A bicycle odometer (which measures distankvww 7ce g5+9ek/ud e9ce traveled) is attached near the wheel hub and is designed for 27-inch wheels. Wha+5ue/kww99evc7 ed kgt happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Doet2yk lz lu 1m/b8x+u;ps 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 eiuk1xll uz;ymb +2 t/8pther component of linear acceleration change?

Could a nonrigid body be described by a single value of th9b-06l0o.*jj b9tkifw scj(zq k0ifq e angular velocity $\omega$ Explain.

Can a small force ever i 8u w6g4umhh39i i)it55fcu texert 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 hands behind your head9 -q)b nbdi(w3h5n tsj than when your arms )5wdth q9bj (bn3-i snare stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three rj9r4-/e, n2k hx4;ggtle7f4:hu tcet o tiw1at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a larjhf 9:e2 ,ohl4xe egtk/g7 untr4wrtc-ti; 14ge 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 slender pnh j yr70do.aca(x)+t2kqrsm9u)d5 t9 w+zd lower legs with flesh and mm9j5or+yc0)r.w2d akt+hn pt axd)qus z7(d 9uscle concentrated 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 (Fig. 8–35) carry a long, narrow bjr6/y5nc 0d5 tv. 6 w,ffo1dvgks jjaxf:wu52eam?

If the net force on a system is zero, is the net torque alsog6/1omhfrhjeapiv mu7.j ;ri;l(q)dr6z(a ) zero? If the net torque on a system is zero, is the net force zo e () afu1 mv aj7q;(h6/giijrd;r lphz).r6mero?

Two inclines have the same height but make di8xog(w(rkmsqp +(b1wd38q69 lgs iiwfferent angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at g(6 i3sgpwklx( (8 q rs81db+w9iwoqmthe bottom be greater? Explain.

Two solid spheres simultapnr;yse*a:y. /wx6n fneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greatwsn .*ex; y:p/6n ryfaer speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius ano *)kpoef1 is9d the same mass. They start from rest at the top ooo ski 1*pfe)9f an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or-g x ;wz jkz.96lbm .;d6wilfk rotating objects eventually slow down and stop.-.giz; wz x 9wk6b.dlmfkjl;6 Explain.

If there were a great migration of people toward the Earth’s esvirsqz.b.5m( : 0vvhquator, how would this affect tsvmbs . i v(q.h:50vzrhe length of the day?

Can the diver of Fig. 8–29 do a somersault with:4gnlsh;r ;isout having any initial rotation when she l;ssg ;r:i4hnl eaves the board?

The moment of inertia of a rotating solid disk about an jt/h32vhol nj(mq6d:omn) 5kaxis through its center ofqn(mh:kt)vdm6 h25 l3/o j jon mass 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 stoeer+ 7jybg ,(sol holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explaineg+r7 jybe ,s(.

Two spheres look ide 7(:krasi /+z7e2v a giai4b4-isidawntical and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determiniwdb:z4a(a/i ssr2+ ga7 v7eikii a-4e which is which.

The angular velocity of a wheel rotating on a horizontal axle points b- 0e9.rqo uuxwest. 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 of this point at the top o xur-e.oq0ub9 f the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rof+kq 4-rsp(mab() 2osmsm 9phtating turntable. What happens ipq9 -pf+s)(a m b(m4rmss2hk of you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quick5dmlgc p:f j 746 x5yain2fsn(ly. As he throws the ball, the upper part nai(4: 6j55cm2xynfspf gdl7 of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservatio9ei 0v*j.lsv e4m(5;wzsqe qhn of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the se( .v;e*sq04j z5qwsi9ehml v econd propeller can operate to keep the helicopter stable.

  Express the following angles in radianseu /j eip27ndi0;0 kwc: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coinuyh,3 6(nra qgcidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on uy3(,6rh ngqaEarth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverge9tt+c9:;,al7 kfms xrhmp +o ss at an a xl 7r9:m ;9satftmc+ ,ok+hspngle $\theta$ (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. Wh*k32f*sq0p2izhedsrgb8 7 ajen the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleratip3kg2zh 8 fjsqra*bde20*i 7son 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 ou b*ps;q0u.7sy er47wc da:u15.0 u uwpds4;y * csu0qe7oa.r7:brevolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. Howxf0upouh lj7+0,5wn v many revolutions do the whn,0ulv 0 uj7 pxw5fo+heels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcula8 w yo7qoz9u.8h--nif jy9ahtte its angulaf.y7zn i8y-u at 9qho -89ohjwr 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 s (Fig. 8z uhn k-6p/inrqbeg/+0dd n0*–38). (a) What is the linear speed of a child seated 1.2 m from tnn r d/gun*qeh-i0b k/06+ zpdhe center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit a1i7hk * 3+vg xrbauu6oround the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poin3h0f nrhs+c2sk)w .mcy u-1sf t
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from t / p,egi.dx .gqjyj3m8he axis of rotation is to experiencemqdj g.x y/p,eij.g 83 an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel 1qs(*i5d ulrs68rjwbaccelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s.1(8iw5rsdlsjr u6*b q 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 v.c jj6 eq/cdna bdb8z*/rw;/$R_1$ 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 aboarn1ks+qnx / lj ts)9v.* tm, vd0rmkl*)izg p4md the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of mv l,/ j1 t.i)sd*rg9px )4nkt+zkq0 vsn*mml 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 uw8 p1lw,-x fqmniformly from rest to 15,000 rpm in 220 s. Through how,-8 1wx fpqmwl many revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 12 za3 :q )e1q9psd2raktyqu g yf)h55r600 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets inh.l5a.*6ew lj fw7oq q a whirling “human centrifuge,” which takes 1.0 min to turn through 2 wqh.lfe7a5qjlw*o.6 0 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm w,hmt*:d:xv vq)mp+ zto 360 rpm in 6.5 s. How far will a point on )mh mq *d,twp:vvz+ :xthe edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/ cl-tlqa0c f9 )sp6o1jmin It turns 1500 revolutions before i)6ja9op -s cfllt1q c0t 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 m02abzp e 10cky+l2lqtake 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have ayzbl21kq+2tec0l a0 p 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 carqhn x-a 1/;;mvmkd-ld reduces its speed uniformly from 95km/h to 45km/h The tires h lmq-na1; kv/;-mx dhdave a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding t ;az ybwa(b74(ow no2a bike puts all her weight on each pedal when climbing a hill. The pedals ybn (oo w2at;w7ab(4zrotate 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 o igwb)oqq6xuxs.x k a;p907 k1f a door 74 cm wide. What is the magnitude of the torque if the forp9agi bo1k6 7)u;0sq kxxxw .qce 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 r-7 6,1oe fdvun7zzvl shown in Fig. 8–39. Assume that a friction torquedoznzvvl7, u-erf 176 of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, ahqi -/ae8v58i1u- ei,2x uy eceon)afre 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 uea-5)hq8c e8i1x-onyei2 vfaei u /, the net torque on this system.

  The bolts on the cylinde.hss ts62o,(b5wrk m9mxlfl 4r head of an engine require tightening to a torque of 38 tks rw9l 5 s4smm l,6f(xo.hb2$m \cdot N$ 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 sphomu1wsd;3 c 4nere of radius 0.648 m when the axis of rotatm4n 3od1ws cu;ion is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of2)it1k ridmvvk.vfj2(6 gm-x 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 ignored (why?)k iv 2mvkf-ijr).6 tx1v(2mgd .    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizzpie axc6-9/ nontal circle of radiux96 /-pczaen is 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 conso94c6f4.gq pbrd9 2sn,xtfrb tant angular speed (Fig. 8–42). Thed tprcsf2x49bq, 4b6rfgon .9 friction 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 o r.p **,gvyllg a(mr9if the array of point objects shown in Fig. 8–43,irl*r a yl gm.vg9(*p 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 oxy fn48es -g-vcj4dos h*gen 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 ku8+y2ss d;phym(nk+ 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 psu d+ smyh;y2 n8k(k+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 a:.r w +bsjxdoa, hp6axrs7 adnc1m 548 mass of 0.580 k dx7 :phw.,rxmjrb65s a+nd saa4c1o8 g. 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, accelerating it from reifn lxiu,wz 8r(o1)v ;r y vs*)sku8j-3dik -vst to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and isx mufeu 8*e--)lbq4)3v mmsd s able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniqes3f u)m-es vxd*u)4- mlm8bform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shupdt7jrz y0.,0+ir aytt off and is eventually brought uniformly to rest by a frictional torque of 1.20p t7t0+ yazr.ri,yj d $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6jtt)p)k k4a;r-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 the action of the forearm, whicv5+3s eh osmn4r(ze3us 51d vsh rotates about the elbow joiovns1 hr(3z3s+4es5esv dmu5 nt 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, 1gua ks/d)k+poym (q2 as shown in Fig. 8–46k+u2m) gy( /ksaod1pq .
(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 twa0ues n u;fl+;o 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 accelerate f1r kpuq5w;dqu-5d )os the hammer from rest within four full turns (revolutions) and releases it at ;-pwk1d )uq orf uq5d5a 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, bgp29t po/4qqn5hoc 0 qk4cx 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 devel;+l6k mghu 8atops 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 7.3f8 6tdujgn9g.o6z /u u kg and radius 9.0 cm rolls without slipping down a lane at 3.3o/.j 6duu8fugtzn69 g $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the supqz:cy .4d lo1fq/b d:m of two terf.c:ydb q1qod p4: l/zms,
(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 d(*km it7hxze)oh9j ,w much net work is re,7k9 d(i)zt*e mxjhoh quired 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 5+xb hh-(*y,dm*dis4nielkz/y hdb 4 without slipping/b*xz5si l d4dkm dy hh-4y, +hi(nbe* 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 +cj 6vt,k7 ph zvs6wf0starts to fall and its lower en kz6w0p, vjcftvs+h 67d does not 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-k7 7oxqb udk1tnw:9e :fg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speqxdk: 77 wu1o9:etfn bed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cf8bx0 rahmsb7o2 7eo0ylindrical grinding wheel b70af 8mbe2xr7oh s0 oof radius 18 cm when rotating 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 :tf- opi)de,b6sv 1q hq2djy 9at a rate of 1.3rev/s If he raises his arms to a horizontal position, ip-e, vh dsdjtq) ofq9:6b 21yFig. 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 her moment of ihds 7 knb -3au+rlg:i(nertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rb -ha k(lig:usn3 d+r7otations 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 sp /w0ji4rctxd9 in rotation rate from an initial rate of 1.0 jid4x/t0 9wrcrev every 2.0 s 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 rotati0 v(rdpg ;;nc6ezrxho 1z5- ebng around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws hr( e -6exrzv 5;zo0;1p gcndba 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.hf0zy 7r:ya;3 d*mbp c5 $rev/s$ 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 Eaiwi acr.s*jr a-kov1jw zj vt*9g51 79rth
(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 zdwrx ,9kkxj9*gk9x p 4j 2m)pidentical disk rotating at angulax*pkrk 9pjm jxx,4)g 99zd2w kr speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at ko-dwcluct wcr x).z17-9a:+zex k e 32.4 $rev/s$ 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 mcj s;6zm 2j4 due*g2tat the center of a rotating merry-go-round platform o4cm6;zj* 2sjt2m gdeuf 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 w8dly qvd7/ gi8ith an angular velocity of 0.qyd /di l8v7g88 $rad/s$ 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 its gy xi8x06i9 o2rfe7+9ezmvw26c po *vye wy/emass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries9g7eoe9 y+*6viwzefw /68 2y 2x0ixpocm very 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 involveu+1on etr59v/jlp i)q winds 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 4hu ti(,0e vcjgp33sdt;j ys,$ 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, i(nk: x/wslm +pnitially at rest, that can rotate freely without friction. The moment of inen /+sm(l:x pkwrtia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-wvoyu+bz:. 8 um diameter merry-go-round turntable tha vu8bw ou:y+.zt is mounted 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 e n o9fxw* l1q7:flf/b)iu)m gbnd of 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. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from )o17wbumf :bf) i/n*lxq g lf9the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the samy , 27 ex,6ypnphn9jxce side always faces the Earth. Determine the ratio of the Moonhepjnycp ,96 72x,xn y’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 z chq vuvx 68lfk1vk;tl(z/20rest 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 cylindeh6q 9jk5z5uwe ;zq5 rf 7ebxn9ka(t. 5.fqrdcr of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calcula;c95 z6 (.kh5k7e5w5b9 ze qrfxqdftun jqr.ate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two soq2l5wpemk1w4+1 imku lid cylindrical disks, each of mass 0.050 kg and diameter 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 calculkm1kq42epi mw +1luw5ate 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 whesm)2al qzw p c0 if/j,d8o8;k xo4dw4kel ($\omega_R$) 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 poom:nls2qo)te hqc t*+-;;ogreat, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off + oe-*n; ltqtoo o2:)q;pscmhno angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollutij xpz 9wj-,;szon automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, wzsx-p z9;jj,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 bnnku 26s6 ) golp*:ldan $H_2O$ 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 horizontal surface a+kn *jpvij6-f7uwb8 (2n2 jji, uf jbzt 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 freen 2 8-4ultzpfegw2+p tly (i.e., we ignore friction) about a hinge attached to a wall, el2 + 8f4z ntuwgtp-p2as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of 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 verxzsc0*x8t *. e y/brd ccgr9q1tically on the floor, and we want to exert a horizontaxg tz0*bs.9xq c rc/1ecrdy 8*l 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*aty f atlo4hazfs*hg6;q -.;/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal y.l o6*qzh-hf4tft;gas*; aa 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 int f183 .c9t)zixnrylkz.;y ddxo a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque reqy kcx ;9f3t)1 zdr idz..8xylnuired to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her dmu*h nvd+ (9fakh)iw5my,1zarms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular hzmn+9idfm (, ay1dvk5wuh)* speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists oe90 a)xlfqy6l1wck u +f two cylindrical plates, of mas+1yaf)le9x w uqck06 ls $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 s -rwbt;gde5;track of Fig. 8–58. What is the minimum value of the 5s ;t-w;bdr egvertical 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 no(-,ur*nx uiz th7yt xdu s;u2;t assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed ;d gsdn w3h2a(uniformly from 90km/h to 60km/h The tires have a diameter ddw(hsan;23g 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