A bicycle odometer (which measures distance traveled) is( w.9znt9j2 dirvxkq a2 uij0: attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch rziqitwxj.ka92 u2 :9d j0n(v wheels?

Suppose a disk rotates atw8u .fxd7f: ieh9+bmw constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the deb7:im fxw8wd9huf +. isk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body 3b54q wha i*dibe described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger fga6l qsi8h+wj: ak. )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 th 8:q0 lxtos.head than when your arms are stretched out in front of ytt .xlh8:s0oqou? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets atgpy.dufwpdlj+l r 81: /dt0 x- 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 yg -.x8 /f0jtl1ld:rup+ dpdwpedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs *yjj( /wm /pwzwith flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is zj/myjwp(/*w advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bem r.u*nt-z9 ll9ltuq 8am?

If the net force on a system is zero, is the(yy gb m0xbu(:dz )mxe1 2w-u6f9ux gd/bds+x net torque also zero? If the net torque on a system is zero, is the net forx-zbub61 (gw d xbs(m/9 dxyu :mfe0u2gx y)d+ce zero?

Two inclines have the same hei .h,y+i0ki9 i0wgc*r8kv v arkght but make different angles with the horizontal. The same steel ball is rolled down eakc9,rir0iw0 vy +*hgv a .8ikkch incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from re eb8u x c)gorof)96-hfst) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incoe-h o8xbf)) gr f9u6cline 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 the same mass. They stati8wjlz./xa 326d0 g3pn nfairt from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the grej td.a n3finx/2w6 lziag03 8pater rotational KE?

We claim that momentum and angular momentum 3aj,// frzyow k bbsbt0jr q3hij5011are conserved. Yet most moving or rotating objects eventually slow down jr0o0/s3b b3 1zbhtr kiy/a5 wfj1,q jand stop. Explain.

If there were a great mq om.c *qitagb85.9 liidv67wigration of people toward the Earth’s equator, how would this affect the length of the da8 g.q.*59oqii7cmta wil6 bvdy?

Can the diver of Fig. 8–29 do a somersault without haqtk0yq2v75h hw1(t usving any initial rotation wheh 1(v2thwqy5 s70 kuqtn she leaves the board?

The moment of inertia of a rotating solid disk about an axis through its cea2im9j1, lvy enter o2lmej1ay,v 9 if 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 stool h 3 +rw0acpleg/olding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? +w3p c0arlge /Explain.

Two spheres look identical and have the same massxk*iy* * )vwgt. However, one is hollow and the other is solid.xg**k vyt)*wi Describe an experiment to determine which is which.

The angular velocity of a wheel rotathd ptxn )g((kzru1y jp2y;e65zh p,j9 ing on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east,)p2kje t5hy9x ((gh6ynd, z jpup; 1zr 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 t;qqg 9s*pa(ht he edge of a large freely rotating turntable. What happens if you walk towardq9q(ahp*;g st the center?

A shortstop may leap into the air to catch a ball and throw it quickdey::thu :0y zzzp700tcym- nly. 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 z : y::dtc0mynye h0t0u-7 zzp(Fig. 8–36). Explain.

On the basis of the law of conserval1nv4icvq/.sm0 eh8 ation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways th0vvm8s1en qi lhca ./4e second propeller can operate to keep the helicopter stable.

  Express the following angles in xo3 2sw:ef2q nvk59qeradians: (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 Earx dq 8cun(7nk7l,rv: jth because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diadj7 l uxkvr,n (q:87ncmeters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000s j9gi2ry i s9/p3j7zc km from Earth. The beam diverges at an anglj2pi9rci gs3 s97/jzy 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 rate of 6500 yqm/v +- :bm .qp(iqtirpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular accq/ i(-tymqbp.qi + :vmeleration 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 makesayasie44)tb q 3hnbr5+ x :(;evl7mnr 15.0 r(7+arb)4n5 eli qb:mv4 ;hrxs ya e3tnevolutions, what is its diameter?    m

  A bicycle with tires 68 cm in dicpzu 9,8hw. 5vnrz1 ovameter travels 8.0 km. How many revolutions do the whhz, nv9co up1 rw.zv58eels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotath5az :9myqs8g es at 2500 rpm. Calculate its angular velocity9m 85 syh:gqaz 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. 8–38). (a2 ska1n7hyjqh42tno5m fpi15) What is the linear speed of a child seated 1.2 m from the2jtypa4 fk7n1h h55mnoiq12s 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 aroundki 0k btai 0,tfm:0(lf2p5lj j the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a point6xk/qmp6sg.7t:qz6n :np+ kqqux n m;
(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 the axjlq1a,c6uboaa. ( xr (is of rotation is to experience an accelr(1a(caqbu6, l. oaxjeration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm,czq bs:l)3 sc to 280 rpm in 4.0 s.)qslsc3,cb :z 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 2b rhrm0h5: 4-u..ln jzxyj shu;vqr+$R_1$ 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, astronautsa( 8 f99lcgjuk aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they acceleraal( cgfu98 j9kted 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 to 15,000 rpm in 220 s. Through h,b, xaiuf; x8kow many revoluxxubf a k;i8,,tions did it turn in this time?    $rev$

  An automobile engine slows dz4p( n+1gko; g(o mpnpown from 4500 rpm to 1200 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 in a whirlin79ac0h sa/5 qmn,2sw l dgeg3xg “human centrifuge,” which takes 1.0 min to turn t exs2 97a,/nwag ghc 5mqdl30shrough 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 /rl/1smcv :mi vcob 7/rpm in 6.5 s. How far will a point crbl7vmm1 / v/is/:co on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 150vu +juky0 h*;f0 revolutions by;vk *+ ujh0ufefore it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed 3 -,kesydm 3,lpwqa.uuniformly from 95km/h to 45km/h The tires have a dia ,3weqmk-pusya. dl3,meter 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 revoluto 0 6y7kemx(rv0 p*gbcions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have o7v0 x (kemy*g6bprc0 a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a 8 xqu i9:xqpwv 396llsbike puts all her weight on each pedal when climbing a hill. The pev qwp6qllxu xs 9:983idals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is the i1-1jom 4mul3iv lsy1magnitude of the tol 1j1lu-1mi3 4osvimyrque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the z (qz p+twjg p;pj0j+ (mp 4tecr9*-vqwheel shown in Fig. 8–39. Assume that a friction torque op c+pq4;mgtrz(vj j-qwzp t0 *(j9 e+pf 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to t l.f4eb 5 qtuw,ro wx8bwd,.d/he ends of a massless rod which pivor dq5t,w./fleb4 ., uwbx dwo8ts as shown 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 ok-8c o/ft+wzto a torque of 38k-fzco 8two /+ $m \cdot N$ 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 inertiqrb5i7 :/ gdwqa of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is throud7w5qirq:gb / gh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a xl:u+ps ;gr-rouw g-/6s sn6kbicycle wheel 66.7 cm in diameter. The rim and tire have a co;-:l sk sxusr+-6gugpw/ n6rombined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod kms0pl/b11bughv8 pu)3v1h t2l*zn jis rotated in a horizontal circle of radius *1k /bu3puzl gl8bp1)nvsvt1mj2hh0 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 j *kf5s:ph +;c6aq hibrotating at constant angular speed (Fig. iqps 5jkc:;*+6f hbah8–42). The 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 of the array of point objects snmax1-d k 4s2vhown in Fig. 8–43 aboutx4nvsd-mk 1 a2
(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 wvs/-rpm d4azvye n 1 w;w+7s4ehose 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 q/ aap0 j.xv e) o.gse-nl.js9the 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 for.o0nlj.a.se )aegqxvjs / 9 p-ce 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 cylindvutv 2 wv;c).jer with a radius of 8.50 cm and a mass of 0.580 kg. Caltuv2 jc;wv. )vculate
(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, acceleratitvg.hbue ql4;-: ,hgkng 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 small hand-driven merry-go-round and is ab79nb 1ep xt2ukm)e4vr le to accelerate itve) 4pt19urb 7k em2xn 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 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 shut off and is eveac3j9 1 h9th*mj9x gmtntually brought un9mxj3ht9cmg9j *ht1a iformly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8dig t11c:f pbgy+2-fs–45 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 t; s;.,q1mxysqbl *lxjm50gy ln:zi p6hrown solely by the action of the forearm, which rotates abou6s l 1:.x is;yx;*pmzqlln0 y q5,gbjmt the 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 thid 5q3y -gev-fvn rod, as shown in Fig. 8–46.dgq-f3 v5 -evy
(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 masses,7f+n4y jtu* r )x4vlnw $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the h kpvij yubn:37 z+9i4wammer from rest within four full turns (revolutiojn7b:iip 9k +3vwyuz4 ns) 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 hawl tg)-l0p:dvpa;5rvth9u/ t kwgo 8 2s 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 torw2ct0j j8; uruque 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 rolq4t9t bl;-m,a3lq oa8mtm0xbls without slipping down a lane 3b, oqm; tqal40mxlmtat8b- 9at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energyxti9r9*zi q 8t of the Earth with respect to the Sun as the sum of two terms,rz8 9qti xi9t*
(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)e:s8ud2v qev mass of 1640 kg and a radius of 7.50 m. How much net work is required ed8 ue:)v2vsqto 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 jnhw9./ djg m:and mass 1.80 kg starts from rest and rolls without slippin9jh wg md/j.:ng 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 itsol;52avs wp* no+sn1a tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.] 5nsv*2aa+so l;n opw1   $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on tj-ns 4ggk +*uehe end of a thin string in a circle of radius 1.10 m at an angular speed of 10.ns *jg-ue g+4k4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniformsq8mn*9 wn kn+ cylindrical grinding wheel of radius 18 cm when rotating at 15 8+9n qmnknw*s00 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:jih3aep y dye))25rov+ nc/i that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speepv +3/ady)i e:n)2ohjr y5 cied 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 inertr 436m-wga/vwqy( quuia 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 is vgmq-wy a ru 6w/qu(43her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate froc -1s:mq/kcha b1i1qc m an initial rate of 1.0 1qbh:/ 1qm 1kccs-ai crev 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 rotating arl )erf59u lxi 7lcpq,3ound 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 thenl9 lep)7c 35,xuir qlf throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figurexxy cz.s3;ki()aiy73rhuv5n2 iz f:t 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 the Eark h,nnwk,2rew g -t9;cth
(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 ideed5-h7 wropp5ntical disk rotating atr5 h-75ppodwe angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 h; rvqap58 kr6$rev/s$ 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-ro8egyao) 3- r,d6f dghs;tex* wund platform of radius 3.0 m and moment of inesdy;xehoe8r6a-,g tfw) gd*3 rtia 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 rsz+*vd 3 th/bangular velocity of 0.*t vb hzs/3rd+8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about halfl) i3*f*yo +fjd- lwg*lp)zrz its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(rl)f3jpgiw +*zl)yz- l*d*fo 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 wkjr, .g-gmu0,n vj7 x,bdjp b5inds 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 k r l40hnk xc4z*/x-b mmavc02$ 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 rest1 yft jx *zs 0g:,e0v,)iugi*aryuk ,p, that can rotate freely without friction. The moment of ineg,uexg0,zp )vi *syf*1jk itaryu0: ,rtia 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-m diameter merry-alae2 :t a(mk8go-round turntable that is mounted on frictionless (atmak a8:l2ebearings 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 rolla4 70 qvwpvvr-sic q ub95+at7s on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L7u+95air70 qvcavtb -pq s4wv, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. Deo tww iv,nhvy(86.;w utermine 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 onu6h wwtv;. y(wo,v i8rbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at avh.kmuz 6s v2+ 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 uniforq y;t qa65m))*ndvdv vm cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque dvtv56qv)m *;)ynaq ddelivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of twovb0b l3xu 09qr solid 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 calculate the linear speed of the yo-yo when it reaches the end of 9q ul0v x0b3brits 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 wheek ((vz jxa19wtd8 qulp6p3usfodvea -w./9 4hl ($\omega_R$) 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, wr3gong:s v:e,dbt9f1 ere rotating at a speed of 1.0 revolution every 12 days. If it were to undergdg:,s1oref9v3 t:gnb o 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 lfjp:vpx w8 hfzu9a)2egkl8 )-ow-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and m fp-we 8xhglk9jp: zu8)2)fav ass 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 an9yce,5ak h-wta6r h4aj1:fw l $H_2O$ 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 hori1)mnv jmg2gw/ndpx;x:rnb;/ zontal 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 ikjl0 aiv/--wM 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 and then released. At the moment of release, determine (aai/ wkj il-v0-) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on tp;bss j1mo9i1h a5ts8 he floor, and we want to exert a hor; t1ph518s9jassom biizontal 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 witrt+pb+ig z4,ah speed v=4.2m/s on a flat road is making a turn with a radius The forces acti,artp g4+bzi+ng on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rocktl ddp-g0a;,z o)ri n/ into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, acc/,0a;ot i-)p zngdrdl elerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, 9 (mjh-;wkkw,kmjc x2making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinni2cmm;kk9j j ,h-x (wwkng skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch asse6d g5c j:pj,xdmbly which consists of two cylindrical plates, of c:d pgd,6 jxj5mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alon/bx,j, + kdfdlw1evgy6d s 4z3g the looped rough track of Fig. 8–58. What is the minimum value of the v,sjefd 1 4kvw+gd6lxy /b,z3dertical 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 y nxce04vt2e:/ gr0h udo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed 6ia+5w gm+ifjuniformly from 90km/h to 60km/h The tir+m+6 5iafgjwi es 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