A bicycle odometer (which measures distance traveled) is attached near thu lsije9j :m17 r6yc .zywk;-)b9tt ufe wheel hufrsk.:l)9j6tyziu 9w me-y71ut cj;bb and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates atzi. :ed g(jvn/ constant angular 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 ta i edjn/.:(vgzngential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid bodym p 9++p5iigbv be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a lar3 zp; z+s5 m8dk a1;cgcimh zze8en6m5i1iq9b ger 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 yf /6 9hnu.b, (;qkmp3yjhsguthan when your arms are stretched out in front of you,.3y/6u9f buq n( jmyshhgk;p? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockj eg:9kzjpt ct8 c -:bo(lj5*fets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedaceb t5zt-*jo::9c pg j8(kjlfl, 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 g b+a ows))skl*,zq;v lower legs with flesh and m)lba+,vgow ;*kqs) sz uscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a livlhyt2xa.3j r saj e1--5a4q ong, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the nett(edqgjku,v99 7 g; kg torque on a system is zero, is the net forckg e9q7uv,t(gg9 d jk;e zero?

Two inclines have the same height but make different angles with theti4memv0,30)w qf*dv :i klm e horizontal. The same steel ball is rolled down each incline. On which inclfv dt*0q3 ke)ilv4 ,wm :0iemmine will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously h/ k:y )nq f9s*xvm4nsa-ike1start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy n:-*na/4qhx9 s1 f k sev)yikmat the bottom?

A sphere and a cylinder have the same radius and the same 6zo+ ef+jhl c-x8oesdf*yx1 : mass. They start from reex y*8c++zdoofsh1 x:lj6 e-fst 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 rotational KE?

We claim that momentum and angular momentuj 2ujl +pn pavwj;2t 0r.kpeu*w*(cz+m are conserved. Yet most moving or rotating;pu u+apjp0(twznv rw*j lj.k *2e2 +c objects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wouldzu/pm6vuy0gz7/l u;y this affect the lengtzmg76y;v pl zu/u0 uy/h of the day?

Can the diver of Fig. 8–29 do a somersault without havingw(3z dr fl)ju;+vz+sf any initial rotation when shlzjz; sf+r w)d(u v3f+e leaves the board?

The moment of inertia of a rotating solid disk about an axid5eu ys;1 elg+s through its center of mass lu e 1g5dys+;eis $\frac{1}{2}WR^2$ (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 a0 ,dq)ulkeji)06te ch 2-kg mass in each outstretched hand. If you suddenly drop the masses, will 0l)diuh qc0ek),et j6your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, .()hxup2vvgy lz ,x8ione is hollow and the otheripxvzvh., l 8u yx(2g) is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle po c4t:nhava(wo) 9fvv 71in 7xuints west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear a49(v:7 anfcx7)1 tov v nwhuiacceleration 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 la7 s/gn g*x.i5 5dhlyzorge freely rotating turntable. What happens if you walk* ns.h75lz5dg/yoxi g toward the center?

A shortstop may leap intc7 e)wsi wvy-2d,an m*ylj.p2 o the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite dir m2)2y7d- as.j evnw,l*pwicyection (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentx) ,g nrdm+ 1(vdkflc(um, discuss why a helicopter must hadfdmrck+ 1g,)nl v(x( ve more 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 rad;za5 u u3sxnt9 tcl 69xbb*v-qians: (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 Eae ci)ov1b9 5nfrth because of an amazing coincidence. Calculate, using the information inside the Front Cover, the bc 15i vn)foe9angular 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 diverges a dz rkp0i)ycf-q2 o(g fs)ix:8ti(pig2qrdyfo :cf z0-)ks x 8) 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 am6f.oj r 0toc)t 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 accemo.rfjc0o t 6)leration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to/(f0 skt 8xou q;qgdkt8m3 jb, another child. If the ball makes 15.0 revolutionot;sukx8mk(38g f,q db0q/ tj s, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. Hybp+vm 4dvz: )ow many revolutions do the+pdv bmv:y4 z) wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates p7wek p 0bs,rej b9t9+at 2500 rpm. Calculate its angular velocity in bew j,s+tp9k0ep7b9r$rad/s$ $\omega$ =    $rad/sec$
(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 maj e+waeuajhe55 x ; (m9pufz*:kes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the line:5e( zw m5e+xp*ae; jfhjua9uar speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around the ik ba662lhho.Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of tvfej gn/hawm n;d( ;7v(h g63a 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 frot)pc09v xx.q rm the axis of rotation is to experience an acceleration of 100,000xtvp09)rxc .q $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its ce uyqx 79,6oota *s6uybnter from 130 rpm to 280 ry*9oyq 66s axub u7,topm in 4.0 s. 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 radiuseuf0gx0i2ph,.dv ,ryuq i:n 0 $R_1$ 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 Moon0 m8ty::yyy/1 7ijn rgnn+wc*z lwm:v, astronauts 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 intervj::g8/ww mr0vc*+yyy iln y 7nnm 1:ztal. 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 uniformlo8 y8:se;becvr quspc*w b16 8y from rest to 15,000 rpm in 220 s. Through how many revolutionss88:sbbv*e ey6oq wcu;pr8c 1 did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. fzpm)j9,nh,jf1 .efxymn4, m4u1q kvjg2sy (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 whb8lj s7nhkcs0 01zbx,irling “humak,0cn0jbz17 lsxb8 hs n centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diamuns-1du* k 0)sb;zhrreter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far wilb 0sz 1h)r* r-sd;uknul a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It thhq,t0ox3 l1 fvq;w/ ourns 1500 revolutions before it comes to a /ot;0w,hx3oqqflh1v stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformluew(rm-b0+z :7m wpd lh,edh*y from 95km/h to 45km/h The tirewm-hw:l( depdb7 hm, e*u+ 0rzs 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 speedyh * mpxbs81w/ uniformly from 95xsh8 1/ywbpm*km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedalbn.o qb*(2 p31botua y when climbing a hill. Th oqyutn*b2b(b.a 31po e 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 door 74 cm wide. What is the tjg k2qtjsjm7 8,yn 9.magnitude of the torque if the forc.8qj92jtjytn 7 ,m ksge 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 shown nh:v; pxe j( b)guf10o.oa 5jkin Fig. 8–39. Assume that a friction torque of 0.4 k0j5ge :.;f jnba(ux)ph 1voo$m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are bh2a 2//wyit 5+j vnxnattached 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 syste+itb 2 hjna/2vwn/5y xm.

  The bolts on the cylinder head of an engine require tightening to a tobk fpy473g48 ( ucqqd,3 ruapprque of 38a kcp7fpb qr,34q3pyg4du (u8 $m \cdot N$ 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 ow aj)yhljosp ki*h/pjq4 u) u(47tm*4f a 10.8-kg sphere of radius 0.648 m when the axis of rotation is th*iw a*4sumjqj j ylh(opp7/t4h)u k4)rough its center.    $kg \cdot m^2$

  Calculate the moment of inertia d,uf imthi)l.)t wl)9of a bicycle 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 ignoredwl t9)u iti.mh,)lf)d (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, lilafp.dfpc(+ v-1kgtq: o+ k )ight rod is rotated in a horizontal circle of ra1) fpt fk+l-.+dpigv o(qc:akdius 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 a23n ku, ctsigcvon 7+2ywi+ 1o potter’s wheel rotating at constant angular speed (Fig. 8–42). The frictiyvncski u ig72c312 onwot,++on 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 poin99.sy z) l flhjg4 c2i74yvjh4zk6t sat objects shown in Fig. 8–43 about2vcl9 fskyl74thg4 jijz4z.9 6) sh ay
(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 twoq(3 xyv)k jsjj7jhn1bk 5z p8:fk+b*f oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniforfznd ril(j*q:yx 5(3 hm cylindrical 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 is the required steady force of each rocket if t( j(*h:qzdnr ilxy3f5 he satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm ands7 y drtqf84,hqww5a, * hak0k a mass of 0.580 kg. *7,dr0qtq y hkf, wasw84akh5Calculate
(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 isqw xyqk 66.h,t 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 tangentiallxe4zz d 7qk)vyh53qq* y 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 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 torxq3de kqzhv*q) 457yz que. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is evenio)q ynr0.t ,qtually brought unifort0on. ),y iqqrmly to rest 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 acce ddsi0n3pidu;)/y1 e blerates 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 b h dvj-q2h 31nngkqe:1all is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the tqvk1n1:2dn q -ehg hj3riceps 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 shown in F*bee0m2sx sl*i h u9q2a(s+rk ig. 8–46.sriexl+9ua (bk* hs2mseq0*2
(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 consist.3basvshw yc ds.r1 cuq;,69*s gr s)ys of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four ful2a)6 *2/cs) rez; c wjeofuyo- :bbjonl turns (revolutions) and releases it at a oc26zjbnyr)e/w2;so -j of bc *:ua )espeed 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 momexn 9 2rhf*0vtant 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 nktww5fm7 f:.(mbp6 dof 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 .qrvq-zrq *9g cm rolls without slipping down a lane qzr q*9rqg-.vat 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respectb6n,)iqdaw1b ) lsan5 to the Sun as the sum of two term bsnld5i)wna6qa1,)b s,
(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 dsyz10tp, i)t of 7.50 m. How much net work is required to accelerate it from rest to a rotation rati1t y0spt,zd )e 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 fr.3gt7u kv u0po *wcy;qom rest and rolls without slipping down a 30.u.w* pqty;c k07 ugo3v0 $^{\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 (nhsykh6.r*m gi z2 gg/f3bf(and its lower end does (yh.6(ggfbfigsn2z / 3rmhk* not 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 w p+ 1i6ew9/in ryijk/.iie1m of a 0.210-kg ball rotating on the end of a thin string iny9i ik6j+ mew.ein1 wr//1p ii a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum oy r0qh 7ccy)kqrt1/2u f a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500cy 12/uqq h7yk rc)tr0 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 ratva6mookv2 f:(s* 1w tve of 1.3rev/s f6vao:vwmos*(vk1 2tIf he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of inerti.nfgs0 h k3vt4 nqm8(ua by a factor of about 3.5 when changing from the strn8.(n4fu 3 qhts kgvm0aight 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 initip,qdunlee8(7qhjgl .zsp ( /3 al rate of 1.0 rev every 2.0 s to a final rate of el7(qu,/j3zn ps8( l qhdep. g3 $rev/s$ 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 its center at a fregvesu,u zp7lr g k.6rkvl6;/pdb4t 7;quency 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 a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of th7ugtpkvv. g;4lus6epk/, l76 rdzbr ; e wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3.5 :8; j h :ffmqy8f1knwu$rev/s$ 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 moment ry 9.r/s1lon8d,fspmum 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 momen s.foqfi 6e 2jk0x di quwvy/5p93t+(xt of inertia I is dropped onto an identical disk rotating at angular ut/x qy. 0ek2xo (+ fd9qi6fvji53sp wspeed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnszek(w 1of- w2e l7p;vd at 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating mer 1tr: k)q:qoazwd4fd/ ry-go-round platform of radius 3.0 m and mome qf w4:odq1 az/rd)k:tnt 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 rotating freely with an angular velocity602gl p,mjutas 1,hdx of 0.,gj61 h0dta ls,x2u mp8 $rad/s$ 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 wet8.cbw1a6yra0 v ;id hite dwarf, losing about half its mass in the process, and winding up with a radiuewyv; cabd1t.a68 0irs 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 pw83 ;trq;gvw89 xbqyexcess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass m9yh,epo *;aa $ 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 rot e- bd9vjorls 9m0)dpbih,5 -mate freely without-mm l9b r,dp05vjd) s-eoh b9i friction. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of n93 p;h:l* i6 yeicy0bd7v aqha 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inert *7 3qniv6i daly y;0h:h9epcbia 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 rop0o c3ms5bts ;lls 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, holding onto it, Fig. 8t ;sc0op3b5s m–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 Earth. nha;.tzn sp/ ksgioq*18:m3 6z(5)q sqrse dpDetermine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon a)*s mp3s6g8daeipz.k ;qsq nt: z/s1nor q5 h(s a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 m/.g st:uj)i4wldl vy; 0$s^2$ 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 cylinde1ua*ha0 5rkx:* k gfnamt8ul) r of radius 0.20 m acquires a rotat * :xnug0kl f1tkr*aaauh)5m 8ional 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/-b8prm lfz ,(v4ef vfr3.jdj disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solidffr38/b dfr4pejvm,jl(z-v. 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 string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, howg:7ncmys2 1*k* cg/4zr -ol tv y5tp8t fkv0qh is the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, w6qeig y4+32 ,hb 8qw crm2i zi/csvmx7ere 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 w 3h/s 7r2xceyq,2im ig6 zv8ib+ 4mcqwould 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 energy store9eeyha19ur ta6b2uy. d in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical fr2euya91et y u6h.b9a lywheel 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 kbrp 9upw99b(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 rolling5gretciq7 pgo0 xh8 .* 9:aaey on a 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 pivot free)wqv(dtjao u 83q5ity d46n6uu 3iu4dly (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 odiqi 3qj5yn)tad644u v(duo u8wu6t3f 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 verticallypleig, cc;d/8pg5d 4c nvy)l 3 on the floor, and we want to exert a horizontal force F at its gdl8c4gn)d;35,ve ic pp/y claxle 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 .xn9no-lkaa/ bj *:qn speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cy/ajl kaq: x9*-bnon .ncle 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 lengthz. ion1iwn s2, 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it frow1 n.i2,z sinom rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, mamz q +z151tvumking reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning sk mtz1vum q1z+5ater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cys,hmc y8 2+qdo-,f :9x ebmwmjlindrical plates, ofb,mqj2-md:eyc+8m 9h,x sfwo mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls ala3i zlgdptr g4e-2 :b0y6b 9dlong the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leavingi:-2 brll4 3 t0pzgde96gdyba the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do t3k9.5dc+ew prdq dyt vv 213enot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed ukt-bl8( soru8 niformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) 8-lbo(tru8 skWhat 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