A bicycle odometer (which measures distance traveled) is attached near thesv7/:m gq1ic7oicvy6 wheel hub and is designed for 27-inch wheels. Wha s gvcoy/c v7i1:iq7m6t happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the t(s+ gc c(-qdd9kwhkef5p) xlbc 82m7rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration?5mwcx kshlgt k df9(dc 8eqp- 2)b(+c7 For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be desj :01nkqpw cy+r3yu3mcribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ev,ej q, g,*pi5wcnu( bier exert a 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+,t7b vhsqw. /b:v;yyysjo)- o b7vdh hands behind your head than when your arms are stretched out in front of you? A diagram mayyvd:/, .y+vv-sbh s);7tb 7qowyhj ob help you to answer this.

A 21-speed bicycle has seven spro,wcp dlrgs0/a 3a j4c7ckets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket o 04gcd,c/7wajra 3slpr a large front sprocket? Why?

Mammals that depend on bei5jyt 939d nm1t s1ruifaj4e h;ng able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explarsa h ;3j1fi5tm9j9tdn1 y4uein why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8– )edhr*+jc ny- b0ftc)35) carry a long, narrow beam?

If the net force on a system istd6;nw)f9ql7rn6vuh6 ,e 2jg oq ym.v zero, is the net torque also zero? If the net torque on a system is zerqfed.6v g,6j6nuy )q;tw l9mvh7n 2ro o, is the net force zero?

Two inclines have the same height but makela up;4rj (t8c different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greaj prt(u;4al8 cter? Explain.

Two solid spheres simultaneously start rolling (froqap )+ybxi;g i.hu3/fm 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 gg/ ha+x.iiq p;3yf)u breater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start from ibv vb89y9qokk7/-ufuu c)-7 cj;tbh rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? kuj)9t9cchyovv77ubi - -b bq;8uf/k Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or vvnhdet48h0joy oqij.7+ 53q rotating objects eventually slow down and stop. j.vo4vh3jy78i 0 qo5 d +nheqtExplain.

If there were a great migration of people toward the Earth’s e9z0c wdr0i1b 8kzr2 gv.hun 0 acqna(1quator, how would this affect k8wu11gzva.d hqr(izn n2ra b0c0 c09 the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotallz05m ;6fc mbl6x*)vtf-xvp tion whem* lllb) 0t6pfx5v v x6czf-;mn she leaves the board?

The moment of inertia of a rotating soli5p4 i,o mc1bpid disk about an axis through its center of mass is io4pp c15b,mi$\frac{1}{2}WR^2$ (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 sittingwdq ye/qoi.*, on a rotating stool holding a 2-kg mass in each outstretched hand. If you s .eidwyo /q,q*uddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have vnfgt :/hh4 eti,*i.athe same mass. However, one is hollow and the other is solid. Describe an experiment to determine which,:ehaftin/*vgi t .4h is which.

The angular velocity of a wheel rotating on a horizontal axle points westu8vf5; p ozc9g. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration zpo85v;u f cg9points 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 edghn0f u3x tee43f gfcs7m.)q+s e of a large freely rotating turntable. What happens if you walk toward the cenxh ctee.3 )gf+f qunm37ss4f0ter?

A shortstop may leap into the air to catch a ball and throw it qj w f6 zsacny1*4b9(qfuickly. 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 opposite direction (Fig. 8–36). Explainwfzjb*9 f qy1ns (ac46.

On the basis of the law of conservation of angular momentum, discuss : agc5 ly5qw*k lxlma+xr./9pwhy a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propell5*a.k ymxx9+l l/g5pa c lqrw:er can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 30 xl7bzuxe 0a./ $^{\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 amazi/t7/hzo k *oxd ,ao+thng coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun ankz a/x /7ot,to*dhh +od the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Eartvdstf/f2o0w-3 wh/zph. The beam diverges at an angle0 -d23wwhto//fzps vf $\theta$ (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. Whel5h :v zxito:4j(, syln the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angu(5 ::,olh s y4ixtzjlvlar acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball makes oum2- 0x jmkb.6t y+ slunf4pj;f-7qd15.0 revolutions, what is its dqn-d.b+s;u fol7k tmxfu-4yp 60 jmj2iameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many ree.f:d6x lq xd- 0gp/ yrj8xy-tvolutions do the wheels maxj.e6xr8-d fl0g:xqdty p y/-ke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate itu0l3tyi1 kfornp6 0 9c1qz xy/s angular 0puyq/ixr10o3nt yf69lk1 c zvelocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 8b47gi7ts*ovd n m8ujs (Fig. 8–38). (a) Whatis4n*m7td ob8 87uvgj is the 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 Earth (a) in itsfwrpe5.: ks1 n orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poic ctmb4ns7d i asg0.t4-lu ix)f4tg* (nt
(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 rotatz ;a( ce* rkij34p8fp8dnwu g)e if a particle 7.0 cm from the axis of rotation is to experience an acceleraw(jgpdc*3np ;k iera4) uz8f8tion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly 6pzqq)tk .y 0labout its center from 130 rpm to 280 rpm 0kztl y6.)qqp in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius o *p/:,s1fj 4 6wv9cwe00lsntdac dsm$R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put wa w7+tdh2gpbcr;i9mc,9lh 2 themselves into a slow rotation to distribute the Sun’s energy evenly. At thl ;p 9wbwa+2dh97 grihct c2m,e 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 e-he ajke27 jv8(wl6h to 15,000 rpm in 220 s. Through how many revolutions did it tureva j hw 76k2j8e(hel-n in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcu9f -trlk:rjh w qizet)a8fxu+3.b 19z late
(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 o4ad90 rb 6mhdhighspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutd0m6b 4 9haordions 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 ; . a9hx*g)ozey2dslbin 6.5 s. How far will a point on the edge of the wheel have traveled in this ti h )*seg.bza2lx;9yo dme?    m

  A cooling fan is turned -s s4jy6xnqzq-d qw* 4off when it is running at 850rev/min It turns 1500 revolutions before it comes to a st4-w qdsx*qyj -6zsq n4op.
(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 reduco*ie i02hv;ib es its speed uniformly from 952ihbe ivi* o;0km/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

  The tires of a car make 65 revolutions as the car reduces b ad:73ay pgj/ukz0(b its speed uniformly from 95km/h to 45km/h The tires have a diga k/by7 d(3:ba 0pzujameter 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 each pedal whtx,;2 evrte9t en climbing a hill. The pedals roter ;92,tttxe vate 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 d:n fcedy+m( hr1:d ba0oor 74 cm wide. What is the magnitude of the torque if the force is exerteda:n dbcdf y(+rh01e :m
(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 io7w2l07/ r6t u i:hcm22mbc htm.dtwan Fig. 8–39. Assume that a friction t/2 t w hm.lmi:c 6ub0t7t 2wha2dom7crorque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mae xl22:t.wf or7zdxmp6-llg 4 ss m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of tglfelr7zmltx. 22p6 od4 : x-whe net torque on this system.

  The bolts on the cylinder head of an engine reo(birzxs 3.y1 quire tightening to a torque of 38x31oz bi( yr.s $m \cdot N$ 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 whensmrw 62 kmkr.7 the axis ofrm kr.m62w7ks rotation is through its center.    $kg \cdot m^2$

  Calculate the moment i(9rzj i8 agu olohal-z3)k56of inertia of a bicycle 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 ignoreo6 8a-)a i rz5j 9zhig3l(olkud (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, t tcu:9k5 w*+3dqqah/kra2 qelight rod is rotated in a horizontal : 5kehwqua/tct k *3ra 2dq9+qcircle 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 sp g 2maoo/q,ff2iotnnw- gir+:i/h+ys;f 5 s .veed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N ;g+ i ro g/,m:2/i5 2foa -+nsfohtv n.syfiwqtotal.
(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 poino3g9y-.c 3t 0u9buz5x pkc* * uooertrt objects shown in Fig. 8–43 ab9*rtzgbx cuuoy*p-053rc k93 etu.oo out
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whong/jk76 8xzswkic f: 4se 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 spigmpalm.sy)p*6etaw*1k+(gi3 tbd t4 :owl -rnning 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 radius of 4.0 m, what is the required steady force of each rocket if thgw**wap-t )dmym 3i.ot:1g ab( k 6elprs+lt4e 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 racvfh995plh 8rkt )//zld+ jax5q8mo p dius of 8.50 cm and a mass of 0.580 j8ml /r)+pohv5kt 9 x/lh 95 p8zqdcafkg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelg wkt* ujkbx9718 e/yxerating 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 smab(:av(dauz:s6 ic-bx n mb0ngup9.2qfjw n4- ll 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 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleratfdwg4n-jiqnu:-cbp 9xaa0 bsb:6n(.vz2m(u ion, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is evexwg1-+xoi( + y:-v5gwagq ips ntually brought uniformly to rest by a fricxw- gg-q1+pyi i v5asg:+(woxtional 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. 8–45j .ugp.r,/gzkzm1 xo n-(l ps) accelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by thr q:2zjtiv:l30* tlq ke action of the forearm, which rotates about thej:t virlq:3l*k 0ztq2 elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, adocbdv z964 d7pko+m: s shown in Fig. 8–46.b6+9zo ddv:d pkm 47oc
(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 of t;9g +lzk/w bkxwo 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 acceleras0)j sw4hz .h4h yy7igtes the hammer from rest within four full turns (revolution. w40h y)jhg7ish4zsys) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia of hi7*zvg ad(u;xpy -4a j4s+rq $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develop xtz0j,nsaso-1ktlr 7 /m)/ rgs 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 wj4( y)kj6 3r7kaju 4r t ie0jy*x,hc;mfkvd e1ithout slipping down a lankhf r4)74*(j;ckv u ei yj03etmyxk, 1j6rjdae at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Eart,cs3f uy/ d ohj/+ k;ovz1pcv3h with respect to the Sun as the sum of two +/jzcsv3 ,hfoyu;1ocd/ v3pk 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 7.50 m. How z* luc 3,meqg(much net work is required to accelerate it from rest to a rotation rate of 1.gzq* ,u (lcem300 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(8 ui ac*7dq:q1xf lzih5*tiw without slipping down a 30.0*u8:faq zxqhi(lt1c 7* wid5 i $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to6 mb/mhep,j:v5i; sad fall and its lower end does not ;vimh,p:5dbj6a m/es 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 rotating on the e+vfz*ow1jw - :1ikfo knd of a thin string in a circle of radius 1.10 m atffz jkoik:-+1 ww1*ov an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grindin8k(x74. xjx w lekrdr-g wheel of radius 18 cm when rotatr.kw74edxx lk x 8jr(-ing 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 sideoqcy( 4m,k 9rd, on a platform that 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 dry9k 4 cq,d(omecreases 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 hecr+,rni4qe:w r moment of inertia by a factor of about 3.5 when changing from the straight position to the tqr n,rcw: i4+euck 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 hela,o pnc+b 5y 9tkc8l:r spin rotation rate from an initial rate of 1.0 rev every 2.0 bc,+ol 9:nt58 pcy laks to 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 ver 5vppq :c t6rs29ypte1tical 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 cenq2 p6evs:pcpt 1tr9 y5ter of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentui.o pr38msp(ca1hf i1m of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of op vrrq.*dy a+7l7s t.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 i3b-s / i onnr/)1juzhy7tnj :qdentical disk rotatqj/:1nn zh n t7u/b-or )j3iysing at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 260 tgoc5ca+b a.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 of a rotating merry-go-round p z0rh b+fzi-8h +kc4ezlatformih0ez++c8 bz-f4k rhz of 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-go-round is rotating freely with an angu2i/g-mh(qr cavjw8 c hk4fl *m iyn:plx5*5(tlar velocity of 0.8 mji/(vl*i lhc8r5k a 5mypq4fhgnwt x* 2-(: c$rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about half pnl u,;vqs7elkhkq0( .md;+cits mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away nom;0.l ec(kpnv+kd,;s q ulqh7 angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 120-:-i whki gy0sa 2a7o7g:vmjv $km/h$ 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 yd 3kpr5w+ ok9$ 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 fre80ssbe*c 6 kroely without friction. The moment of inertia of the person plus the platform i80sb es*co rk6s $I_P$ 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 ay m9)jfynz7e : z15 wuit)vy+r 6.5-m diameter merry-go-round turntable that is mounted :zy) w9uf +t)vy5yi7ej1zrmnon frictionless 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 the rope lying on8g0l1vm* 7hcotms p-,r n8roc 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 0gp8,r1cl7mtnvo8m*rc s ho-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 the Earth. Detm9du5c(fg -m.ujf zv;q*zr+q6 h m7rm ermine 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 orbmq uz rh*m+gq m7f;z6-u jrdm.5 v9fc(iting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from resyx y6 t9uroz 6r4b/eo;t 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 radiuzzv,5t:6xgs m s 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by xz5 tvsmzg6 ,:the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylinb 1)tvhoxv(/n drical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass/vt1h)n (xb vo 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 isg ord3n0z6f)oz q 5j/e 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 times as great, we*s(q548xjdoa j ldym 9re 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? Assume that the star is a um 4j(sdq5x joa9ld *8yniform 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 - h(wam4dgygjo ;1g7y 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 mass 240 kg, a-od 1ga7;j yw4gymhg( nd 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 acc7w2 m(j+c1l teo ;aan $H_2O$ 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) izuzv- a(at,ry 7o;40t /baofs 8mi,qxs 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 * / (,s qcxmadlkv1.aee-sn0mM and length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally andme.,k1(n0*aal /dv cm- eqxs s 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 + f2)gmvj 4incon the floor, and we want to exgfc2 4nm)+vji ert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a tf k5335k1)a krmxcvaiurn with a radius The forces acting on the cyclist and cycle are the normal 1c mx53a k3ai )f5kvkrforce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 and 1y pytwa/be,qi; m5w+8r8x nnbegins whirling the rock in a nearly horizontal circle above his head, accelerating 58bep 8my 1n/yrxw;qn , w+aitit 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/ f e7j-h,2w noz6ldn6,xaneg and her arms as thin rods, making reasonable es/oaeden2 6,lf,n7nj6zg xh-w timates 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 body.   

  You are designing a clutch assembly which l/:tu3m48pxzt lfa 9pconsists of two cylindrical plates, ofl 9xlzfm3utp/ a4p :8t mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Figlc(,nq +fdiu1(,vvb;.6gifq9 vv is 9xv l/wo. 8–58. What is the minimum value of the ;6 x vd9 l oq ,iqv9cwnfvfivis1ulb(vg./(,+ vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do u a2sb)4k.pgsnot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly fr6 fpe)r nla/x i o77wtr9ftv;(om 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration xit) lf rpt6waf/ov(er;7n79 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