A bicycle odometer (which measures distanceh4+;gd kvier( ce * //0dbu-w, mngkji traveled) is attached near the wheel hub and is designed for 27-inch wheel ucbe*ge+ihk/vkn jwd4;/d-m0g ,r( is. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constanm)c2yq*vom+s, 1wmb,0( lt xgjosl5 st angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increaty0g1, swo,ol)x qmj+( 5m2vlcs b *msses uniformly, does the point have radial and/or tangential acceleration? 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 angular veloci 7(.nnxnx (en*ljmy lc,o9bq: ty $\omega$ Explain.

Can a small force ever exert a greater torque than a larger fophfu5 dc+xu*: rce? 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-8t1 au .gpxqo.up with your hands behind your head than when your arms are stretched ox 8a.1pgq.u tout in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and thregi g0mk0gad42winc :d 8)prkl2r/ . bde at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which ge rnrg gki:4w0ml)i8d .gb02akd/p d c2ar 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 low t8jkl e75iryo,zj ;h(er legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of roh7r8(k5 jtyj;i elz,otational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long+zvv*cz8 0dl8yoicm-6hko9c , narrow beam?

If the net force on a system is zero, is the net torque also zero? If the netabakeaw ;6/z /7t1 htn torque on a system is zero, i/ t b;h1ta a6nw7/kzaes the net force zero?

Two inclines have the same height but make different angles with the horizon* 1olfr0gi+urkr m4b2tal. The same steel ball is rolled down each incline. On which incline will the speed of the grro 4b+*u0 m2lfrk1iball at the bottom be greater? Explain.

Two solid spheres simultaneoqlqu3 x:u(roizv,qq 6dc5 aug;67m 0)fgql4gusly start 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 greaqzuxco646 d0 q5 fvq,:u)ugiq ;3gl q(marl7gter total kinetic energy at the bottom?

A sphere and a cylinder have the same radius m ldcg6-2*zho .n q9j5fz,fku 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 czh z2*gkn5jqf u9o, 6fml-.denergy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or rorh/q,3rknv( hizuwl 0 kpslgf*3d/16tating objects eventually slow down and stop. Explaln 31gw0z3iqf/rvs/ hk *6( rdkupl ,hin.

If there were a great migration of people toward the Eaihe4fk9iy m,1rth’s equator, how would this affec ,m4if1h9 eikyt the length of the day?

Can the diver of Fig. 8–29 do a somersault without having a8v1uqg/. c ,q 21 oqo9atqtu4)jhsz xony initial rotation when she leaves the boxsgo4/t 2zo .qu)h1,qqt jqc o8 vau91ard?

The moment of inertia of a rotating solid disk abo 2vdnqt2 q/wf6ut an axis through its center of mas2 nqvt2/ qwdf6s 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 rotatinyylxn/jb ( z,5g stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity in 5 znjbx,(yy/lcrease, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one icobp4 b fso2m57w (zevfp+f0: s hollow and the other is solid. Describe an experiment to determine w(fe:0f2p4p7v bom+z bwofc5 shich is which.

The angular velocity of a wheel rotating on a horizontal axle points west. Infthazi9qlqk9 ,9; f t5 what direction is the linear velocity of a p q,iq ; ta5hk9f9zfl9toint on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of5gw8mh7z lc4b a large freely rotating turntable. What happens if you walk toward the cenc8 m7 hz4bgw5lter?

A shortstop may leap into the air to catch a ball and throw it quiczvc8*i:0b rl* ix)ary9slk 33-smuu c kly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips anml93i c 3*8zx lrkr-aic0u:bssyuv )*d legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, n2mv o6sfvk v2:cr1mt8k gf0 9discuss why a helicopter must have more than one rotor (or propeller). Dk8 t1k:vmf2rfv9 ocm6g n2v s0iscuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angeha96*)ze8i dj jwan/les 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. Calculat7zihszdupv8s1ma vy k 6:: o;8e, using the informatum :svi7ys 8z ho8vd1 :6kzp;aion inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000t)qbtb5 ir6r/ km from Earth. The beam diverges at arb rtib6 5q/t)n 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 t;5lz 1ee;o/rnrx* u;cs-too yhe motor is turned off during operation, the blades slow cor ;y; xeznroe-5o s*;ltu 1/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 nc bo+p3**2:da :fqi,vrba 5 t y8ugpc3.5 m to another child. If the ball makes 15.0 revolutions, what is it+gy8q5o*bac pv:d nuf :p2, 3r *tbaics diameter?    m

  A bicycle with tires 6,8u,e(h qin;5i)fd r fzmi /jjbuwh368 cm in diameter travels 8.0 km. How many revolutions do the wh,uu 6jnibf i r5()i3/dwm;ze, h8fjqheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 r;utlcg- kp 7:cwifv3:pm. Calculate its angular velociti:uf:vcktgc;w-p 3 7 ly 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 hd2+x78g giklone complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seat2dk gg+ix7hl8ed 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 Eaf1 cswq(t7f:s3 vx/w6 qoz9xprth (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 poinxho1+6 hs3jj h(pt .06fklccyo+f( ss 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 fb l.dc;+l wva(,8e cqnrom the axis of rotationq,wan(l 8.bv+c lec d; is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its centee8 7yd,k)duay io-z .mr from 130 rpm to 280 rpm in 4.0 s. Detkda,-yi.)my7 dz uo8eermine
(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 radiu6n:1x b*/p u c/e0zbo mah/wuys $R_1$ 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 Moew 3 cga19w3:sgwxzan)+e)ja on, astronauts aboard the Apollo spacecraft put themselves into a slow rot31 eww) 3ax)9gn: cwasjzgea +ation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can 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 15,0m*o542,25; s i e u1iq7wrp-st lj/ylcfvgpkk00 rpm in 220 s. Through how many revolutions u *jpreg- 2fki4 s;,vq5i1t5pl7m w y2ksloc /did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to ;qj)bxd 0s c+ gt+ /qbnvroo771200 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 flying highspeed jets in a whi.3 7.wrm0w ai0wutv vlbk1/ furling “human centrifuge,” which takes 1.0 min to turn through 20 cov7w uf30.ruwbw l km/1tv0a. implete 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 q:2 ocffju(ti wh+4z/from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this4ctoz+ :/ w ijuq(2fhf time?    m

  A cooling fan is turned off wheng5.d1* ff zuht it is running at 850rev/min It turns 1500 revolutions before it comes to ath 1ufgdfz *.5 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 unifor06-a c 6nxj mltxq*.gdmly from 95km/t a 6cdxnql0gx6.*-m jh 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

  The tires of a car make 65 rxr 8ofz3k)n4 :b w5qgaevolutions as the car reduces its speed uniformly from 95km/h t85 )3zon raqwxg:fk 4bo 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 en9b /mj9xysg 8ach pedal when climbing a hill. The pedals rotate in a circle 8j9nmy 9sxbg/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 hzo2 h2y+fu;(xm4gwx is the magnitudexf(x+u hzwymo 2;gh24 of the torque 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 shown in 9n dcz s7lrc7n77jmq7 Fig. 8–39. Assume tha9l7cnzmj7dcn77 r 7 sqt a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are -ch ao39yjz78oplo 9e attached to the ends of a massless rod which pivots as shown in Fi399pzo- c87hjoayl eog. 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 system.

  The bolts on the cylinder head of yus, l;(xl0uean engine require tightening to a torque of 38;y ,0eulsl (xu $m \cdot N$ 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 inertia0 eze ysnv)9r)9ab9ikqzfh,2 of a 10.8-kg sphere of radius 0.648 m when the axis znb2e rf)z h,099ak9ie )vyqs of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of in(4h ipbcs/vn; ertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of bi4s np/c(; hvthe hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of 9hphjo uwl o*-n/ t5-ua thin, light rod is rotated in a horizontal circle of hljoh/upt95 wnu-o-*radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at cozco 2ksp .c 1y8xz9:rxnstant angular speed (Fig. 8–42). The y1rzcs .xzpc:k2 8x o9friction 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 ofeeg5, okz+ 6 q bw+o/npkv8 cmoo4+zn6 the array of point objects shown in Fig. 8–43 aboukzmv 4ooq+n gwcke bo+ 5p 6n+eo,8/6zt
(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 s6rhx0k(lhx,y( d 8 6m6 remtjoxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning aoaz7ty)6fnz - mvl 3*et 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 the satellite is to reach 32 rpm in 5.0 m3z*7o n6 e-taf zyl)vmin? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a d i:drn me-, 1j6an2 v)k8xrhomass of 0.580 kg. Calm ,dnr:2d)in6oh jvax1e k8-rculate
(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, acc,u 9au1s(uln )vuo:abelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and ;yfp5kmv) c;q tz 79xrn0 m/ro-2d qcdis able to accelerate it from rest to a frequency of 15 rprmm)kn59rx ;7 td2ycq f0zv/ ocdp;q-m 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 rotating k4:r: m vggw-za. yr1+ y3xwwalti(9gat 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque-:4aggwm1z(wy 9: 3y gtkval +xwrri. 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 accelerates a 3.6-kg ball axiq-(e..h rmn/y y.jx t 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 g pf*b+2w,z gkthrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps musclepzfk*2, ggb+w, 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 shown6 )) fo0typjyc in Fig. 8–4)y jc6o)t0fpy6.
(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 con ( /rb2 gfdmm7/yn/zwcsists 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 pu,d)+p g vei k.pvfet -d )w.elb-3w2within four full turns (revolutions) and releases it at a speed olw. id-ed eg) .w f-k+pu e2v)v,3btppf 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 mom 2juk*r0qt s1jent 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 ofo ok,rbo6o eey9re.6*kt .,vh 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping n m x)vcwz8ti: mwt73 ,6:irhx 8wnix5down a lane at 3.3 nx m6 x5wic)7nrith3ztw ::wvm8x8i, $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respe ayyy*a,/m2r wdm(rj-ct to the Sun as the sum of two ter(-j ay2/arm ydm *w,ryms,
(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. Howfh m zsxb*0kmgaxyg f9+d 8:8) much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assumey +ak g s*)dmf9z0: xhmgbf88x it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls with:t m;v)mqdxzyiu aan--hk5 w* 9m,y 6kout slipping down a 30a mhzm:yydnw 56,*a --um9x)v;kkqti .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 startzb+ 6ddlgh,( (tzf* cfs to fall and its lower end does not slip. What will be the speed of the upper end ofdzt b(6d zg+chl*,f f( the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg bs 8wzvo)8wr3ckwvpox. wgbv fc7 bo ;mz( 44;*all rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed of 10.4(f;z7sbmc ww*8 8ow4 )b ;4krvz3owx vpoc .gv $rad/s$?    $kg \cdot m^2$

  (a) What is the angulah-mp-c xdn .p66qmn w*r momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rot-m-x n p6*.wmnp d6hcqating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a ,d/5lj do m4f)awz,3 nsndsbop4z7 )qrate of 1.3rev/s If he raises his arms to a h)f4nsp 74b5mnsw /,,o 3lz)daddojqzorizontal 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. x6rx6kh (rz eph,y,t5hr;x- q8–29) 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 mak6-trh rqk,xxy zpx6h(5,;hr ees 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial ratt97)e j/tjlpn e of 1.0 rev every 2.0 s to j9 elt)/7ntpj a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertjhh(ylyagof,e2*h 6cj4 128rfyc bb8ical axis through its center at a frequency of 1.5rev/s The wheel can be considered a jy ,h(f*a hcbgcy2frh8eyjo86b2 14luniform 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 clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3l . /oc3 h8hzhq8(jyih.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 moment (99dagbjkv5aum 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 dropped onto an idmb c-iv idm 6jvoureu5w. :(p9fb9 w1e3or *t(entical disk rotating atf-3 u9.15oumiw b:v(de6pb ov(cej9i rmt* wr angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ak8. /7fw,kw wcvz i-cat 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 thes+ bw:x8qb od- wmb6t* center of a rotating merry-go-round platform of rawwo68xs :m tb bqb-*+ddius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular veloevi2g zh-u9vvaz cmxc8 )55 6ocity of 0.8 v59ha)v68m czv o2u g5xizce- $rad/s$ 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 eventual-)t 5tciyuhj 8s9q3die0 dc,kly collapses into a white dwarf, 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 new ro)yct kuq8che 3sdj95idi-t0,tation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 1,qmrxepxy . 8vy,q 7u320 $km/h$ 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 c: qp/n5rb2.k.wr/ f rse) hzm$ 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 xd esoy6f)hynzytasj ;d :* l1 lay i(6l9(0r;freely without friction. The momenx 9n;(zdold)ef ;y(:stlh 6 1s0yiyl6y *raajt 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 a 6.5-m diti h ly 0/p)0f,,jedj9dgj* udameter merry-go-round turntable that is mounted on frictionjuihdgdl,j *pyt0/d f9,ej0 )less bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of th:/ea-2fe g +9za*avqjtjz.io e 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. 8–50. The spool rolls behind the per2jfze+ae.i gv/9 t*-: qzajaoson 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 th5gy .5ylx2tw )lrvq t.at the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (abou2.y)t5xt 5v llwr qyg.t its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest atl(71 eex -ukpdz .x(nn02knka 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 ibpl7xcj, 3 a-ch4n9i ln 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 acceleration. Calculate the to7cx c9b,4 j3lanlh -pirque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.05 lzkpt.r3mx r n1r:q180 kg and diameter 0.075 m, joined by a (concent:pqz .l381r t1xrrmknric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long 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 spe sx)fp u,1va;:npw. eged 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, w83tz x-2me9 vps-uwoh ere rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse t 92hvpse-tz8o mu3x w-o 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 u+tjj1vjst6 29fbq- jkse energy stored in a heavy rotating flywheel. Suppose suc kv9j21 qb+tftj6sjj- h a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(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 illustrateskn9 bldd6 zx140xjd;pzi+dy9 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 (hoopjckqtt : 9m: lzf0ae67x2ye)v) is rolling 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 freely (i.e., we ignore f.ue ai 3hk1sb;riction) 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 the1u3bsi;ehk.a 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, and wegzxgi(e1yyn3+ ;7,lml 6 yz bl want to exert a horizognl;ly(ze1mlyg7x36 i+ z b,yntal 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 witzy d:ove2,: peht6ts 63 r2kkj,; dwbth speed v=4.2m/s on a flat road is making a turn with a radius The fbt;tdv2w3d: eksyre2z :j ok , tp6,6horces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of leng:pv1vn 1/ rrddth 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torquenvv/1rd rd: p1 come from?    $m \cdot N$

  Model a figure skatere;3vgr qhdi0 sx(4:f x’s body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her bodydi(0gsvx;hexf3 r: 4q .   

  You are designing a clutch assembly which cov,a4x:bp8ihf t ++ 1aw icy:lkg:das2nsists of two cylindrical plates, of mass 2sy:4 bti, w:hckpv8l+axg1+ fia da:$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fi1f:2xp phqrvg0 srb( n0zth40g. 8–58. What is the minimum value of the vertical height h that the marble must drop if it 1hbrn phfszv00(4 q2ptr g0x: 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, bup.ctenmfuz90l++ ep /8t 9q1jv l/b vyt do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions amc k8j37orih2s the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (j8ch irk273moa) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s