A bicycle odometer (which measures distance traveled) is attached near the whee-j4*sk.h 9( :sdmvp4qkxfy wnl hub and is designed for 27-inch whvs*4y(km :4sjpq -wx.9 dk fhneels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant anguyjxyb/ 8y(p)d-r xc-t lar velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For whic pt8yy-x)rxdc bj (-y/h cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be descf , nw0 0en -z0n4pct aqdeo2pbszdw6ne; /6a.ribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expla jl;a ;kr(el.rl+erx(i ui )1uin.

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- ,b+sqg bi-8 ps/gw-+pzw* ljmup with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answgw+j -b/,pgilsp +s8zq*w m -ber this.

A 21-speed bicycle has seven stgla2 5c yp 7: 0g4v7zrsjfvt2prockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Whg5vj 47tl0 2tzpyg vc7r :a2sfy?

Mammals that depend on being able to run fast have slender lower legs with fleshzno4+diq 3b) c and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distributio43bqz +c) ndion of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a l78ms w(vvm2ctcw e20 song, narrow beam?

If the net force on a system is zered4obuv:7 eys8iv9x;0 j i*uz o, is the net torque also zero? If the net torque on a system is zero, is the bo*d9e8zij: sveiuv70 u yx4; net force zero?

Two inclines have the same height but make different angles with the horizontsdtk1 7vvc+;h0bv)o cal. The same s c);vv0db7ksc+o vht 1teel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres si drk9yt8g.6kqmultaneously start rolling (from rest) down an incline. One sphere has twitk.g9 k 6yd8qrce 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 tdc ay ei .o(qzso06,j;he same radius and the same mass. They start from rest at the top of an incl.oojid6;sz 0q c,a(yeine. Which reaches the 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 conserved78h8ts sdj y/t. Yet most moving or rotating objects j/8t8ysdtsh 7 eventually slow down and stop. Explain.

If there were a great migration of people toward the Ear9hsby-07 :dljf27xq dja6jy dth’s equator, how would this affect the length ofds 0: yajb-7jlf9q2jdxh7y6 d the day?

Can the diver of Fig. 8–29 do a somersault without having .u-7iny7 yuali;l1fgd 8bd 2zany initial rotation when she leaves thy1ini7g u.du7lblz 8 fda;y2-e board?

The moment of inertia of a rotatingts dko 26kx9(7ml*c:s d e;se3x 5agtt solid disk about an axis through its center of mass is m;7:5xetakk ct6es *o d(sl93 txg2ds $\frac{1}{2}WR^2$ (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 hkz,a -b0zod 29/hw na3zn(jumass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Exp zh n(z w2zjodah0,39u/n-bkalain.

Two spheres look identical ancve1c2)z urd:u1)/3 jymun2( daif0 mull*e rd have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine whicfel2u ru3cl2r1j) )znm md0c/1 ud*yueiva: (h is which.

The angular velocity of a wheel rotating on a horizontal ayjrw .cd 1mbt3ej-x hu83)vi4k8t;ww xle points west. In what direction is the linear velocity of a point on the top of the whe8 tw4b 3hwtwyk3i8m-d uej j;c 1)rx.vel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a*s d bi8+2fdlu large freely rotating turntable. What happen8*u+fib d2lsds if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw ;dbu6l lybwh2 c0e -d6it 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. 8wdbhd2- ;60 cuybe6ll –36). Explain.

On the basis of the law of conservation of angular momentum, deovvdql j8mt h7au/ 5ct/+l2. iscuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propelle /t.h aq/djo+2 mevvt5ucl8l7 r can operate to keep the helicopter stable.

  Express the following angq:ldud;,ay z4ge k -1kles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate, using tn-w p5zwpmex h 24+k,phe information inside the Front Cover, the angular diameters (in radians) of the Sue,ph- xmwpzk 2w+ 5np4n and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from 7jixxo:0p/ z y)cx+ki cf,a0gEarth. The beam diverges at an angl ,y iop xcjg0i+:xxz)c0fk7/a e $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blende2kh6 zsl- ryj 5d5i)m)1 jnkmrmo:f2or rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the bladejrm 2y n2o1i 6zk5)sdkrmfm:)jhl- 5o s slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. I;iszh(x7ko x q;co7w4 f the ball makes 15.h 4w7 ;(io;kc zs7qoxx0 revolutions, what is its diameter?    m

  A bicycle with tires 6n bvgiw wh1 ybfneo)zn:6c2d9 tg)6-+8 cm in diameter travels 8.0 km. How many revolutions do the wheels makfe1 w+6)6)2nw-z idnbchnbyg o:t9 g ve?    $rev$

  (a) A grinding wheel 0.35 m in diamemql2 g .nb:or3ter rotates at 2500 rpm. Calculate its angular velocity in n:2o 3bl.rmq g$rad/s$ $\omega$ =    $rad/sec$
(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-rounbbhl 9c .6pz/-*5 u ydxxyy,cxd makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 ./ hc5xxcy,ubzy*d yb6 -lp9xm 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 th lp sh:h68.tj1zda*voe Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a point 0uuw1,.ws( q euq .nvw4 mibu,
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm frorj9fra.5( .hoiz is z0(s *ehgm the axis of rotation is to experience an acceleratj( z0iof.grhhie s9 a 5r.(*szion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 13tzi52o.z )n;d*+7zj9jrie n+beo f c k0 rpm to 280 rpm in 4.0 s. Determinoni+ krz ct;72 i)+d5boejfne*.9jzz e
(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 -fr* nacv,24 obk(lld $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts z(03nda)* m,l zrb. cvkuad( baboard 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 intenvml c3).(za0 bzrdd,*u k ba(rval. 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 rpm in 220 s. Throu( vz vo0ac;v +y3x6wrrgh how many revryz c( o+wavv;0v3r6 xolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s.casbey:xg/4m6 1han 4 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 “v.0 2n p;i2 rs8s 3hrfzc)0+mkcctsfdhuman centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its finalntm8p rczdv h0i0f22 3r.cs)fc+;ssk speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6. j cehkrn)581t5 s. How far will a point on the edge of 1et8)hcrnkj5the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running azv1niky8 7 ku7t 850rev/min It turns 1500 revolutiizyk u78nk17vons before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the ca th;l 66t i eb4a11lxuw;a+bepr reduces its speed uniformly from 95km/h to 45km/h Thepta+ewu;1a lb;6t h1be6 i4 lx tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speibsz/j o4/05objj t+ qed uniformly from 95km/h to 45km/h The tires have aj0i4 bo5j/js bqo/tz+ 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 a p+l0 l s(5g6kiqn3qkon each pedal when climbing a hill. The pedals rotate in a circle of radius 17 cm. glkkqs50nq36p(+i la
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is . ;1x(ggjh1u 0qf sk,/8cn emh6yojtt the magnitude of the torque if thqnf1/jm jgx;,y.o0 us hh6kct(et8g1 e force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel show2hxumdin.gw:+f * h. wxv/;tmn in Fig. 8–39. Assume that a friction torque . hxwm/ .;n2dv:x+f hw*gmut iof 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 mass4hlq, /v+od wb1uj 48 5hmhxrgless rod which pivots as shown in Fig. 8–40. Initially the 14g d/mhh4 +x 8vj5,wq obluhrrod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to n cs97rn u(qe(a torque of 38 qs(9 rcue7n(n$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m when thevc qr6x 56byxp63d6n5pe e7jv axis of rotatiox6pqy6 vev 6rb3556x 7 cdpejnn is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm i7 fj wok-h8zc*uo*acpb-6;sb n diameter. The rim and tire have a7uacpoof 8cs--kz;h* w*6j bb combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end os; +huu m8sfdj7auc0e1l zz*8 f a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculate ;csl8z mz8h+eas*u 1fj0ud7 u
(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 whee6b/+ d na2v xrqtcet988g urwsc:(ss:l rotating at constant angular speed (Fig. 8–42). The friction force between her hnedt6r :qw(sc+t98ac: g /u2 sbxrs8v ands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown inug :sgp vv;,a) Fig. 8–43 as:gp; ),uvvgabout
(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 oxf52+ cun fx5cwygen 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 correc.ape,bqbu90d:rxp0 q t rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satelliteq:0rb ba9qx , .ed0ppu 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 cylin:tl jw ro; v892*z:yjqk(s)x thdq5 elder with a radius of 8.50 cm and a mass of 0.58*:herzk( ldoq2sv: q y9)j;wt8 j5xl t0 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, accelerating it from rest tkx ;mins -f,-:ra)luho 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 sm8,6l+ jqjs3g mvrj,a7s9tv4, tdv q pyall 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 ch7q rv9svj4gt 3as ytj p ,,6,jl+mqvd8ildren (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 eventuall cl4y sn),sh6ry/;zf uy brought uniformly to rest by a frictional torque of s)nz4fh6cyr ; ,yl s/u1.2 $m \cdot N$ 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 aom/ 4 vgruu).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 the action of the forearm, b d r 9vbha7xz.8*i8x84atuvx which rotates about tb8dxi atrvx7z xah8.u *8bv94he elbow 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 considered a long thin rod, as lri6f ;4vtg*.mi p7uashown in Fig. 8–4l4gir6;p7fia*tm u.v 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 consists of two masses,9bw 6ueeq+y c,9 s,ep /fuw:wo $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns (r;h 1.cwir9 nvax.k(fxevolutxhwk;virxaf.n. 1 c 9(ions) 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 a momenttp/d l p,m+-udk up2c) 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 devel2gny8 y cg*(u0etd r87nopf2tops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without sliup ;tygm.u13 fpping down a lane au1 g. y;pu3mtft 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect htv0*aaaoa57 to the Sun as the sum of twooaaa5 *v t0h7a terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How mucha+ q-/ izw *bgby,h01udy32sc 3zjw jn net work is required to accelerate it j bnysbjz3dw0a3+ g, zwu*c2q /- iy1hfrom rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from reqf0y7dd)h7m- sb 8lgz2 uf s4qbhx;i-st and rolls without slipping down a il)4fh- gxs 87qys f;dd hb m07qb2zu-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 stixb ,vr7g-s- 8 7x/qoyw 5qulower end does nv7souyx/q5 -gq-7t sxir ,8wbot slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kluf p.axdw;4; g ball rotating on the end of a thin string in a cir;fuwp ;xa .ld4cle 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 cylindrical u50+2cfxexxo( q7 s b5wagu+vgrinding wheel of radius 18 cm when rotating b+5sef(0oxx2xgu qv wuca7+5 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 qps./bjf 0i -dyh*lv9his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to ldh s*f-/0. bqjy vip9a 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 i3my9q8v2o g 7rohbc/v ga7-*m2 zfk len Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from 9h /v-lko7ze mmfv23g yaq o8c r*2bg7the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rac5.gmg;3zk79pi(p ab53uad q u ztiz/te of 1.0 rev every 2.0 s to a pqga 3;i5z3t7acub.gm9z(udz kip 5/final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a /,cp c7puv7sl vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform dpcl,/s 7vpu7cisk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skatery2(c j;o*tet ec8dt(r 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 mohpx*wmgkxhte)6/cr;. 7 /dpz uug 70bmentum 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 djx3)/w r*s+ k lrsu/azisk of moment of inertia I is dropped onto an identical disk rotating at angux r+kzjw) 3/ss*arl/ular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a(d xzxmlxx,z nl7 z2/+log;0 jvoyx 16t 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 0acs9yd( hok8q;c5vm at the center of a rotating merry-go-round platform of radius 3.0 m and moment of iner0 yda85cs hvqc9mk o;(tia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocity of 0i 16w*tw; wq-trpt6bx.8 rt1btq p x; tw-w*iw66$rad/s$ 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, losing0pki//q)izk;v/b+ cvq 45bp(cfncv e about half its mass in the process, and winding up with a radizcpb )kq cv0+ (ki5vi;//nbqef4 vc/pus 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess svgqn (im69io8m5g7 nof 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 v0bj fi5/avb 7xrx66f $ 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,r2+ uco-t izj, initially at rest, that can rotate freely without friction. The moment of inertia j, u2o-rtz ic+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 diameter merryt31 z3 ihygo*u iyt.;t-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 1700.;tt3o igyi13zy t*h u $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying st9l(q2dt8kciksy/ w4 7l3zi on the top edge of the spool. A pekqz7y4t l9ii2klw3 s8s( c/t drson 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 side always fajiiljj9(9fm r 0 ff*u/ces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its /j9(0m iuij lf*ff9rjorbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from re: kt pl3e-1se4 u-smwqst 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 sh7mswd l .g;zo, o)gam-ape of a uniform cylinder of radius 0.20 m acquires a rotz; d)7s,g mwgoaom. l-ational rate of 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 solioq ngw ;oc;0s(d cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical 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 str0swogo; (nqc ;ing, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the g zg f9/fh; gk1,yf.oiangular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as f;8c4w bb+-pj1duoi x great, were rotating at a speed of 1.0 revolution every 12 days. I8 cb4obp x;1di u-fjw+f it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use ener9z )u s8m/zggah+* nxm;a ov,ngy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diam a,hg;8 /gavz*znmo+xmsn)u 9eter 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 anj(enoh6 / ak9t $H_2O$ 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 sg mk14pqn5 f9qfn ++nvurface 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 qjvj n n83r*:i(i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceler3n*q nj:8v jiration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on qrd,. njke- ;gg /lc.p(ynn( dthe 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). The step has height h, whe .e(dlnc j .q-gnyrng(;pk,d/re h

  A bicyclist traveling with speed v=4.2m/s on a flat roadr;l mfw.sycx;1 vd+q 0 is making a turn with a radius The forc 0v+dxc;r;f.wlm 1syq es 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 of length 1.5 m and begins whirli vu5*mqb0b3o4x 4s hk 20z kr)bg/xzxyng the rock in a nearly horizontal circle above his hhv5z/qo zsk3mybb 24*4)rg kxu 00x xbead, 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’sw:h oh :)ryfba(g w92;spbpdx1/ a8c m body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with :f(/p)a:m1;bco2xws rhp adhb yw g8 9outstretched arms, and with arms held tightly against her body.   

  You are designing a clgvja-lb/ucks .p 5u )ohjgzdti,2 64, utch assembly which consists of two cylindrical plates, of mav j6,/-)5 s,uilgocpzbk 2d hgj.aut 4ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rxka3w u bqk3iieqi3q1n p*(+0.i4 xnvough 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 highestk1n3i(ii4q vpqu*0 a3biwxxne+.qk 3 point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but dyzx3p h:5alw :o not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revw0ehivv.f++ .t;eox5 szny0 a2xt/tv olutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the anto/2w+vaznxy.v5h.0tet+ ;xev s fi0 gular 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