A bicycle odometer (which measures distance traveled) is attached yq5kf t/yqavb*.,. k gnear the wheel hub and is 5*gf y.qa kb k.qv,y/tdesigned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Dosd el1q4q21 evm.el q.nzmq,rpo :( 1tes a point on the rim have radial and/or tangentialm 1ezq1 q enp, l.sq(4e2.t:qvlod1rm 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 single value of the angular veloow6mjr pvr-1id7n(y:n4b)z g .; w k*ovwgyu0city $\omega$ Explain.

Can a small force ever exert aq:hvdy)(pyyj +zk;;xh6 dm7q greater torque than a 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 hand;m j.o f3mamqhs q,w0k4)3.oy4p dwcfs behind your head than when your arms are stretched out in front of you? A diagramkomm,q.oqp 0c f3wm.hasf;3) 4wj 4yd may help you to answer this.

A 21-speed bicycle has seven spro6nehp o09*ke2d s fw+yckets at the rear wheel and three at the pedal cranks. In which gear is it hareyo6+s*fdwe90 n hkp2 der 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 front sprocket? Why?

Mammals that depend on being able to run fast have czv -c7lrwk- /v cs2y+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 distributio/s cl r cyvz7+w-kc2v-n of mass is advantageous.

Why do tightrope walkers (Fig. 8m(p/t fxl8i550 ewg: zd-cakv –35) carry a long, narrow beam?

If the net force on a system is zero, ipu* n9ye - r.eoxt/7dns the net torque also zero? If the net torque on a system it-e.ny xn p de/7*or9us zero, is the net force zero?

Two inclines have the same height but make different anez;h.bxbtha irlt vli41; )v51up aj(t 7 d,(dgles with the horizontal. The same steel ball is b ub ji.,vt;aed) l ax4 t(it;h1pl75z1v( drhrolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) dsa zc6r5-z9s: o9jptoown 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 9sjcs-:or t oap 6z59zgreater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius tfr7;j e r/60gidtlo: 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 ha:j/6o r7fl 0rt;eg tdis the greater rotational KE?

We claim that momentum and angular momentum are conserved.e1 (z 5qyd3cbl Yet most moving or rotating objects eventually slow3c 1e dqbl5(zy down and stop. Explain.

If there were a great migration of people toward the Earth’s equ(qk2qz0 i xci 6cd09ry jo6om7ator, how would this affect d07qq 66cy zk9c2jo (mixo0 rithe length of the day?

Can the diver of Fig. 8–2zqi:l/p,ve x p yvs;;s.1bv 5q9 do a somersault without having any initial rotation whenys vz,p1:;vvsl/5xebp q qi;. she leaves the board?

The moment of inertia of a rotating solid disk about an axisdryvb+ d aa4 c9rr sn(*g.0j)c through its center of m +cbcrd drr(g*9jvyn0)a.sa 4ass 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 rotating stool holding a 2-kg mass in each outstretm /hmhd/*7k ,i avf b*gd9e6pbched hand. If you suddend6 e*,ih/b*b kfdap7 v/ gmhm9ly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow h clc2fh,cl7j*a 9dvjfe1*n: and the other is solid. De7lf 2h9 vjch,dn1*fja* lcce:scribe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle 6j tdu5vk8+fypoints west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleratut8y 65+j vkdfion 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 2l+b/ sintyz+ y2yo3 slarge freely rotating turntable. What happens if you walk toward the cenlyz y 2+sbos/+tyi32nter?

A shortstop may leap into the air to catch a ball and thro/ux (19 0 gcglvwi)kjxw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the oppo0vj 9lg)/ukxgw( cx 1isite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular x ),ud7:rbilal diq8 6momentum, discuss why a helicopter must have more than on)l,:b6iuqdxd 8 a ilr7e rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angla9n):u qxq( eqes 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 dvx39z5+ r4ofm9 *hd fr2xmi famazing coincidence. Calculate, using the information inside the Front Cover, the9 f+dv 23rdf*z5xhr4 i m9xofm angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directf*h 7v:9lob xhed at the Moon, 380,000 km from Earth. The beam diverges at an a7*f l9hxvobh: ngle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor is turneq 2pst1x dpf2ch2dt;6d off during operation, the blades slow to rest in 3.0 s. Wt1dpph ;2cx 2q fstd26hat is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anot40 c (2hqz:z 1jr.ziqvw3mnvm her child. If the ball makes 15.0w(0q. r v3mncv24q1 m:jzizzh revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revk tz+atq2 68p(ef rz6w/*wok polutions do the wheel q ewptt/koafz6(kz8 w+p*26rs make?    $rev$

  (a) A grinding wheels *1m hi03i)pqw ishn3 0.35 m in diameter rotates at 2500 rpm. Calculate its angular 03h q*m1n )3hwiss ipivelocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolutiohe by73n8 pjm2n in 4.0 s (Fig. 8–38). (a) What is th p2ehy3j7nbm8 e linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earthx. x/ d :vs3+epiffn,i (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed wi+p,m1 8 i,k0j )0kjgefijlg of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle e dl.7q8w:xr d9pc:b l7.0 cm from the axis of rotation is to experience an acceled:pq9 wc. dlexb:r87 lration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its c h9t:v5pe-lkwbd . v3nenter from 130 rpm to 280 rpm in 4.0 s. kn-3wv95 db .vt hepl: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 9ykj nf1oyfv h ds)3t :2f.kw.$R_1$ 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 x xf hv2:/q34xy wci2qaboard 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 spacecraft can be thought of as a vx 4 qxchqy /2wi23xf: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 t:c5mocvo8kw qn9w18 from rest to 15,000 rpm in 220 s. Through how many revolutioo 5nt 8cmvq81o w:cwk9ns did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculatoqu,7:-d: iuomh-zvve
(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 fl-q thk ;o: jt-ptvml(+ying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete re v-+pkt ho(lj -tq;tm:volutions 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 un0dfzc/ 1bt/ criformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time? 0tzb r/cf1c /d   m

  A cooling fan is turned off when it pj.311v:l+,vi fsd t)fsfpgbay -l t: is running at 850rev/min It turns 1500 revolutio,slpt 1fft-ib )sa.+v:lp d1:y3fg vjns before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformlyr/3 s*3zhq xrh from 95km/h rh3*sr/ zq x3hto 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 revolutions as kc-46z jptbr (;mkhm.the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.mpztr; -.6k k4 jc(hmb80 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 weits5m 4)jeu+2 avg +jzvght on each pedal when climbing a hill. The pedals2a+ +5tgzu )4smjjvev rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is the mago +si(9 +4nllue:k 5-w6am8a ov qtugxnitude of thgv+ia+ u ols:9nqlo-a6e 54k8wxu(tme 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 Fig. 8–3s vo tp,kob:x7-jt7d(9. Assume th7 ,s7 dvtkoox-tjp(b :at 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 attached to the ends of a massless rod 9 /kk6hxmgvooibp 9g3a:d:c :which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal posi 9v:xi3dgb6k:9goap c:km/ ohtion and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightendr g e:1/fau+ving to a torque of 38 ga:efuv+1 r/d$m \cdot N$ 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 /jn f -kfp6ee8nb+kz )10.8-kg sphere of radius 0.648 m when the axis of rotation is t)nbnjk+pe f6k/z -ef8hrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicyclu7f:gohabb 0 :r7 skm0q-q6w w4-b u0gmak8ehe wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be k ug-0uma70ew0oq:grs abq7b h4 6-wbkf8 :hm ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thibv f/:vi or51uorye-/ n, light rod is rotated in a horizontal c5 1oyvuierbov-f// r: ircle of 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 constant angular spek va804ff,mmk (m3oq 6nwi r1zed (Fig. 8–42). The frictionkk34(q n8a1mi0fm fz 6rmwov, force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of poin nb5iwsi+9b 86xsc7nmt objects shown in Fig. 8–43 aboutb5bn6n8xi ssi c7+9m w
(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 oxygen2d53lv;c m ehu 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-l(4jy jt9kx4wr-n- vx,rfqs1z6kqz m3: m ay at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radiunma4j4-z- yr m( x1,kv f-ws:r6jklqx9yqzt 3s 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 uniform cylinder with a radius of e0.p;7r 0hrkb79dmt-q i obgf 8.50 cm and a mass of 0.50bbdg ftr9 kqir;meo-7. 07ph80 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swq szsf(/ 1/wnqings a bat, accelerating 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 8.gx2ti;+r 1 lm uizxcvmda/2small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of di28+c;.mtxa1 /2 ilzmvu xrg25 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-xggy:3eqo 7o rpm is shut off and is eventually brought uniformly exy g:7q3-o goto 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 acceleratesd.:egy8xz2rw*khiy reo9c/6o0 rs i * 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 bal 6k-gq n2t*xuhl is thrown solely by the action of the forearm, which rotates about the elbow 2gkn x6tu-hq *joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, aschkv uh-p66+ a shown in Fig. 8–46.+pac6h6uh-k v
(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 consize i*ix3 :6zk. otozh7sts 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. hgmr) bc:n+fy4v-0 u;dmrg within four full turns (revolutions) and releases it yd+)gh.g gf:nv-4b;m 0r crumat a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor ha4*vtj q/ 0ltvls a moment 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(g 3/enx+q; bu;gfatftd9po 6 develops 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 rolls without slipping dlbyap 8+dub179j fpr-own a lane aa 7 -b8lrdj ubf+p91pyt 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of k;ulf oj; .imu :;3ch zlw.5wkthe Earth with respect to the Sun as the sum of two terj:wkf oz.ihk.;ml; 3c5l wu u;ms,
(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. Ho zk(/ roxgyv g-ztgjl8 n4885cw much net work is required to accelerate it vcr5kjg8y tng/ 88z(- xzl og4from 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 without ,a,q0 cqvxzx5 sl xqv,caq 0z5,xipping 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 balanced vertically on its ty3ya zd4t4k y(ip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation o4z4dty3y (a ykf energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end ;q n9kql il l;hw/3q,arybg03 of a thin string in a circl lhkw3b9 ,r aln 3q/;qyi;0qgle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angulaffyxd+tm 4 9b ;(q(gq)la nk0tr momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotatingt)lqt+gq9yf4kf b((m; xn0ad 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 c+bm*au)7v fup-mah( a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, -v bf*m)u7( aauch mp+the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her mog8:d cky*r;r41r+vzdidpp6 ez,t i(k ment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If ipcd* 4tp e k z;(+8riv,dk1drr y6g:zshe 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 hwt/:*:d65ahs ly1 sioy-f5 lrjv b 1hspin rotation rate from an initial rate of 1.0 rev every 2.0 s to a fi5j6d::s1w -fbys hll /5rviy a1ht *honal 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 vertical axis through its center at a+b+jgcyd avy of(5l(t,; tdm. frequency of 1.5rev/s The wheel can be+ja o( ldf5myt.+gy;( vctb,d 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 clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3.cya(i e g -mczmg.f::.da/,hx5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Earmvibe a 1h)0itj: b5r7th
(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 ofxa42u*n vh4zk moment of inertia I is dropped onto an identical dikux 24v*4n hzask rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 ezh6 h.d9iy4y $rev/s$ 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 centn(,w 3xct-js ar3(b(u,u7 cp q*os yrher of a rotating merry-go-round platform of radry-*qw7(cnu3j up,a(rtx s3( bo,hs c ius 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 /jeh3w b ld(d4an angular velocity of 0l3h wjdeb4( d/.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 0iygw2p/ds*e gai2u0white 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 aw2s egyu g20ipa /di*0ngular 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 wh3-n jchi 9m4ginds 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 ydu*nivel3 e)p b*6t .$ 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 reswiy;udcv9 7b rq.1ii( 2hl92xu1f xkqt, that can rotate freely without friction. The moment of in wb ldiuxf1cqui1 .9q29 k72i;r(vyhxertia 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 stan ,.p 14me;.1-iw: i j nhx.yhpl;(qwexkx vxihds at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia oe; i.v:1ih.pkxl (; q,mp.nxi whe4xj w-yxh1f 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lyiwu.05y zfjwl aw+c*;b hb.r 5ing on the top edge of the spool. A person grabs5 bw+b h5jfwru i*;zcw.0.aly the 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 Earth such that the same si 6qx;mu *pnizh sh:u4,de always faces the Earth. Determine n:uh64m zu qxp* his,;the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from re kp7qsi*4,*kr0ic7 o+u4jg .xroybx hst 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 o 5ndvx7 ,fcdg-f a uniform cylinder of radius 0.20 m acquires a rotational rate of fro dg-fxcdv75n ,m rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks+,par).+g/v nm jrfs b, each of mass 0.050 kg and diame sv np.rg+b jam+,rf/)ter 0.075 m, joined by a (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 isf:; br2nrr8yzv3z)ols c:( nj the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 timess1drwl1 m 7ipxdzlmv)/m+t+ : as great, were rotating at a sp+17vpm )d 1mx mdr wit:slzl/+eed 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? 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-poll)+wd )xeiq:xy ution automobile is for it to use 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:q)iyxe dwx+) mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates ,: 1t rn2dt4xzhxfm s9an $H_2O$ 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) ixn3 ss+: owd nlay7-0.ragtr,s 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 ignh,vj7g7nv4ew,5 fmy pore 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) ngpjv,4 w5y 7m h7f,vethe 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,r/nj-att0 . mtkaqw +, and 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,t/-ata r+nmqkwj 0t. step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat roads- -p,gztah.xi1*h3f yz b2xc /iri8a is making a turn with a radius The forces acting on the cyclist and cycle are the normah xxcf.h z/,baz- s-ipi*2g3y8 i1rtal 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 length 1.5 m a9ye yn4 m /*yke3h9h2n, ojqeknd begins whirling the rock in a nearly horizontal circle above his head,*q e9yey 9n /3mnjy e4h2,khko 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 -k ; sojnbw9gu.(neimld 8- 9sa 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 89niw d ;gs-9 nmb.ojukes(-loutstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which cod.y (: bji/sa1k4jcmpnsists of two cylindrical plates, of mdsa bmpji.1k /:cy4 j(ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 almo(62v- sntlpoocz (( ong 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 oocosplm vo2 n (zt6((-f the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not f(n6sc z-t saq5y7bq* assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its spa pg+ .e7/s ,yre;mwmneed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of eacrg+ne mm,;a/w pse.y7h 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