A bicycle odometer (which measures distance traveled) is attached near (: by,*u4l swv2i zf hbr-er.athe wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wyr :2irf,z.bshl(a-* b4w euvheels?

Suppose a disk rotates at constant anehir; 4d1x9ygd:ehj)o5*bm k gular 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 which cases would the magnitude of eithed:om )rx45*;k hg1 yde9ibejh r component of linear acceleration change?

Could a nonrigid body be described by a single value of the angup7:zq fp 0+8kiuuo h dnw6.5pilar velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a laikuuy54 bb dbdx ;;0r1rger 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 wi8:d: kf4z2jjq dtjotq :x)sg/th your hands behind your head than when your arms are stretched out in front of you? A dia:fj:4)q dt: /s2q 8dgkztjoxjgram may help you to answer this.

A 21-speed bicycle has sqq )y8hnp55aw even sprockets 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 o pw)y8 q5n5aqhr a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs withtz k1z, f26u r.,fpcs5b-xq vx flesh and muscle ckxv26ut.p sf-zb z 1qfx5,,c roncentrated 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) carrymc*392wekjxe eyhx (x 5 tn4/b a long, narrow beam?

If the net force on a syste kuj wu.ylq5cqw9n . h5e(5m4is5urj+m is zero, is the net torque also zero? If the net torque on a system is zero, is the net force zero cy.j q.+w 5l5 5nsrku9qwjh4u(u5ime?

Two inclines have the same heigh8 m7:j0lz v;crcsv xe.t but make different angles with the horizontal. The same steel ball is rolled down ;s v 0z7rx.jv el8:mcceach incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling ; w82cj pjhwfp +)(yuj(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? Whicpf8 yjw +2hjwc()p u;jh has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder hai-5,ql0fgwo g ve the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the qgo gf-, i5lw0greater rotational KE?

We claim that momentum and angular momentum are conc3z. r. ++ cm) .iclrgces:mguserved. Yet most moving or rotating objects eventually slow dimuc3+c:g.+m l crze.c) s.grown and stop. Explain.

If there were a great migration of dm* 8 82tgt qdkxf2js5people toward the Earth’s equator, how would this affect the lengthgf8j22x5kqd8 dm* tt s of the day?

Can the diver of Fig. 8–2cce9ql/pm/*f j 5f:.6xfyq a h9 do a somersault without having any initial rotation when she leaves *. lq/5yj 9 :ace6f/chp xmfqfthe board?

The moment of inertia of a rotating solidpn:6qt*9dc. )imbl yo disk about an axis through its center of mass is mb.9ot) cyl *d:pq6 in$\frac{1}{2}WR^2$ (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 rotat zifs 26hsv+*8m3 zhvming stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the mass zhh zms26smvv 8+*f3ies, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However,yh)xg)tede9l(8lqz6 one is hollow and the other is9xldq)zyg8the) e( l6 solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotatkm ph4ajdq4 u4-e(7 gaing on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular accelerm e(kqd-paj744 a4uhgation 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,-dq tr+2fmd i of a large freely rotating turntable. What happens ifd+, f qitr-md2 you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly) zsedx/mr:i3yn p p x42nuh9+. As he throws the ball, the upper part of his 9u) x ed2rhpisznn3px4y+:m / 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 law75 mdlm( smy4g of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keem75sgd m(y4 mlp the helicopter stable.

  Express the following angles in radians: (a) 3*3-/;lxmi8 9j p zt:z;z/7fuxhxv nprdf8cfx0 $^{\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 coinvl 3x v 7r/*:oduyk)rmcidence. Calculate, using the information inside the Front Cover, the angular diameters (in ror /vy* x)7um3 vr:dkladians) 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 Ea y0wwaz:/ui,t rth. The beam diverges at/0yza wtiw,u : an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor is turned jdd3 x5ddv 1:woff d: dd3vw1d5 xjduring operation, the blades slow to rest 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 child. If the ball mjdz 2ai6qn5oag)aj : ;akes 15.0 revolutions, what is its diame a6 o2;aqj 5iazg:nj)dter?    m

  A bicycle with tires 68 cm in diameter travels 8.l1 q( lwf2xen;uce7so/,(xu a 0 km. How many revolutions do thox(f 2q;u sue1/ec xa7 (w,nlle wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter8 0 arjjt3s5mhfg ddo.-y );ua rotates at 2500 rpm. Calculate its angular velocym )a ;udja5t3 .fhd-gos80 rjity 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 :gqkp az8qvxen,g;:9in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m froq kgvq:zg;,8p9nxe a:m 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 t, 56ep(qgdy),p hhufahe Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ocvysaf06zy (z2boy42 f 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 from the axis o* *e h1uki2. ;ee* 0lwubpwgydf rotation is topeib*2e0wk uy. 1dgw;*h l *eu experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly abopvu i6g)i3w lv0uq puiuict2(t* 0g69 ut its center from 130 rpm to 280 rpm ppv0i 0w2utcvt 6 u*uii)l (ig9ug36qin 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 radius5z2ykjc/m,fq bd,ah 2 $R_1$ 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 aboard the Apollo s ltg*jesernp+2p :7 o9pacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trige tl *p+j2e9s o:7rpnp, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,0zlcph- fk5du pb9:h.d;p 7n;v 00 rpm in 220 s. Through how many revolutions did it turn in this ti;pd:;nphukz7pf .dbh lc-v59 me?    $rev$

  An automobile engine slows down fror o2 9k1zghyk9m 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of f:9j ,we. /gtx/e0hr.qvyqrt ylying highspeed jets in a whirling “human cee,q y0we//y.j9g.rrh q t :txvntrifuge,” 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 diameter h*nucx3oji1p9g 5w pat48 d4q accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have trav ux8qpn cjd phow4a31i94g*t 5eled in this time?    m

  A cooling fan is turned off when it is running at 850rev/e h rzfe.f :(7zz9yc(qmin It turns 1500 revolutiyez(f(e 9qfzcz 7 rh.:ons 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 car r9djk,1g 9g1et+vhl z reduces its speed uniformly from 95km/h to 45km/h The hjt v,9r9+g11g kzledtires 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 ijn(u vgh:uk e)/*)rva( om g2lts speed uniformly from 95km/h to 4uhj vr (n/ml)eokagg:u v)2(* 5km/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 wkohx )km7ynk/4) r-seka uc*2eight on each pedal when climbing a hill.re4s m*7 k)/ya2)kkh uxkno -c 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 oru8 /xx(u jfdx(cu-8lf 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exerteudj/cx(8 lux8(r x u-fd
(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 torquekd 2*r,yet2nyocsg), about the axle of the wheel shown in Fig. 8–39. Assume that a friction ty2r*2, eokgn c,)sdytorque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the enqwcf9z0 nkoo/w,+ sob l(ic: )2 lr,bbds of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horcrwn+9qs/lfbcoi) zb w :(02kob o,,lizontal 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 tighte6ccm,hl nt f(:ning to a torque of 38 l,cmn fhtc:(6$m \cdot N$ 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 0.6q7k6 h a2pfsp,w(f zh*48 m when the axis of rotation is throuh2(6f*w s,7phzapfq kgh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rimigxbw+ 1c 0it8p ,t2/nrczf( w and tire have a combined mass of 1.25 kg. The mass of the hub xi1gr wt2i (ncp/ cbf+w8t,z0can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated ilbp+b *,m.;zw l) oe8mpqu sh4n a horizontal circle of radius 1.2 m.eu4+ ,zsl )q l*8wbompbmp.;h 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 constant angular speeq :x pwkz+q/pt: 4dgc,d (Fig. 8–42). The f +zxkwgpq:/t4:d , pqcriction 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 arrayg89 sz:ce akv2c q4l2z of point objects shown in Fig. 8–43 9 vceq24z8:zl a sgkc2about
(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 atomk(msmxc ky z382qls2j5u8 /mhs 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 spigp)trslsqg m) juqf/y p 9,8s )ah) lllw)-;b4nning at the correct rate, engineers fire four tangential rockets as show)lpgj fywhls)ql tsbmq, p) ua)s;l-89)/gr 4n in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a unif qvtk0r;hesq+l 95cr z q1bk-r,l)4fs orm cylinder with a radius of 8.50 cm and a mass of 0.lr qr r)-1lz4kh0,bqc 9;5qss f kve+t580 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 sg ghthlx; ::7from 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 tangentiaz5s rhzutg wz,* h.l./8i pn*ylly on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in nw ru zg,zl.8s/iy 5th* h*.zp10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotajm 9/hoki5 1cvting at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torih/vo5 j 9m1ckque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accel * w/bwpmt86wrerates 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 action83wwqd:sanwo. 46 s h2zvwl ;.d5juby of the forearm, which rotatesljwv d5u8dn sz.32 b6;w.yo: aw w4qhs about the 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 showxuk 7z2gntc78 n in Fig. 8–46k77 ut2g ncxz8.
(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 consis)w4 2 rjy7jy) zmurs6mts 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 frf r-x wea9xk*sb fv.3e55a)c7z*oi hrom rest within four full turns (revolutions) and releases iv-iazb5 f5)fcewkx o*73rh ae 9x.*srt 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 of inertifms; 6h(xya (la of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 280 lr/(pemk n2*r: s.wkb $m \cdot N$ 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 cmmcgp.o nm8z 55 rolls without slipping down a lane at 3.3.5mco8 zg5nm p $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth wi n2 2p9 ltw7r3xz/oqquth respect to the Sun as the sum of two terms u273 wqxoq2tznpr l/9,
(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 vwfrh y)-(qr: 1640 kg and 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 per 8.00 s? Assume it is a solid cy y (r-:f)hqrvwlinder.    J

  A sphere of radius 20.0 cm and mass 1.80 trf ix:o*5d + mf+2qlrgf u(1o* bjvc-kg starts from rest and rolls without slipping dowmi1tdqf*r (2b l:ox*grc f+-ofj 5+ uvn a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to iaj *km4*( ymuqb7c 7kfall and its lower end does not slip. What will be the spb7y4k q(*c imj *ku7maeed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momekq) z hqgl;.+vn66 0nxz bez1hntum of a 0.210-kg ball rotating on the end of a thin string in a cz6x n.eh;16zlqz nk+hbg0 vq)ircle 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*deg7y.af5vw h zcl46-kg uniform cylindrical grinding wheel of radius 18 cm when ro45ahvcy.gdf7l*w z 6etating 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 platf0(aoib55 aqcqpo 97des.mz 2vorm that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the 2aq0omscb5 .pv ed9oazq (i57speed 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 momeng fnqlcs*) rf7mugf4;*hu x ..t of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angf u*f mcux.h * rl;7f.)n4ggqsular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from aab lwb*vrg;t ,uv,6iru 01v/a n initial rate of 1.0 rev every 2.0 s to a final rate of*vwu,; vl1bbti0 / a rg6r,auv 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 vertical axis through its center at a fj+ -lh pxzp4c)requency 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 whepz ) cx+j4pl-hel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angul5vrqn* m2sm: 7vop* pvar momentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Earts-,3 8:3+ djixukl6blg rs wszh
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto a1m4icpu e jymkoh1hk 7/s9 y31n identical disk rotahp1y/ mcj1y 7soeh1k4ui9 k3mting at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at oe; x+ st0 l+tis5v.oc2.4 $rev/s$ 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 stwwwc v74msrd ps l1)4x87xw c7ands at the center of a rotating merry-go-round platform of radius 3.0 m and mome)4wcw wrl7w 7d8pv4xm 1 7sxscnt 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-gou yy /)ctt1:cv9 8gwk0eehta1-round is rotating freely with an angular velocity of 0e0vh kc)wttcu1/t1yegy8 :9 a .8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white b -bcmn52j1ara1q s ype-:i /cdwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s newb2cay-bq j 11rim: e5c /p-san 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 oaf08 s;.yp ygf(s)mwas6 aq8c1ufgir;1)gsexcess 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 spos a4 /+qa6 0rxxyg8zy;.ey$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freely xsxal2 ap/0l- without friction. The moment o2al/-0 axxs lpf 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 atog+ll m6smp b.5 ) *mnh18zhkd the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inergh mkm6n.sbzl o+l 8* d5hpm)1tia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lyiy9 7mk f3kfg(6,d inftng on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. Whayd9kft 6,ifk(3mg7fnt 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 alwaj6na4lc m2bazk6 -x.v ys faces the Earth. Determine the ratio of the Moon’s6. xzjln4m 2-cabka 6v 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 re;jykys s8ywhy;+jy 0 7st 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 shape of a uniform cylinder of radius 0.20 m acquilkf4y8, 7ps.ui7xr*lyti* w d rb*zs*val;a *res a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by * k;7wi8*4 lf.,tr a*ybxps ys* ulizrav*ld7 the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylin(iqcivve 27bm. *we* sdrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin so* *wc2i7emv(q.vbis elid 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, how is the angular speed of the rearmk 5bj f5pm.k1 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 siznd8n8.ses6 hg3o0 ctk7b 7d kxe of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its masx sn03 8ke8g7 7cbso.t 6nkdhds 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 energy p 7r*jmdpx - dvr+.jy8stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flyd+rpmdj7*r vpjy 8-.xwheel 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 illustray whn v ph9,+8f+huvw8tes 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 uagn-j 9txlx;c2) i4 o b4vmx)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 piv kx yuou8x9 r.-j0xl0uot 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 accelerati9y0oj.xk 0 uuxlux r-8on 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 the floor, aaihhoi7t8)fg*q .( od4slf z) n,9k,nfcge(jnd we wafci,, )hgond.* hko7ze(s( tg)ffi4j8 q n9lant 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, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn wiy)1gfs b8h(s ag6;i;p zik4llth a rad1;4 ) s(zf6ylaklh8sib ;ip ggius The forces 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 q5/xw(yhp9g)x:b v+dfqfz 0k 0.50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above hq9xv y fxfg(q k+pw:b5d)0h/zis head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arm0pz /s*o9vwid s as thin rods, making reasonable estimates for the dimensions. Then calculate the rativodzpiw*09 / so of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which 9eao 7h+id ,oop(hikw//csr - consists of two cylindrical plates, of+o /dprc,si- 7okahi w(9he/o 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 roll yu 7/dm.v78jref cw:fs along the looped rough track of Fig. 8–58. What is the minimum valuewy ru/m cjdv.7e7f 8:f 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 asw/tsr, u)5:xq3k cx*lde+ y kasume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolsmzc 0w1nzdr.6;leyzn53be 2z k- tp )utions 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 angular accelerationyw;m-p bte 5zzrn2l0zk1 e6z). cn3sd 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