A bicycle odometer (which me:4 j60qkcm;* diacqo yasures distance traveled) is attached near the wheel hub and is designed for 27-inch whe cj6*q4dy 0;iackmoq:els. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim havay vg,mh z3;02/jjvzg e radial and/or tangential acceleration? 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 l2jh gg;03,zyjv/av zminear acceleration change?

Could a nonrigid body be described by a single value of the angular veloci *(e yqwwwhyue 30,o2( ouztt;ty $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forcki/ql2y u8 i;g4ohc i3,gdif2 e? 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.ppe9jph .3ui a sit-up with your hands behind your head than when your arms are pje. ph9p 3u.istretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprj) o 8zegxq 6yvx+7 zo6c)0o9g+mf :.iw hbnakockets 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 toe b. k nwoqvh+ojfoxx+mz9:6z6i80g7)gyac ) pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slehav/o sq/ics2/1t jq, nder lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotationa/ 21,hvcots/sq /aj qil dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walker8sc h:t5yx* uzs (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the8msu3+ bws8polf in7gp 2)9og net torque on)b9s o8pg f m2+ln8ws3opgu 7i a system is zero, is the net force zero?

Two inclines have the same height b5yuahnp.sh a.l.z : h0 -fjp0tut make different angles with the horizontal. The same steel ball is rolpa.hah5 l-t. yhuzjnps00 f:.led down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) downw5c i *4cxh1cx9i vam4 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 great4 i4avcxcm 5x 1w*9hicer speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start from0e t;ldp p1mem8p 3adra*2hd7duw3 8r 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 has the greater 3;u 71hwdml3 de 8*at 2d08pdepr pmarrotational KE?

We claim that momentum and angular mom9a pu)2*,g-vc9 ;: osfk4z 5 unupkjhqvba( mrentum are conserved. Yet most moving or rotating objects eventually slow aukpa9 j42m5 :9r vzn g)u-pfobv ;,*(hckqusdown and stop. Explain.

If there were a great migration of people toward the Earth’s equator, j5mt)(g0x))jof: e ltpl l8zd how would this affect the le 8jlzdmt:)e 0olp(jxl) f)t g5ngth of the day?

Can the diver of Fig. 8–29 do a somersault without hacopa-7,lly5 iving any initial rotation when she leaves the board?,pl y-lci5 a7o

The moment of inertia of a rotating solid f9zfhz u6i 37cdisk about an axis through its center o7h69fu zic3fz f mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stdu*amy3;z7: nyzr vz:pgt, 1/q 4di tdool holding a 2-kg mass in each outstretcqygz,:i r4 3yd7ztd:da tvp;mzn*u1/hed hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have t :n,srfl9qgj, he same mass. However, one is hollow and the other is solidsq ,l:j ,9rgnf. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a hhqldoa8 )b v*3orizontal axle points west. In what direction is the linea oqab8l3) dvh*r velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large fr r8v;homi2u*g1 yvoi7eely rotating turntable. What happens if you walk toward the2ir *hgvv7o y 1;uomi8 center?

A shortstop may leap into the air to catch a ball and thf8*r or, i5xpfh-at-vw q;y.s 3.wv alrow it quickly. As he throws the ball, the upper part of hish 5po,;l8vra.yi - xta 3v fwswr*q-f. body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum,7da ;m*lsliwse - *l py(32(leztqyf8 discuss why a helicopter must have ly (z;alyfs li7e*8wq(el3p- 2t* smdmore than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (q)s ;r7*dbgqjmw.r g/qx v 7t 0fdk,clvb.r7(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. udti2 te)f8f -0sduy)Calculate, using the information inside the Front Cover, d -e)i)82y sftdu f0utthe angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam dtwwu0370cri0 f h -auwiverges at an anglew07a 0wiu0 fwh- rc3ut $\theta$ (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 ratej5sa ny+62u xz of 6500 rpm. When the motor is turned off during operation, the blades slow to rez2 snuy+6axj 5st in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another(7xr ts 0ozuumt6ry+:64 noh g child. If the ball makes 15.0 revolution o 4 6zxuot(+60snrgmt7yrh u:s, what is its diameter?    m

  A bicycle with tires 68 cm in diameter trq i3jgtzk+h *+avels 8.0 km. How many revolutions do the wheels ma* jhqit3z++ gkke?    $rev$

  (a) A grinding wheel 0.35 m in diameter+fy juk+1ads )*j uydq;zr-+f rotates at 2500 rpm. Calculate its angular velocd)+k q+as *ju1f urd+-yjf;yzity 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 inkx flh)srx/yh5x7 4 y .ric(+i 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m)( ir /k.cyy4+xxilsxh 7h5rf from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angula-ph ,r3du5bzqw;x.eb r velocity of the 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 h+ d l.d,23srhhroq3q a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm cp6x-j)wg rk0 from the axis of rotation is to experience ankw -)j0c6xrpg acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformlyrxm0n fm.0x.of.( 8j - orh3ia wazcu7 about its center from 130 rpm to 280 rpm in 4.0 s.z xm cr oxun -30afai0h(o8 .wmfj.r7. 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 eqnq+m, )vy3,n 2txtm98/aea dip 0gr $R_1$ 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, ast,u4zaf-nut; r ronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can bez-f;,uurn 4 ta 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 rwzj icsx *n13/est to 15,000 rpm in 220 s. Through how many revolutions did it turn in th s3iw1j*x zn/cis time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Ca. 2sib jvln2+x(ym505 vjvstylculate
(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 h-u ru)5b ltg e,* (0wdy.ytxawhirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speede 5)-a lygxtuhbw0 (.*tur,yd.
(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 accelerate9j/g;go:gd -zxvnae1o 2sr k (f:gmos)rp+ g;s uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have trav+:fr1sg)gvoe-zdr o xn m:g2;;( aopg /gk9jseled in this time?    m

  A cooling fan is turned off when it is running attxr juhr1p e86 8ogc)4 850rev/min It turns 1500 revolutions before it comes t xpgrt18 j864ro)h ueco 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 thes, rj8nlgu--if hhi)1 car reduces its speed uniformly from 95km/h to 45km/h The tires have a diamgiihus)l- rh- f1n 8,jeter 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 speed unik xa , 4 *es;ozq67ske0rb)pav(ktdnd4:kn *pformly from 95km/h to oek*n sd:kd*kk6 zaeq ) 7p,pr44 ;(0snxavtb45km/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 pugd6hw cqo m.7;ts all her weight on each pedal when climbing a hillw6q ;o.hcm7dg. The pedals rotate in a circle of radius 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 ddp; 2sd+x5 hez:x(a qgk4a(odoor 74 cm wide. What is the magnitude of the torque if the force is exerted4;q :sod5(p( xa2xdghkaz+de
(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 shown in Fig. 8–39. k2 yg 4:t p0ed9axjv,gAssume that aet,4kg y9ag0:vj x d2p friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attac- )wx97tu0evxs s7o(kgn zhl:hed to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this s:t )ehx sxsug7n0(vkl -97 zwoystem.

  The bolts on the cyl)m:za3:gu kj pinder head of an engine require tightening to a torque of 38j3kgm:a u): pz $m \cdot N$ 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 h4j k9xn69cc nof radius 0.648 m when the axis of rotation is through its cenn9x6k9 4hcjnc ter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter.yd(n(th(f /hu The rim and tire have a combined mass of 1.25 kg. Thf ((tnh/uh dy(e mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball zo/ -77gs-v1 gsp m4+ubpc awton the end of a thin, light rod is rotated in a horizontal circle of radiuss4-zvwug a +-p7c/pgm bt17s o 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 covrhk1u3i n4iyq bf:u n :-97ernstant angular speed (Fivurnhqr7f eb :k-ii4 :1n9uy3 g. 8–42). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point ep8:- hh /dhplobjects shown in Fig. 8–43 l-dp 8:ep/h hhabout
(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 wwvmqq+*5/k qwt 1n+o those 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 cylindr w;jy( )sgz na(66 5lbiycj0ncical 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 m, what isy0zj(byn6j( gc;s 5)wicnla 6 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 cy8e m/u ;nyngekngzz0+k1 0i(v linder with a radius of 8.50 cm and a mass of 0.5g k0;kz yu80izn(g+mv1/ nnee80 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, accelerati1/fed:) g g5d4xaqe kung 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 tangentiqhukayi :gu7 ghe(oo ,) d/d,3ally on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a , qyu7akh i/gh3ou ,)g:e ddo(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 isn81:m5 1w8et rfoyk vv eventually brought uniformly to rest by a frictional torque of 1.f1 5yvtewo1v8:r 8nmk2 $m \cdot N$ 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 acceleratv28p q ldxo,ms3u(:i wes 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 solel3h y :rmi0yswk8;l:dsy by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest tsi; y:dsl kh30 wy:8rmo 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in3)gv v sapj )ik3b n6hqb ny(1k*(rgn; Fig. 8–46.arpkk;(qn6vig) vsn3*)3 1 nj(bybgh
(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 i) f 9zd6 pq5xyci3pz,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 accea;dboaugfiyvdt4a -m, *+wvqlo*ib- /51 j d*lerates the hammer from rest within four full turns (revolutions) an; /mod i*1yaa-+ujv dt*vb bdl-qwi,gfo4a5 *d 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 moment ofc cu7/xe( w * ;iou,m7xsxg+fg 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 19/lrgd0 karaof 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 a dzcm; mbf;7x*qmv v )(35wguund radius 9.0 cm rolls without slipping down a lane;x3(zuudbw qm v vf*mg7 c5)m; at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to thyk0 m)o8km (xlcbx;2*iqg*fuzzn b 7 6e Sun as the sum of two terms,m*z7qo0bk8cn b (fyu2 xgi)xzk*ml;6
(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 an (ru ar0asctd).,8ykcd a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per8acdky,0 rc. ra()tus 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rv,w/ bl :ucc0jest and rolls without slippi/lvbc :j wu0,cng 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 vert9j.:z5lq zbydically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Udlyj :bz.q9z5se conservation of energy.]    $m/s$

  What is the angular momentufguthd npk,u- 6 opb /(:q ++bp7v:mbom of a 0.210-kg ball rotating on the end of a thin string in a circ:p6:v -7/ubuqf p hk dbmtbo+pn,(og+le 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 grinding whnc(zs8h: znzc(6an r 8ugsq4+eel of radius 18 cm when rota cg(6 s8+ zza(n8sn4nu:hcrzqting 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/ o9)z *oexx)z76j 9kwmvt rth rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotatiom 9z*o) )7tw xro9ek6/ jzvxthn decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her yf6xyx 5n+ simgw(f,p5:/ fgdmoment of inertia by a factor of about 3.5 when changing fr pdgg5y( wnm+6xs,xfy f5f/i:om the 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 t jo p,ixi)9s:w8 n ac13e/t.th eje s/qm7l.mher spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final ratxh 8.pjos :. mt/n 9tiic)qet ljewms/7,e31ae 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 rotatjb p wgd; :lo46*:kvylc,ynw *ing around 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 3n;yvb ,g6w:l*c*4: j wlypdok .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 skaten69z*a0yel mo 9pgw 8yqth*.tr spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Emy+rs 5tb+/wa8(0r6g uj k oycarth
(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 z ub8. -p7) *eoadqwdsof moment of inertia I is dropped onto an identical disk rotating at angula8dp de 7b u-s.*oqw)zar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4x0ygwgt+kmf0 ;8/ze v $rev/s$ 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 ojgmve)(b5igd kk: i1,ek5rjm*l8 .t of a rotating merry-go-round platform of jd*e m5)gkoi 5jrk8m1b:vel k g.,(itradius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is (c4i; xq ornkp8(u 71et3yscurotating freely with an angular velocity of 0.8 r( tpo1k8 n3;u c4q7(xecuiys $rad/s$ 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 haltb4rqt198uq0e4f jqcw4xd l 3f 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, wha84qdt3u0 9 fw4lx1ctb4req jq t 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 of* rmx4;rwadrwnob2p78d(srp b /1m. n 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 /:gi( 5artyp4im,l h/j- nhht$ 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 aad 7x u u.lx+vvek1j;(f-j7ont rest, that can rotate freely without friction. The moment of inerexk(.7 uxj-f 1;duaoj7+ nlvvtia 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 v..l (op*fbpsstands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionles. p.ov*(bspfl s 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 ryl avtkca 9;/5+ w qb/fq07cpvolls on 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, holdip;c qy av lw/q7tfkb59c+/a v0ng 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 faces the Earzgzgbz ( zv*qfd j:51g3e-k d9th. Determine the ratio of the Moon’e*d3 zk zq1:(v 9g5d gzz-gjbfs spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of ,6 (pplalm;lc4c7iq b 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius y) g2ezol/yk: 0.20 m acquires a rotatioykl /ge o)zy:2nal 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 solid cylindrical disks, each of mass 0.050 kg azv:ogr*1ptl 9y03wuw nd 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 energyvwg 3 z:ruypo10 wl9t* 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 rear wheel (z(gg1h 25pjj l$\omega_R$) 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, wzx7v u-3(y qazocy82xere rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to axvo 7x(-zqzu 3ay2yc8 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 automob mwi4 oj n-g-ar0qy,+vile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”ayw40j o-mgr-ni+,qv
(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 illustrat9q )norsl fm2/es 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 l3c s); w*ry-ic gv4wjqgg,h .horizontal surface 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 pz7wbmyee -f -0- hqd(gwi3*mwivot freely (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 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 e0 3dihwe7my -(zwwmqb g f*--shown. [Hint: See Fig. 8–21g.]

A wheel of mass M ha: (9m vikvl.qfs radius R. It is standing vertically on the floor, and we want to exert a horizontal for9vv qf.ikl( m:ce 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 spce1a 9r+: vdtpeed v=4.2m/s on a flat road is making a turn with a radius The ford:veapr9 tc+ 1ces 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 hxn,y/nzg .g *sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does yz hg.xn/g,n*the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylindk,v ; qpq l.5i zpe8n:zctkip/6mkm5;er and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, ak :68tncv i;pzz.il5q kpe;,5/ mkmqpnd with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical pl lw)6pbh 4ebug;s3 ct9ates, of mass 4p9 tb sbehg6cl3uw;)$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 loopek-iqdemcp+0*0--ff/ hno zs qd rough track of Fig. 8–58. W-sf+*- 0fk/ndq0cqho zmp i e-hat is the minimum value of 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, but do not akqs1 :.+vxew assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions an3l5j j-8flm9l qcf6dx6 tp7h s the car reduces its speed uniformly from 90km/h to 60km/h Thllf7 6pqt m-dc59n83 hxjfjl6 e tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s