnitude of the torque if the force is exe3ikjj b ,,g2e3w93 ppzkxxdm;rted
(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 z8k( 0 lrt 4aes9p/mccshown in Fig. 8–39. Assume that a fricti/0az emk94lc(csp tr8 on torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attac s2d b-zkc0 m5:yj* 6tpcrih.f h8-pvhhed to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held i-sc0h2-k vh*pfi8jryh .5 6m czpb:dtn the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head o(ojm4a ujyo0 -f an engine require tightening to a torque of 38 yo a-ju4 0j(mo$m \cdot N$ 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 itt/t,ut p2(rg nertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its centegtt/p2( t ,turr.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicu3 qc9tw8gy dqoyxj x7-;e3 *uycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub cayucj qo9 7-u3xx t wgqd*38;yen be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizorf gt0x 8;*ujlsjwmo:i9f3j/ntal circle ofl:9r 8/xijm*; jftg 3 fjuow0s 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 cooav ,mzt/z5q;nstant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N tz5q/t ,vmzao ;otal.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of - e-olwfe* xrjh07xb :point objects shown in Fig. 8–43 aboexoh*- jf0e lw :-bxr7ut
(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 two oxygen atoms whose to/ pw:)adhr)zcd( agw ;vl8c l8tal 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 c/ : : nrk lulq;wvaqn9ia:c;4fylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 ;:n;ar 4fuwlq:v/qlc9ina:k 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:lry ecz vyo5t;4+f d3b6 hoj: of 0.580 kg. Calh bodv y63jy5 o4tz r:le+c;:fculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, k e+ g mafs3iw+t3 9ts2cpxu)*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 tausba6u5s)618kjjg 8 +jp ur xmngentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10. gj6b816 ) 8rkuu5sxsupj+ mja0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional 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 eventualls db 7+qzt75 oo) pm4jf4)caouy brought uniformly to rest by a frictz7o+ 5o)jodtcb 447ma)fsqu pional 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. 8–4ifdl+b/3rjnm 1m5n+ o 5 accelerates 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 t2 z 9frc*bdr,b3h tvjtm9;ld7he action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8v;,7dt zrl32*9 cj9rt fbbhdm–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 cou zs8j0a:6 sbtnsidered a long thin rod, as shown in Fig. 8–4j z6sts:0ua8b6.
(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 co7lox33rzbk p:3. )mhl99o vp io*x hionsists 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 fr8wu/rm ,u 1 c +pu8ocfxr;um:qpf-3mhom rest within four full turns (revolutions-mu r+q8p :ouu1;3x fruhw/cf ,cp8 mm) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has p psg; 4cf9 +3xhnuwl kb)+/jta 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 develops a torqvm5g--wozhw* s*,znyo ;ue/j ue 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 radhc*2r)ew6z0v1.epoc yua ql( ius 9.0 cm rolls without slipping down a lane at 3. z ).ep awcvy02r6c1h ue*o(ql3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sumw6015*a 4au+r .a ydtxzn;cihvq -hlj of two terms,+ ;x60u4ahah id*ynqv.at 1 -rz clw5j
(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 mrbs2 w+dvp c80uch net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assum+rb vw0pc8sd2e it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and px jl z0z3ri8 r etp60+(8zgucrolls without slipping down ae8pj+ x r038lz(u0zc ipt g6zr 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall and its g356hd3gi pdj*790xaiz ke dtlower end does not slip. What will be the sp56397 d g*3gj azpx 0dhiektdieed 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 bam-yhv9j51(*pfh/s 8xsy ghxull rotating on the end of a thin string in u sv h(xp 5-/yfxs8mjyh19*gha circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cyli -ybrz,tz/xcye: (mkp/n +3windrical grinding wheel o-+kye3(xy zrt/izwmb/pcn , : f radius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that b3 xgeh1t;hhh2 du0j 9is rotating at a rate of 1. 392gehh bxt ;0dh1juh3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) cabyn gq++nlb kc 68g0k(n 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 n8glk+ kbb qcy+n06(gtuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of 1,y8 bvrsx /oq, n8n+3fw5nchj.0 revsq+,, h nnfrbwv/ 83c n8xoyj5 every 2.0 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 arou7nq plnpe/ 4n5ef m5a:nd a vertical 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 potter then throws a 3.1-kg chunk of clay, approximately shaped as an q4n:m55epna/lp ef7 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 figure skat;q4uogaud*u 1er 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 momvb0siup7x;n;71gz 3.crv hia entum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped do;,t 4igkfql8 xy;f:onto an identical difdty;8;fl4kx,o g: iqsk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at r:d7j0 tdub *i2.4 $rev/s$ 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 center ofisdu(93gm a x:o8f9 bt7yi z)r a rotating merry-go-round platform of radius 3.0 m and moment of inertia 9 7sy b 39xdr(iu tazo9if)gm8:20 $kg \cdot m^2$ 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 anvj6jz8v8r mqr 1-sa( ugular velocity of 0.8 -jrs8u 8zja 1(qmv6v r$rad/s$ 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 / k0e4dvf+9*r bjbndfhalf 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 bk bb e/ 0d4vf*r9n+jdfe?(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 invol dm)c77g sa s80a/6axn4 epdehve winds in 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 hr6 )yxi 4ps+;z cxbp/i 7ao)d$ 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 rest3i jv rnzf vv.o28nq.9, that can rotate freely without frictionvr.qiv2 .znjov8 f9n3. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diame6ztn i*;j dwp/ndw -q1ter merry-go-round turntable that is 1;6jniqw t-p z*d/nd wmounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on thpm-qi5n4 72 r1 xizxwq/9lx coe ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? Howix z1q5/l27pn-x4 wm riq9x oc far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. Dk-m( r 312: *k+vkbcekqfxwmqetermine 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.) r q ck-b(mkvf:mqk e23 x1+wk*   $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 y4: gds;t*2rjw1k a 9a5vuqram/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.:mfsp7uf1+ga 20 m acquires a rotational rate of u:mg a+1psf7f from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg a:yn 39l z+h xy2bw hmzbtb16x,nd diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameth ltyn 3h62z+xb w,b9m1yz:bxer 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 the angular speed of oi5g:a)uf m 4pthe 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 wo x,d(+:qdz cq)ibsdp4wqk27 ith 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 process, what would its rotation speed be? Assume that the star is (d),:x p4wczqsk2b d qq oid+7a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy store8sne 7.rny nfr/:q gs.b4l*ffd in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical f .bfn 78.nnrf 4y:srfse ql/*glywheel 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 illustrav:3e cf0 9 zk*vzvd1-tqkmrw0 tes 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 surface at speed v=3.c3umxj 6 +3nyj3 $m/s$ 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 fri1c6y4ua4mzq /r- f i y8zof/gmction) 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 acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. -cf6 u/ m4 zifg1zqa4yry8o/m[Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. rx3x spdn9dp 2as5r6, 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 it rests (Fig. 8–55). nxas,x5dd r3s26ppr 9The step has height h, where h

  A bicyclist traveling with s1 p cpzrr;c;2xpeed v=4.2m/s on a flat road is making a turn with a radius The force1 rz;xr;c2ppc s 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 into a sling ort ;, 6ormiz-sf length 1.5 m and begins whirling the rock in a nearly horizonta6 i,m-rzrs;otl circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body ass56qosdi 8wyx1 8(rp zfx 0c+o a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the 5wc(8x sqf6oio xr+1p8zd0sy angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylqk008o izx6 rq+ z7g n3ah-nfeindrical plates, ofhqnz iqr-e673af 0 0+nzox8g k mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 loopws hq2-f8 buc9ed rough track of Fig. 8–58. What is the minimum value of the vertical height h thac -sfubqw9 8h2t the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assumejes ojgkc4+f11*ow .h $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly x1cg l0-,+;lazfmwjwfrom 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration 1gzlwc ,-f+a jxm;0wlof 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