A bicycle odometer (which mw68cnxwd7;jg m;f o nu*j/-bieasures distance traveled) is attached near the wheel hub and is designed for 2;c/m6g;*ixn8w w fu-d7bjjno7-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on thenxc+i579trd jz 1o 7rl rim have ra7o7ldzr+5jicx19tr n dial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a sinwlkf muy. j;11gle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than 0m(my3sbwq d tcv1e l l-+m6.ea larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behind your head a /4)* wctozcnthan when your arms are stretched out in front of acco/wt4z n )*you? A diagram may help you to answer this.

A 21-speed bicycle haex6cz1u2-a)qfg)uy s s seven 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 yz)a - fg62s1q)euc xuharder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender llsl (+)rx(okoower legs with flesh and muscle conce (lo+()lsroxk ntrated 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 j z* dgox(2armwb8j 6/(Fig. 8–35) carry a long, narrow beam?

If the net force on a :p)u 9jc*v dak jg:y:tsystem is zero, is the net torque also zero? If the net torque on a: j avc gu:*9t)kpy:dj system is zero, is the net force zero?

Two inclines have the same height but make different angles with the il 77pubh9qo 7horizontal. The same steel babi lo77 hup9q7ll is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start ror*/6it ++.t)cjvmit qmjx x2wcs;gqddr29z0 lling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incli 26idq ;jm*ics0gm/ v)rwxtqz+xdr92jt .t +cne first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius)w76r yhrvs / q3fy6rd 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 th 6q3yryvh6/r 7srfd)we greater rotational KE?

We claim that momentum and angular momentum are conserved:h-1o-fflf 2hcgbq g ,+kw5i 7hrh( qf. Yet most moving or rotating objects eventually slow down h f+hcqq-gf:h15wb2hfl7,-g( rifkoand stop. Explain.

If there were a great migration of people toward the Earth’s equator, hows 6i 18 qhn;a;ps;cea nw8ob/f would this aff aiena;wn6f18so8c/h;; sqpb ect the length of the day?

Can the diver of Fig. 8–29 do a somer:xn p yvr oz(9mans4..sault without having any initial rotation whev nn: zayox r4.m(.9psn she leaves the board?

The moment of inertia of a rotating solid disk aboufuxhgc8u0t 4 +t an axis through its center of mas48x+t u0guf hcs 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 an:ad 2 6tvo,(jj;cqh+/r kmf8x 1engm rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity incr6jkjn,hgnodvr t: ( xam+8/f; m12q ceease, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howes4,5a0 )cqy/ byrv ociti/; p.fyks*s ver, one is hollow and the other is solid. Describe an experiment to detebi ksfov0,c)r5c/ayi/4 * s.tys y q;prmine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In wh7f/hhv56/n ehn/d 9qk)n0 dz mbzwht8at direction is the li/ b/ nnz9evqfhw nm08 576hd hzkd/ht)near velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large f8 tdp3n ,4jqye.myu h ujsj622reely rotating turntable. What happens if you wpus8dqjnm2e 46ujh,2.yjt3y alk toward the center?

A shortstop may leap into the a8;; b yrnxifl4ir to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips any4bin rxfl8;;d legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discusz) k kbp: 1mj9ldee5f.s why a helicopter m 1fz5.embk9)k:l p jedust have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians:wytpig - wyk360/8jac (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. Calculate, using tv9ts 7t)c4txvdznl:; 48gjd che information inside the Front Cover, the angular diameters (in radiansvxv4j 9zc nl4s)ttc dd;:7gt8) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,07 (o 9*bzcz *wssdc.kr00 km from Earth. The beam diverges at an(9zbz c.dk7w*s*ro c s 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 blenvki.7 h4+jg 6cyh fp/)uzrsxm xrq;,6der rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blax gv,7r6c/qumh6 fziy h+r)j ;4kp .sxdes slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball mak hogz 4p lzai0lk7ol95) (7.ymyy7 kctes 15.0 revolutioya.574ll)9yp zki o z(hltg7ock70 myns, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many zuw* ) i:ec0;/jjdey8n)vty srevolutions do the whee * /cjy:w )veuis;y8z)nt0edjls make?    $rev$

  (a) A grinding wheel 0s r(syf.-(( vbhlv9cr.35 m in diameter rotates at 2500 rpm. Calculate its angular velocity in vf (lbs9vs (r(h.ry- c$rad/s$ $\omega$ =    $rad/sec$
(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 compdcx kmkhm73 . ad kjvepg +g20e-+a6; +lw1qxqlete revolution in 4.0 s (Fig. 8–38). (a) What is the linear sp+x-qacxk.w me6+alkh3k q mj01 e gdg72v+;pdeed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around thy/*mrr1kq1d amp ga6o*x yw96e Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ofjwys5z 39kmd 5 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 particl7 8dw*sz my:xo t)nm0ye 7.0 cm from the axis of rotation is to experien)*z:od7m y 0s8 tywxmnce an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acceler:-e n h3/qvexeaw nk6 (/rqv;kates uniformly about its center from 130 rpm to 280 rpm ieq k: v3(ne6-xweran; /qk/hvn 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 radius ;9 0(bafzp1 wh; jpynr48b bba$R_1$ 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, astronauts8i b(e4a4g bvty gjm3 b.(d6to aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spaceo4b4ed6j(ag 8b.iyt t (gv mb3craft 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 4oye -b9882 fhc +a5lzjuioupfrom rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in thisl-ohj4e+a52zf 9ui8u 8ocb yp time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 ks5 : gvcho-z(/t2frg 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 m lb15t47n7ruecymyi -5-hv c of flying highspeed jets in a whirling “human cc 7liu emtcm5-nhb- y5 4yv17rentrifuge,” 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 rpm in 6zl qq)c8z61pg .5 s. How1zgqczp8 l)q 6 far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns ( x .olb pcpkg4t4-+wzl ;e8ea1500 revolutions bep44wkalxgo-8+b .e l;czt e(pfore 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 revolug1 (f/0rrp hyetions as the car reduces its speed uniformly from 95km/h to 45km/h The ti r/0gr(hy1pefres 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 re* suwjuh6 80y rsk+dn-k8sp1v7pj8opvolutions as the car reduces its speed uniformly from 95u 60s88w 7pko1r dk+ jpuhs y*ps8nj-vkm/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bid l cr 83,81b:od5s97rflfxqg 0ru pzbke puts all her weight on each pedal when climbing a hill. The pedals rotate,0fsr3:7r pr5dulc9 z 8ldf8qxgb1 ob in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of amu+ t n88,n ujvq,i,ga door 74 cm wide. What is the magnitudv8mt,ji, n8n,uau gq+ e 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 axgj+pd);7hw k)oi dg- yle of the wheel shown in Fig. 8–39. Assume that a wokjd ;dg))ypi+-h 7g 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 attached to the ends of a massla*j7n fir;m3rj s0t8g ess rod which pivots as shown in Fig. 8–40. Initially the rod is he70 gjfrm;s*t8ari3nj ld in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinders:bx 62lcpf*6hkway7h bf) p- head of an engine require tightening to a torque of 3826hf*blhkpyxf :)b-csa7 w6p $m \cdot N$ 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 0.648 m when b myeck wzl5q1as 5(,0the axis of rotation is through i1y 5( c5zmbqw0s ,lekats center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter.i9,q di1/amtb The rim and tire have a combini adb,m /ti91qed 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, light rod is rota: 06tzdqvg zm7q2h: zjted in a horizontal circle of radius 1.2 m. Calculz mv6z::h tdgqj02q7 zate
(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’unn5)e nmm3z6uru; a 7os4n9n s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her handsn3usrnao en ) ;u46n97u5m zmn 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 okp ifu..g 0ky*f inertia of the array of point objects shown in Fig. 8–43 a.0i pk.fygk* ubout
(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 total m)ys9jvh 8a;3u) ihckx ass 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 co 4j xl3/gz6st()g gyjwrrect rate, engineers fire four tangential ryl/ztjg gj w46g)x 3(sockets 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 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a unifm(jg85gzhv4 m w4exo*orm cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calc4 owmxg8z(jv* e4 gm5hulate
(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 restf/pktm(3 -v6uhh3 ooc 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 meb:en+ f-b6; fj1aqc lhrry-go-round and is able to accelerate it from rest tcbq ; fnf:eh+16-l bajo a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is s8cxn1we4v 4 r rgmz3-bs7y emce7v .7yhut off and is eventually brought uniformly -mzymr8 gyevr7 1 cen7v4.34cbsxwe 7to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-ke 5-v.cgz mo9ug 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 ,joyf3y7a5q d-khdgk/ h;ga (the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from ;yaggfk-qha 7dh/d ky ,(jo53rest 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 rlji.q+x3u8c 0mof )dvod, as shown in Fig. 8–46qx08coj+)3 vdl mif.u .
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists f9gy7k* y7 al-:xrhn qmti guue63f09of 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 resxrw yl6f1:(a 6cnz7up/xss5 at within four full turns (revolutions) and releases it at a speed of :s r75(6 zp6axnaclf1yuwsx/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 inertia of.uaymotju;f-.9hh 9s $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops 0 hctzd5z*zmr834 jzq+ k 8:-fgaghhr 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 radius 9.0 cm roll3-e6 +uds*d3p s ( yjdlty2+dugwonl(s without slipping down a lane at 3.3wtd sdld2g3es6 oy-(3ypj(d u+*lnu+ $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the snts )nfzq 64j:um of two jf qs)tn z64n:terms,
(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. wodn,2*mjp4s50 m. How much net work is required to ac* d2,om4nw spjcelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls witho.4o,fr. grjxu ut s .,xfj4.rogur lipping down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanzpt). q4.l)o oij+sycced vertically on its tip. It starts to fall and its lower end does n4 cz)t+sqolj.py) oi.ot slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball ro) yhhu5d1; urqtating on the end of a thin string in a circle of radius 1.10 m at an h uqudr5yh;)1angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrijp4r46kv- rt;(g:(hwt; npqlb m(h ihcal grinding wheel of radius 18 cm when rotating at 1500 rpm?j 46iw4(g qlkrt-:hhb (p vmpt ;(;rnh    $kg \cdot m^2$
(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 tha6 tfa/e6iej. j/)vlglt is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation jgve/66jlaf iel/. t) 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)c01 g,l z/d-bx(erx(y .sqn 5 jmze,sq can reduce her moment of inertia by a factor of about 3.m g(rnszdl- s5 xe1j(zybx.0,, c e/qq5 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 angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin 41q;zt cwx2x.i0 gcdolg 1 ju1rotation rate from an initial rate of 1.0 rev every 2.0 s to a fin21x .1 g; jgdl1zcxqwct04u ioal 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 rot kzdt n9e57htbqwy36 o4ted*x)s ;4nli;lpe /ating around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 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 afts3pe olx5n 6l9w*ztdy 4h)n7k4e;ettbdi/;qer the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning aru(g96axv8g i wucor )6uq0,w t 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 momen2bnv/8bizq0 ctum 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 identqdpevie , uji-g27fts 6 7sp fi4n+)q3ical,6)dqf e72iivi 4+s n3teu-sj pfq7gp disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns s jt/s2 ol+lmi9((njk6:u ojvat 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center .sug fh/jydo;*mi8wwq+(i4y of a rotating merry-go-round platform ofy4gow + m;sfhyjd* .(uq/wii8 radius 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-lkm 8hp7ih8. +t:lkf rgo-round is rotating freely with an angular velocity of 0.8h8r+: mk fl8lk7t.h pi $rad/s$ 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 dwarf5d ,qkqhdjz;bs3n9lqcj( 6h9 , 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 angularjbqzk h5c d;l9dq9 nsj6(qh,3 momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 12j+ jy(mbk;7lapia 6 x70 $km/h$ 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 5huhgewrx.a-/xns( /m 9hx+i$ 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 platforvc */two b2xis -w1l1mm, initially at rest, that can rotate freely without frictiow21- tli s1m*wbocvx/n. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at t-yte+ xgu *ykdqgu289+s6b lwf3gw1mk(d9bzhe edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless btzk2leb9fudq+byg1dg6 uw3 -k*m9sy g(xw+8earings 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 tsc.xb2os.+* .igm+0v t kdtushe end of the rope lying on the top edge of the spool. A person grabs the end* b sti +g20ovs+uc.. x.kmstd 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 Earth such that the same side always faces thermpeme:*-ybu/f1i 4sg m3b)e Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latte/ seb 3r)y4m em:u- 1*pgeifmbr case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerate -wzz d7d :q4(k-agjxms from rest 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 + z6nt ggqb/c)vh wk/6acquires a rotational rate of from rest over a 6.0-s interval at constant a kng zgq6/h)c/wv +bt6ngular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass :n2utvg cru ); nrq-/l0.050 kg and diameter 0.075 m, joined by a (2/ l)vnu ;u rngqct-r:concentric) 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 speed of the re qfsm 6o hb2:obf4n0h/kj ndr1ov5;.a t4*qpzar 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 timel iu04ok2(f 4)1 g +zas fh.d k5ublnc+snb6fws 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 mass in the process, what would its rotation speed be? 2nfug h + .sk51 04aflzd)4subnfboil k+6w(cAssume 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 w hzf7 f9ba+a)energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km withouf w)+ z7a9hafbt 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 illustratkea. qhe74ac/ ixe( g-r8 z1byes an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizrda hf0;fime -5:c-c q pr)h5eontal 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 sm9.opp dsr;) freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and r.dp)s s;mp9o then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and -avpe z2hvm*y*1z;r m we want 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 heighrzpy-*1; 2vazem * vhmt h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn wz-msgfk+or9d)1br0.fy tr5 *btl a t 5ith a radius The forces actis 1+f)tb0arrr z5o ft. 5*9-kldtgbmy ng 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 rockmd)qg6 x bau/v.iu6o1 into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above )xau v1m /qi.6doug6 bhis 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 arms ahl4 g l,i0,s6rm oe9xcs thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretchedeg 6r, 4holxml0is9,c arms, and with arms held tightly against her body.   

  You are designing a clutch assembly w0g4yyk(b kl .lhich consists of two cylindrical plates, of ma.lylbkk0 4y( gss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 tracu*vspn1 ner bve.w:, ( 37w-nxrhya 5gk of Fig. 8–58. What is the minimum value of the verticalya31 nrrn(bhxu,n -w g5.v* p:sw eve7 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, bu-2qgm4;v 0 6lm /sb: pqztrb7yb;hvrkt do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces itr6 kl ) b:o w 5yk-87f3ubafhh*m.j6oqin(eevs speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleralbne uy7wkreoj5a .mih:v3f)k8b (- 6o 6hf*qtion 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