A bicycle odometer (which measures distance traveled) is attached near the wdx wi wdn.7/4c3ij 2 +)lperkpheel hub and is designed fori4w2)k d. n 3x+ecjwpd7 rlp/i 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotatesm//s.iqd *n3vcz7 ycg at constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linea gcq/ .szvn*/id73myc r acceleration change?

Could a nonrigid body be descr/-bo+ vr fej nrz)nuua(s 7.q bg815yjibed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Exp4ff1o/nx6 0 q/9:lh6tr dn0yta8xyu ylz nl(ulain.

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+d*qc/b eg6wxg/ 2zm/ vqw62tfrf8vf sit-up with your hands behind your head than when your arfgzq/ q6ve2gt/cm w v8 w *ffx62rbd+/ms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel1b3r dg+ bs*b,j7o( 3hl haj3nlltbt9 and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large frbt (l3blb7j sh3+* onabdh ,l13rj tg9ont sprocket? Why?

Mammals that depend on being able to run fag-ih1s*sngn hq 4 50y*kea pcz,*b yf2st have slender lower legs with flesh and muscle concentragnk* gyf*pz0,eh i-*s b512hynsc4 aqted 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 .k3lj5iz9lnrg: tkjsl . ,c*w (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If thjl*o/0t mhm l zrqu kb48-)/hhe net torque on a system ioq lu b*h)jr 4/8mhmlt/0h-k zs zero, is the net force zero?

Two inclines have the same height but make different angles with thcq exu r3x7.h9e horizontal. The same s7c3eu9.xq x rhteel ball 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 rolling (from rest) dxooh3muhdk 2i 0fq5- /own an incline. One sphere has twice the radius and twice the mass of td/qfh-uko2m5 oih3 x0he other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and t6nkd9sw jamn,n l2;aj;n 9w qzz:h8; dhe 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 nnhdwzn6slm:a ,j a ;;9wnj8 dz9; 2kqhas the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular monb4ks8nw 4i hj/mf 3w4mentum are conserved. Yet most moving or rotating iskn438 b4fwj/mn 4whobjects eventually slow down and stop. Explain.

If there were a great migration of peohf4mhi:j ; k 94x5zzntple toward the Earth’s equator, how would this affect the length of the dfk5n:h4;4z m9iz jtxh ay?

Can the diver of Fig. ) ypta s4f,mkhdb7w4faq3t( :8–29 do a somersault without having any initial rotation when she m :s7akqy4f)b3d th4af(t,wp leaves the board?

The moment of inertia of a rotating solkv1b 7t( ggxy)(ec 7fsid disk about an axis through its center of mass is e g)tc((sv1f y7kgxb7 $\frac{1}{2}WR^2$ (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 eachwz - p-4 ihc2bzho-*kx outstretched hand. If you suddenly drop the masses, will your angular v b ihpx-w--4zohcz*2kelocity increase, decrease, or stay the same? Explain.

Two spheres look identical andh0 gxqf d, 1rpu+wfk h0.zd4f3 have the same mass. However, one is hollow and the other is solid. Describe an experiment to dhf.qk+hd0fw, x034 rfpg1uzd etermine which is which.

The angular velocity of a wheel rotating on a horizontal axle points wesyax7dwtbcv( : x;p:q3 t. 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 acceleration q3(ct;:bxpwxv7 y :a dof this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge o )lgqmf)qiev+n ,hs,c;;t 9vmf a large freely rotating turntable. What g ,)+qm)mc,;ne lvvh t;q9f ishappens if you walk toward the center?

A shortstop may leap ,1s 4 :uon xco9c)bkiz,/utybvk6i: n into the air 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 and legs rotate in the opposite direction (Fig. 8–36). Explsnui:1/t6 :c,x)yuio ck,obbzv 9 4nkain.

On the basis of the law of conservation of angpj 89aeq xp8;zular momentum, discuss why a helicopter must have more than one8j;8 9zepax qp rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radiandd wfwf -zfl.*:rn6 vn/)) reiir;qi+s: (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 Eavt w(mwjale2;f e4(/u.e cm )mrth because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in rf2jm.w(4a/(ve;w )em tclum eadians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Eo s )s;r6,n7 hahqb3-lzby(mj arth. The beam diverges at an angl-m3jbyn 7; z) q6alhs(orbh,s e $\theta$ (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 rateyo4ejo, h;g 5)kwz 8gv of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular accw4 )jzk8ye,gv5o hgo;eleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anotn /,hcdrdw gpvob,n+ *56lk/ )wy mnk8her child. If the ball makes 15.0 revolutions, what is its diamet ,kny,l+/85pvomk/)nb6 dch dg wrn *wer?    m

  A bicycle with tires 68 cm in fxvtc,5+0od ldiameter travels 8.0 km. How many revolutions do the whe5,xvo tclfd0+ els make?    $rev$

  (a) A grinding wheel 0.35 m in diameter ro,/;igm o)-r thp 6jjijtates at 2500 rpm. Calculate its angularpjrh / im,tj;6g-)oij velocity 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 sambl2 dn8)3p) tvv/aoc-3z yq (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m3vn/ p)z2-vcam8b ltqd y3)o a 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 jvhet) n7p- mhyg1,d ,4 x3ag-5 abugporbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a po1tc3bo i*s1h1ix bfk1int
(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) mustzwetct. -5y .1bkj )mq a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleratitc.mb1ywj 5q )-kez. ton of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 1e;5 rik a.usb.*k3er sk; uz9z30 rpm to 280 rpm in 4.0 s. Deter;usu e a zsk.e. z5*;3bri9krkmine
(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 3vgxv(c 4q;e g(sx f11 ubtd3t$R_1$ 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 y/ct i)z1x 2oa,4w fgespacecraft 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 c241aiye,czgfx/ ot w)an 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 to5a/g vs7gy vwy0/qopqiy r)0: 15,000 rpm in 220 s. Through how manq:s)vqra yv/ ypy7ow00i/ 5 ggy revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.o6td:x,akl((r t4 r as5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying high, i 7phg .:ec6kflwhf0 *tfc) 4gf(kpjspeed jets in a whirling “human centrifuge,” which takes 1.0 min to tu)7(f,6fhg .h4:cjfpwlg kci0* kpt efrn 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 acc4+e4tv yayqm )elerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of tm )ayvt4+yq e4he wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850re.*yiasa,u6mv bug yj53 yme3b s-pl/(th: p8y v/min It turns 1500 revolutions beforp.mlu 8s ptbe y:ibuyg,y hj3-a6v5s3m y/a*(e 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 re 5faoddj fz1i rp---ee)ja9w9duces its speed uniformly from 95km/h to 45km/h The tires haved aw1da - j9e) pjir9fzo5--fe 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 its speed uniformly frsq ct. wigdzw9: je,7e. g 4*jzvo)n+eom 95km/h to 45km/h The tires have a enz)otjs .g,+zdg*7v9 je i eq: wc.w4diameter 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 weig :)lm 0kjj2gchx5z/ liht on each pedal when climbing a hill. The pedals rotate ii2j /hm)gx5: cllk0z jn 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 Nfxcl.rc r+z8: on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exerc: r.+c8rzx lfted
(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 tocmdfnow*, 73mrque about the axle of the wheel shown in Fig. 8–39. Assume that a fri 73dwfo*mn,mcction 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 massl5qyw/l3 snpv 2ess rod which pivots as sh 2swvy5nq3l/pown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque of 3878n ljii 12c- 1:)xaedqq - epyfc1ggjg y:8xj --jqi21fep 7 )cq11necli dag $m \cdot N$ 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 u3nlbp 6 l+n+jsphere of radius 0.648 m when the axis of r+p njnl3+ 6ublotation is through its center.    $kg \cdot m^2$

  Calculate the moment 5 ((ifomqqb*rof inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a comq*orib5fmq ( (bined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on ttxf.,+-n nh )elzh1th he end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculahh hl.x+) e,nt1fnz -tte
(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 p7iz 9adl4 ;zn hnh3g:wheel rotating at constant angular speed (Fig. 8–42). The friction forclinp9 ngz3 ;:z4h7hdae 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,7fd pm9kht+ m of point objects shown in Fig. 8–43 hkp,7mm9+df t about
(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 ox x*x vu5u;hm.fygen 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 at the correct rate, engitn3dn7a k;a h)rv* d-gk* wpz)neers fire four ttpkg 7 d w*hnv*;-kza)n)dr3 aangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and zgta+j25l6+zwkm a.*pg.ek d a mass of 0.580 kg. Calculkz2makdt+lg 6*.+ peg5 wzj. aate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest ta:bzonjom i;rh*pdc ) f+7 p 8r4wc/0fo 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 8h jbmwxk3 c.-a small 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 8j.bkhxwm-3 c acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor roty3)d,jk hz5ga j4 gku9ating at 10,300 rpm is shut off and is eventually brought uniformly to rest by a fr3u)zj5g,djyk4 9kh g aictional 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 accelerate iko9d).n h,kss 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 thynv v 78:es,eqrown solely by the action of the forearm, which rotates about the elbow joint under the action,8vv:y7e ne qs 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 bp*1ag fcj2jru8 3/ca ilade can be considered a long thin rod, as shown in Fig. 8–46.j/*cu3 a 8fjpi1cr2g a
(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 two masses1xfe ei e4mt*o.)ezept++/nt , $m_1$ 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 accelermpg.w6aloh 3kq43 i fz60uau, ates the hammer from rest within four full turns (revolutions) and rel63 g,a4 6wlzapfqi3humu ok0.eases 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 hascxb6lp l e+)-k 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 develops a torque of 2vo a8 t*arf(1y80 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radiu s( yc-h:ijn;zfprjpr;c,13bs 9.0 cm rolls without slipping down a lane at 3.3 ipc;:r s3hfnjy jb(-z;cp r1 ,$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energyk 87ww zi,cze: of the Earth with respect to the Sun as the sum of two termwic,:zz78 kews,
(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 kgkl oa,hn dc:jg6j1ym1 y wy. k4al(9*z and a radius of 7.50 m. How much net work is .a6kgjcl 4wn9yydya 1(:zl j*k1hm ,orequired to accelerate 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 6b jzbr37 wgw;without slip rwbb3g76wj;zping 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 tip. It starts to fall andf ,opx l,d8m/i its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the8/olm ix ,,fdp ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum o d-/ vms+4km s7kq:tqunm alv1/5j;k lf a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at a7m+ln: al ;vmqk5s/t4 vsk-k ujd /m1qn angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding:mo j,sbvz )*i wheel of radius 18 cm when rotating at 1500jv: *mo)s,zib rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hanln:g62.ez j)xw 5mvqy ds at his side, on a platform that is rotating at a rate of 1.3rev/s If he raisejyv6 l).x mwnz2g:q5es his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce i5 xarkehz-.3goh3 ,cher moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what ih, hxo35gakz.ric-3es her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial ra8sa2ty)*g-sbskv a 8j b dq)0vte of 1.0 rev every 2.0 s8)v a*8tsyv0sj2 -sda)b bgqk 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 vertical axis throughf n jkr7 pl/:l;wh1fq zhek900 its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg a009phqrjf z/kl1hfwk;en l: 7nd 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 momentfpr y7*e+9 gfn4jwr;kum 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 mosphx j6: wdw/:mentum 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 m 1 vuwqp5k)((omhn fbxvfw670oment of inertia I is dropped onto an identical disk rotating ahqxuk1(5 p0mw 7fvf(ob w6v)nt angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2z0e2z lc tlx47/kbkd(hmm f 1..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 platl.pjbhg,0- lk 8 * 6mxpzbx9pnform of rk ppjxbzp8x.6hb9 0lgl-, *mn adius 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 free- tbk/z3zlfz- ly with an angular velocity of 0.8bzz-3- k/zltf $rad/s$ 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 whi1l-isew5u nwz+ulg, 9cf 4,pite dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing rp 9uw1g-l5e z l+ui,f4,wcnsiadius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in bvng *.eht.xau mu :-.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 w89pvdi ioxl :ek*),cf.*t dq$ 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 freely wixx0atgfh im7p,7+ f h(thout friction. The moment of inertia of the person plus the platform ah, g+ithfxp7 f x0(m7is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m dia 1r0xjqvw i(p2( tbwx-x1e qy+meter merry-go-round turntable that is mi(tpxq yj(01xw-xr e2+w1bv qounted on 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 o ub6 .+uuk(orvf the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig..bu6( uruk+vo 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 alwa*bvhy nspwki5e*9. tpfy)w 7/ys faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to itb n p)eyy/h.v*75 i9fsw* pkwts orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates fz j x.c8 e pt:js.4hd7ezlf*)xrom 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 ur+dm/is *jn: uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. *+ mjusri/d n:Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg t-zq.)b)n2e q pgkt)a and diameter 0.075 m, joined by a (concentri)2zt-q e))qatg bn .kpc) 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 rear wgocdj) 3xcz()heel ($\omega_R$) 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 kiqp60ld*+ ju f,(1sakkmng 1 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it wukdksp*jigk 11ln,0+qf a(m6ere to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use d qn c70*bk4xyenergy stored in a heavy rotating flywheel. Suppose such a car has a totyqb4*0 nkxd7c al mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates a1*(wly 6mczszn $H_2O$ 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 horizontattuxfip) 1szwim/(mzl* +2( dl 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 mu+5m6,99o l,xlh rtwgwmjr4 can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) therm,ogmh 6lwl9 5mtu,+r jw9 4x 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 flooihsd *-t ,j.4-fn s*oja8jkepr, and we want to exert a horizontal force F at its axlee j*ftjas,n kso-jd8-p*h4 i. 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 ah1 0ed,r ya-us: wp0es turn with a radius The forces acting on the cyclist and cycle are the norm h:esu p1ywa-,re0d0sal 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 9;fu*psxrng 7dc 8nz1 and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feaxsrgzn fd;puc*1 97 n8t, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid 0h p+21f85hqbbawm ys6ud9 bbcylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculp5bb 086sq+fb 9au2 yhwhbdm1 ate 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 consists of two mc a g zlw8fkwe+5(,h,cylindrical plates, of mas(5mw,h zf+8,lwaekg cs $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 l ,8rk;g. vc0ksveq1 xdooped rough track of Fig. 8–58. What is the minimumxqkg vesk.,r v;d80c1 value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not xpnec38u3svh0lf5/v(a c6gntwgmk 2qa1o */ assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car rerd7ek gx14pa:o d1 vn6duces its speed uniformly from 90km/h to 60km/: nk6dag4ode vx17p1 rh The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s