A bicycle odometer (which measures distance traveled) is attached near + 4dn+3(gndpb xyusg6the wheel hub and is designed for 27-inch wheels. What happens if you usgsb3gp+( 6+ ux dn4dnye it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim al:zv ;c:nl;hp. : ta,v)zizthave radial and/or tangential acceleration? If the disk’s angular velo:vh::tt zznv);. a,z l ilac;pcity 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 valueko8s(gaw jx482-b 3v8 maup nc of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a y2m-w+,s11 2z8bv5nveouxk vl*ka uq i1t i.slarger 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 thadfgvug x* 3f1;n when your arms are stretched out in front of you? A dia;ff x*v13ggdu gram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three gu(akhi5 c35y at the pedal cranks. In which gear g yu35ck(i5h ais it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs wtaz,7:d5gc :kc z1ar nith flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distzna1 kc:r5dc7 a,t:zgribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beam?u bla civ18ef6wdlg - a *3wn4rlox+2.

If the net force on a system is zero, is the net torque also zero? If the net fvha;;aj1tq;5e 0j9ho9 lakj)hq z ,atorque on a system is zero, is the net force zehtq9h o5 j ,qk f;;ae)alh019jza;jvaro?

Two inclines have the same heighj(4 0b dl6./ vye waqrdw.omf f7sm,1ft but make different angles with the horizontal. The same steel ball is rolled down each inclines4q1b ,ol ef wfvadf.7 ydj/( .mrw06m. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from res ld9tmv7w*yp ,t) 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 t tdp9,wvyl7*motal kinetic energy at the bottom?

A sphere and a cylinder have the same raj s;(6f gw..k vohkm2*ck6r hxdius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which (;krm*cgo xkv6s6h. kf2.h wjhas the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet inu og (st8)+gmost moving or rotating objects eventually slow i8gu )(tgsn+odown and stop. Explain.

If there were a great migration of people toward the Earth- c(0i bphopdy+9,,snui8r4z4dx+g tkbik.m’s equator, how would this affect the0r b z ho pg4i(ximtnp+ -d9bk cd.i,4kys8u+, length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotati6 acl7p4ch +vbon when she le bhv+a4 7lcc6paves the board?

The moment of inertia of a rzci)g4 o :v*zeotating solid disk about an axis through its center of mass isvo 4z*)giecz: $\frac{1}{2}WR^2$ (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 massiidld hjkxs-p f1(s3:qws+/ . sf3vh) in each outstretched hand. If you suddenly drop the masses, will your angular veloci+-j w dk hli)sx3/hssi sqf:dpfv(1 3.ty increase, decrease, or stay the same? Explain.

Two spheres look identical and hav 6zo15ooi3j cu5cdw0 ze the same mass. However, one is hollow and the other is solid. Describe anc6ooc 1zz 3oju5wi5d0 experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. l w:*ah1re6(lkla5i c In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or 5c :6ha*l1ker(aw llidecreasing?

Suppose you are standing on the edge of a large freely rzb /zenynas : ) qgx/:27yn)fqotating turntable. What happens /qya zy b :)/fgx 2nz)qsn7e:nif you walk toward the center?

A shortstop may leap into the 7wb/ cz*a 4y hj7l8kkm-pyn, kair to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you nkzy4k pb ,7c7/- lawhmj8yk*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 conservatio o :s;it2u6l)o5ggm ben of angular momentum, discuss why a helicopter must have more than one:i6sgb )oet;5lg uom2 rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radiank4+ow 6q5 raiws: (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 bec 3or 6tt6e4l9x yc6t1ws0 h *:qsm+kxwfgz ez)ause of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.l349w+1 zt6z*hf s:ex6rqxy0kg) c ose twt6m
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The 2tzt 1/ag i.x6uki6zr beam diverges atx6iriku gaz/ z.t26 1t an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. Wh59iyd 7fvqf9u w +om4cen the motor is turned off during operation, the blades slow to rest in 3.0 s. f+ uwfo4dcvim59 y79q What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m0szx z13*m yfl to another child. If the ball makes 15y3s0mlx zz1 f*.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 kvszr2x 2+wn0z m3kf 0vm. How many revolutions do thx w32mkf 02vsrz+0nvze wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rrzi3mk 6gn1:,se ezyr 9ll8 u1(d3hd xpm. Calculate its angular gxhsnd y3 :,z(ie3186r9 lr du emkzl1velocity 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 4ri7uf 5xhbekx2 n,x9u) ) jd(n75uant.0 s (Fig. 8–38). (a) What is the linear speed of a c br2ujxtu )n,uahxeki 7 fx9d7 n(n55)hild 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 ,o)fi -i; sg mb;azct4xt,o8l around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speednk1qs;f a, p1d6+ik5ju hj9gu 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 roii .r,90 q*ve7n oduwdtate if a particle 7.0 cm from the axis of rotation iu .v*d idne,o7i0r q9ws to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates unsgmt 16pt2.w pa)moiy 5,h;j fiformly about its center from 130 rpm to 280 rpm in 4.0 s.s)5.wht ,mpfoita;g m2 p6jy1 Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius 7)h wwsk; e:un t2re4v$R_1$ 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, astron4srv +*vj-qu dxqia.ixjm54iu23m d 7auts aboard the Apollo spacecraft put themselves into a slow rotation to distribute tj4-mu urvxi74id q+3x vj5* .ais2mq dhe 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 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 15,000 rp;f(r 7nz* grt ao6lgj2v- e+ehm in 220 s. Through how many revolutions did it tu-gg(ta; o*nrv6z2fe hre+ j7lrn in this time?    $rev$

  An automobile engine slows down from 4500 rpm toh wp*mwv10r 0: /idrkw 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling 47i: sqipc,t9yj-b 3 k1zyeee“human centrifuge,” which takes 1.0 min topy ee47 -193, q:t jicbiksyze 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 unlw xnbzqk:7 (nw 2n0 *6 zcrcex6dyi.(iformly from 240 rpm to 360 rpm in 6.5 s. How far will a point onben7ywr*:w nzx6cd .i qc(2n0kx6lz( the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running uby71 1.lswxmat 850rev/min It turns 1500 revolutybu wm.7x11s lions 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 wpnp zo q(9o33revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tiresn( wz3p 9qo3po have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions asmmm *.f vb)q(1 lww4li the car reduces its speed uniformly from 95km/h to i)w 1qbml.*wfm(4v ml 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 puo ol15nv8lsf 7ts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of 17 l8vo5sflnoradius 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 the0i tmrfdf91r0 end of a door 74 cm wide. What is the magnidtf 10r0 9fmritude of the 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 torquej2lu0sx3wgvoe 4f q-lrt047h about the axle of the wheel shown in Fig. 8–39. Assume that a friction tor4 thlu23 0ql0jo-gs fer4vx7wque 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 masslesz:1ju 7 vvheg sg3o.s ,y:beh-s rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then r e.seo y3 h:-bvv71 s,gz:jguheleased. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a t1k9zs+, 2 pgkylek yhyz)34ahorque of 381 y4ya+92kh)ykzlk esghp3 ,z $m \cdot N$ 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 inertwd.;i e29 -l ecn74iq56jlpdxvnb6mj ia of a 10.8-kg sphere of radius 0.648 m when the ax l;n p4qinxm-cei7. 6e 29bv5 djwljd6is of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicyc t8ir3 4d,kr fbdac((of3fs;vle 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 ignrboaf( d(3ic3t 4s;v ,rfkf 8dored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated ink4av( i s54ppfzwna)/ a horizontal cir pfi)5 z(nva4w/a psk4cle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating atbnb- r57whc8 ge.-kum h 8agf. constant angular speed (Fig. 8–42). The friction force bm .8hwkar beucfhbg8n.g7-5-etween 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 inertiad-/8 r) jkwtldqex4pgiw+n4hkg,g* 9 of the array of point objects shown in Fig. 8–43 abo 4nlq8d9hkgit,ke gx+4w-)jwpr* dg /ut
(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 total mass is82j.q. mwn0e z qox+1 a:lfpvn $5.3 \times10^{ -26}$ 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 sz+amo0 ez+ 6fuatellite 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 m, what is the required steady force of each rocket if the satef+ +o mza60ezullite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylin ylvs718 wn ,tw*sbm,tder with a radius of 8.50 cm and a mass of 0.580s7 81slw ,tvn,myb wt* kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat,wu z*yaco-mo.u oh/ ;u)y pi88 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-dri( 739w.wcfhixxi nh;z ven merry-go-round and is able to accelerate it fromw 7(wcxn 3. hfzix;hi9 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, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually bro+c 5w2l0 rvwplm07 ciought uniformly to rewiwl2rc007l mo + vpc5st by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accel-z g o7aossna81+ 5llmerates 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-k hdt w kj o8h81ath(b.m( 2l(t(bzlz4fg ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the w2ht1t84z o blbatlkh(d(m((j fz. 8htriceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thzykvh8sz 0g-+in rod, as shown in Fig. 8–4zksvg+h80 -z y6.
(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 masfkz4++ gjeknkjjk1vfvi e-gf m;g 5y ,k4//-yses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four fub* ubl::* der7qg au;fll turns (revolutions) and relead fbq r* :ug:;bau7le*ses it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a;pls;,mz .d ko 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 torque of 280 hkvuh f03gd: 8$m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping down a sc (-e+b c3b fpg-dic)lane at 3b(s3-)fi gcdc+- pecb.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to zevo o. -pna8/vn. k;pthe Sun as the sum of t nvo8.n- /za.pvpkeo;wo terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. Hogg.8+o yep*qn/cnp1 n-gn- ax/ f(cepw much net work is required to accelerate it from rest to a rotation rate of q * /gna./n8 (-yp -pc gexop1+cgfnen1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls wyf9,hb/ c n i6kn3:jzaithout slipping /,bicn6ay93 hnf z kj: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 tip. It stapvw:(ikh(t5 (sp+ 4m jmihw8(y ie( wyrts 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 grou(4pi(+ k wmwsiy(p 5hj:t he8(mwyi(vnd? [Hint: Use conservation of energy.]    $m/s$

  What is the angular snmdko+ k6z6gy0e*-,0x4c te ;byc hhmomentum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 1 0s*c,k+n;6cg6 ke0-xhebyz hdtym4 o0.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylio5b *z zs5um8ondrical grinding wheel 85o *sbmzo5zuof 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 is rotating at a rat3:e2oz abclwgz5z 8f/e of 1.3rev/s If he raises his arms to a hor52 w: bgf/cz8ezoalz 3izontal 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 /9pkn kt(mjkw:v z7c2 shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the 7vzkkmcwpjk t/ :9(n2 tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin ros k;po6wokmbj gm;i/07v; 3bstation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of 3 bo3 pk 6okssb w7vmimg;;; j/0$rev/s$ 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 itruwk0r:xr+:x s 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 r: w k+urrx:x0a 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 figm6q-y4e*g zrw: qgf4/xc xz3j 01ifwu ure 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 momentuc.db5 li6+q nlm 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 5(bggc hrdsh5e 45xh5 I is dropped onto an identical disk rotating at angular s(5hg5 s hb54hgdxcr5 epeed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at)zik ch7 lu,yoe+ w75x 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 center of a rotating merx 8eai41;e9z 3 wi7 1jznaaexnry-go-round platform of radius 3.0 m and moment of inertia 9;e7n waax ex9n31z1z ja i8ei420 $kg \cdot m^2$ 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-g97t rwc7 d(f)ixl*iiho-round is rotating freely with an angular velocity of 0i x97 tr*fwih d7ilc().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 g+9 ccwc4v* ua wqd*7*n8nldowhite 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 nlqcc*7*w9v+ 8 d4*ogwdn caurate 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 excess of 12)xd,zm4- mbs* cyfa n00 $km/h$ 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 8+l)et inqo8y$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate ukhd).v.jzrm q2l0c6 freely without friction. The moment of inertia of th kr6l mcd.vj.uq 0h2)ze 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 sta /hopxiq: ;iam4hihj0d*)j ( z+heg,qnds at the edge of a 6.5-m diameter merry-go-round turntable thaa j+o g:,h;ij/zmi0h* q4h e(xp di)qht is mounted 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 x 1 ta3vbud m0oc/;ek,the 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 behin kmae,;ox1utv 3d b0c/d 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 side always fj fe0/otfe ah)ro-0g .aces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the/-g)otf f h0e ae0orj. latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates fb 2..r btj3)6xud qwgogmuim 1qlx0 9uo8+ ay4rom rest at 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 4)l z b+6qgwkgshape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate theg+4wzl) k6bqg torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of ma 4bi8e1:qlvtv,/vdfu ss 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical,:vv tuqb8i41/d ef vl hub of 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 the angular speed of the re;jq8ov1 xpj3s+ 6 yoqear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great,v u:vc+hs0t8 g were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform spherugtvs c0+ h:v8e at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollutionesuwyaeprhe;ril5(2 .q81b 6 automobile is for it to use energy stored in a h2e5uy qihr(w 8bs 6lr1 e;epa.eavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an / )ozldn4acwyo9ls35 $H_2O$ 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 s wo1u*dfaop 1ckj3,0jcc3zm4ib68tvb4 s9fb urface 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 pive8w :;/x ahfzbu.x er)og0fo5,naf*zot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The5z;rnwazfaf* ,eo/xf bx:uo0 g )h.8 e rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is stane 0pmzcsb (f))ding vertically on the floor, and we want to exert a horizontal for) pzb(cm)f es0ce F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s oni,xk +2(3dym , nzyw vym6pl0z a flat road is making a turn with a radius The forces actin3 yz d0zx6k mmy(piylv,2 wn+,g 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 of length 1.5 m andx5qsid/qe3 m yd.)a3x begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rp xism5/dqa 33d.x)q eym 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 solid cylinder and her arms o-flu u )ax6ka ,3obe/et* nm5as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater ,ku*x)mlabf 5 /36-eeuoatno with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindh 2)pmt hnye 4gj:ziktkf-+8*rical plates, of mass :28kj) -g if*4hmpz+nttk ehy$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 33ce vp e/ec;-b 5nlsmthe looped rough track of Fig. 8–58. What is the minimum value ofecebcm/nv - 3ple5s;3 the vertical height h that 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, butx, cjg s2b ug+ppgui+:/6t)lh do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reducek/ffubqwcux8 yw;) /x6fqyu1+-/ q xhs its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the a +6 ffy1xwwxhqu/)x/b 8qc/ u-k;fqu yngular 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