A bicycle odometer (which measures distance traveled) is a1/j 7ouhgygzq8cba,x zo6as3 e54f z5ttached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicy7oa45,5zzxu/3cs1zggjhey of8b6 qa cle with 24-inch wheels?

Suppose a disk rotates at constant angularcupbj3 uz. 7(r 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 accelz37.pu u rbjc(eration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the anguj t;q7 -a2ot)uq0 lqk;h9dbgular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expmxl-p0khw(v:x +.jfl 5e 9 hdhlain.

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 dox7:nv-myl7tw v *-hfe a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to l7:mv-*wyt7f-nvexh answer this.

A 21-speed bicycle has +3qzvr666y02w jc acpf wv/x nseven 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 or a large fronty3xfr v qn62 w6/v06+cwazpjc sprocket? Why?

Mammals that depend on being able to run fa 9.skn2*uey7/he hy dvst have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageou7k vh*hd.e e2yu9s/ny s.

Why do tightrope walkers (Fig. 8–35*szyx 8 3svv6l) carry a long, narrow beam?

If the net force on a system is zero, is the net torque alsx+i66jm. yw/ gbkc fj:o zero? If the net torque on a system is zero, is the net for:6.c 6bkgym /+ijjwxfce zero?

Two inclines have the same height but make differentrgq6(f0 * f ;sot2: hscchkp7x angles with the horizontal. The same steel ball is rolled down each2sq0;hokt gc: sp h76crf f(*x incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down al-o(. i. t3snhan-i ; ofo0cvpn incline. One sphere has twice the radius and twice o . oh.ait -i-(;0of vnc3snlpthe mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder havevln s2h(dgi7/ the same radius and the same mass. They start from rest at the top of an incline. Which hlg27s/nvd(i reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved.+ryvr.:xx0ftr ) t8bi Yet most moving or rotating objects eventually sbt.ryi)8: v 0rr+ tfxxlow down and stop. Explain.

If there were a great migration of peoplf) qztig),n1 ae toward the Earth’s equator, how would this affect the ,)gan) t i1zfqlength of the day?

Can the diver of Fig. 8–29 do a 27 a; 4bu5m syyq0vjntw1w1zcsomersault without having any initial rotation whenwq50yv41m tnj;cys2w 17ab zu she leaves the board?

The moment of inertia of a rotating solid disk about an axic6gx o f5omlbdx4)) 1ys through its center ol om1codg 4bxy5f6 ))xf 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 rotatinmhmv4sqmp3v j1j /9,h9 f:c8nfvn g)ug stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular vsfvfn/3 jvn1hu99 4qh:) g,c8jv mpmmelocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. H :fuo*kefp7z9owever, one is hollow and the9 eo: *z7ffupk other is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a h(tf2fg:xeznklw /j (5h xa+4norizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angula+ljf4z( he5t: xk2gnfaw/ x( nr 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 fh :p(zrm*;et edge of a large freely rotating turntable. What happens if you walk toward the center? zt(ermf:hp ;*

A shortstop may leap into the air to catch a ball and thdg30ug3qm83f eme cw 4row it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you wil um dq33wm830cg4fe gel notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservati4pbdyh+ l0rk1 on of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second hby4d+p rlk 10propeller can operate to keep the helicopter stable.

  Express the following anv nb fjl *qnmx 6+,tc/t:w,d4bgles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. w6cbar1 6xiu;Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen6c1r ; wbaui6x on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam p1dmz qo1k ;nx+ed y lj2z4/q/diverges at an angle yd/+zdl eon1 j1qqzk/2xp m4;$\theta$ (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 ratt.,mg 2dxkl/gs1f/ uqdf d/ f7e of 6500 rpm. When the motor is turned off during operation,k.,f1sm/ gx fd tq l7d/du/f2g 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 levoiq r .1lf 02,: t2zebyfpvg)del floor 3.5 m to another child. If the ball makes 15.0 revolutions, what i r22fpvy.d1ti:f eq)boz 0l g,s its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revoludce y o/*60h k+7:,jctadexdo tions do the wheels make? 7cyc 6a0de:h/ox, k+todd je*   $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its anguy.yvjf x2lab3fr/- rtu-v +: ylar velocity in -tju 2xvfr yy.+-lyrvaf :3 /b$rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in + r:lte4kj 3hu4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated lejtk r+3u 4h: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 +ginb- y5c7n q of)b b*cvggg+:7;mw, i keu3gvelocity 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 a poinn/ig1;i; ykvgf7 2r7awv3v6k ht7ni r t
(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 )q vgigjpb5o:9km t/( axis of rotation is to experience an acceleration of/mko(:q pgigt9 j b5v) 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accel/wz, pw ss e, -m6hevo4kz,z9ferates uniformly about its center from 130 rpm to 280 rp6ee/z4skf p z-,w mv,9shoz,w m 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 radiusmjf1t44 4uij;y5wvji s6yx,s $R_1$ 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 a, o qmdqajr*-g8le3jzq+ 8 l2/-8 2ewatkonmApollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy e2w-,2r g8azdn8k+q-ll e 8ojaojqt3qe ma*/m venly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates unifo80y04gjdfgb0c*arur/ iihr/ rmly from rest to 15,000 rpm in 220 s. Through how mar8/ug b04rhjgaf 0dr/y0 ic*iny revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 al/cfm bqzn7 1k(r,h7rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jetssz6cu hfbiybby/4,l+4fa 4o , in a whirling “humanhyl4,f6bzac 4+yu,ob4s/ ifb 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 diameter accelerates uniformly from 240 rpm to 360 rp movg-i*e -8 ek dquw(l4lx)0bm in 6.5 s. How far will a point on the edge of the wheel have traveled in this eb*(w-ox mkq4 g)l 80eidv l-utime?    m

  A cooling fan is turned off when it is running at 850rev/min )fd; nop7deilt7 *ld(It turns 1500 revolutions before it comes to a st ()deo7;ddl * flpi7tnop.
(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 reducessvw 6k6q(++wmqtt8uc its speed uniformly from 95km/h to 45km/h The tires have a diau6t qtv6wkcq+wsm(+ 8meter 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 undarbp815k l b di/iq40iformly from 95km/h to 45km/h The tires have a diameter of 0.80 m/di8 i0 qplra14 dbk5b.
(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 onk/v9 kyi.b: auu78wpj each pedal when climbing a hill. The pedals rotate in a circle of radius 1u.wi/7akk8 :u 9jy bvp7 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 tpig +7yluf+0m-a c9vyhe magnitude of the torque+ac-9+i p7f yu g0yvlm if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shoz53ttl3k2o+bmf4j7iisv;i zwn in Fig. 8–39. Assume that a friction torque ofim3;z4sott3 bz2vl 75+ifkij 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a m ;grn z2 (:b1qkgh1e,iognujr3c )t :jassless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magjiz23 ):nhcub rk e,q1g;g:r(1gno jtnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening tgkhry 1ttva r v.q55(-o a torque of 38 ytqg(r-rkhvt5v1.a 5 $m \cdot N$ 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 ueh c0rgpz tr : 2b3sef75.cl-of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its center. 0rtg7r:ec fcl h2pu-sbze3. 5   $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle 4bzr;96ykfiuk,b ,+e, ecqnlwheel 66.7 cm in diameter. The rim and terk4,+ie; 6yl,zc,q9bu bnkfire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin e 4vn6y2+ 8dhqcmeno2, light rod is rotated in a horizontal circle of radius 1.2 m. Ca24eqvo8yh +2ndcmn e6lculate
(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 potn 6ng3wyv ux,)ter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands,6x3vg )ynwnu and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects sh/u) mj;weu-qv own in Fig. 8–43 ab-q/ uwjumve ;)out
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose tota)xi)7gwnvh+ c l mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct r+w dfuc2o y+(1s5 cjms5xcf j9ate, 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 each1j(off95y c cd2s+ wum5 +sxjc 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 cylinder with a rad1cv +1cay t;meius of 8.50 cm and a mass of 0.580 kg. Ca1et +c;caym1 vlculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest to0q* ik+mg ( 97gdz-t lis/xbxg 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hano)0o(jsla4c k1jr. mkd-driven merry-go-round and is able to accelerate it from rest to a k 1om.so jr)(4lc0akj frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rot;bu op,r4c9e a2:4 smi x5s-(vfayjz fating at 10,300 rpm is shut off and is eventually brought uniformly to re;e5abuxcsfrf is m42(a-4 ovy9 ,p:zjst 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 accelea .x1x1gbi.u *jdpgncog1 7/orates 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 acx,(yl9kgrd c;tion of the forearm, which rotates about the elbow joikg y;l9c dxr,(nt 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 rodcexs24ni- 7,g+njjsh:vh: w xj sj:3m , as shown in Fig. 8–46 ,:h+gej s3ss-nh xni:jvmw:c4xj7j2.
(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 c bsc w(k)o9:k0;aki)ulj nz0ionsists 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 restg;)4 *qbkaiid within four full turns (revolutions) and releases it at aai;k)*q g 4dib 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 iner4 /memg5eoe ,wtia 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 d((r5,urm0s . nzo 3dnuxrk5otevelops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and rrt nrcn-5t d 6kl.mnp3t/g3f 7adius 9.0 cm rolls without slipping down a lane at 3.3 r.5 tkfrp c7g3 6 nldttmn/3-n$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energyt k)3+r xtlrm+ of the Earth with respect to the Sun as the sum of two term rk3x) lt+mt+rs,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much net wzu6 6wcchj/g 3-ptk l8ork is required to accelerate it from rest to a rotation rate of 1.00 revolution k lp3wcg-86 6uhjt z/cper 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.bb248w4 wx(1yjrw w m0j55l-iq wiwbr80 kg starts from rest and rolls without slipping down a 30.0 1 bi502 rw-w8w4 qywbb(5mwi4rjx wjl$^{\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 tkq6gczl:r il nhb5 +p1h5n06bip. It starts to fall and its lower end does not slip. What will be the speed of b 65kh pb ilclr10+g:hq z6n5nthe upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-vsj axoxtwlz gfb )*47+p zs4 6-c-gb3kg ball rotating on the end of a thin string in a circle of ras 4z-gspb4oja +c v-*3t6)zw bx7lfgxdius 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 cyli8levzqje7 ( 8qndrical grinding wheel of radius 18 cm when rota8( zql8 evjq7eting 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 a6gc0e8bap0l w)6o wl9eq e2oh1hc 1eyt his side, on a platform that is rotating at a rate of 1.3rev/s If he raises hi92qo)e1cchbalw 8ew0pe0yh61 olge 6s 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 p fba3+w.4( (ovt cqhgin Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck positioqv ho3(wat+g4 fcb .p(n, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her s k9kg3 it1on*cpin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final c9 1tnk3ikg* orate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vert-y: y/5nt+ utwxob7b uqvp,x 5ical 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 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the n -:b/,xo7u5pu 5yy w vx+tqbtclay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skr x5+ya et zedf;56oq+ater 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 momen 3pm 0djwt;vo:tum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is droppey4xa1:hv gjq*smi 2* id onto an identical disk rotating at angulimqs*g: 2 4*v1 yjhxiaar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 wd6 j,sp8kiw+ d *ve0- wyy:qm$rev/s$ 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 u82 r mz7bs:wdstands at the center of a rotating merry-go-round platform of radius 3.0 m and mb:w 8mus7zdr2 oment 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 velocity of kcbc mi i-4 nosh-4xg0w*:x w90c49*:skicw- xo ig0x bw-mn h4.8 $rad/s$ 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 dwarf, losiw wc;j;fyj4tq-z8xcr; u6a-h ng about half its mass in the process, and winding up with a j-wtwj8yhx6fcar ;q4c;-uz;radius 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 hc 1:vpn4mwi4 winds in excess 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 3+97icn w-fvny u 2upq$ 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, ini -ovi2 k6gpi)dz,y/ tltially at rest, that can rotate freely without friction. The moment of ineivk pg6dt)2oiy- /,l zrtia 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 stanul5y5-bm nd cm1ck 7:qds at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearlc-71y55du nk:mb c qmings 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 rollsgje4g+ 2zxq)mk mu b72rhryi u07+ :io on the ground with the end of the rope lying on the top edge of the spool. A person grabs qyk)2gx be4ii g+z: 2u umjrom7 +hr07the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the h8w.he,w:fpv+ruur 2 Earth such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axishw p+uerf vh.:2, ruw8) 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 aonrtu3tv e ny+g j2:48tu-w h.wiq (-r 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 i1 flb:y ei.p:dn the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleryed flipb:. :1ation. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of massyiy *x h* 8ukupg4s-*3bwmml * 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.005yiugb h *xy*- kmw8u*lms *34p0 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 thezzz87c.ef r6ry (ub2ab/hk e0 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 Sunemk6s +o1og +e, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolutieo+16e g+smk oon every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform 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 st61pwz3uxn 13 qknc5a xored 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 travenk q 1xzcpn1x3au5w 63l 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 uw,c9x ,)* wpz* akh*dtzlqo: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 om*p9,taau c 3tn 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 leoil0 9-y;c edrngth L can pivot 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 -rclo 9e;yi 0dof mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radi(e3x*cy v iik)5m:ki1ms*jmn us R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against whimixm* vk(5 kji3i )necy :ms*1ch 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 i 7r4zo(7g9tfcys .ojis making a turn with a radius The forces actiti r4o fg.j7c o(s97yzng 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 rockh2/g2 qyek ,. bc6eval into a 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. ,ck/.e26hyg2 vae b qlWhat 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 h5lre-e,71 )fiyrmctnof) j x 9er 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, and with arms held tightly against her jxl-9e,ifcn temy71) r5) fro body.   

  You are designing a clutch assembly which conrav(k78:tv3c mfmg 4 ksists of two cylindrical plates, of masg8at vmc3f 4r k(:v7mks $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alolk678susx . 4.ghthrnng 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 leaving the track? Assxr.47ks.lgt u n8shh6ume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, bukxsd;5giac1qh5;n 4u)l8lkut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformptxx32/0pc m yr;s; d7u:gz jhly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration rd3xmsyh up2/g0zx; jp:7tc ; 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