A bicycle odometer (which measures distance traveled) is attached near the wheelblrr y/0s x5:qb v3*ilm+y0zc hub and is designed for 27-inchv: lc+bbmrz0 5 s3*yyli0xr/q wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angiptywdt7cqh0 1thow/9f2 9 l )ular 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 woul9it/)fw 7qtt91hwd2hco y0lp d the magnitude of either component of linear acceleration change?

Could a nonrigid body be descrvw0pp/8 -p cdeibed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a grebfh i-16g5x,s 7c4ilgt0ubo qater 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 behind2s4vgidoj -s9 your head than when your arms are stretchedd s2s goi9jv4- 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 thredmye * nwz.un 9n0jj:v+v.jx p,9q+yae at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a my +z:apjvxn.* q yjnw+ 0vj9.d,un9e large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs wia p5kdc( bqn*k 2sm( i(/ye9dmth flesh and muscle concentrated high, close to th *5dk mdqn((ski/2 (emp9yabce body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkeisk7 qco3dl1x 9 8ke:srs (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If thelt n6i(.*pci+ zk+w wz net torque on a s6*wwinz( k. zl+t+c ipystem is zero, is the net force zero?

Two inclines have the same height but make d3 sknn*z c .0o:nse0 *ypwq2odifferent angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the botp c.one0*zw3:ssyn0dnoq2k *tom be greater? Explain.

Two solid spheres sidwnk cvegp7czo( 55:v +ock)0,wm0c3t1 jj rpmultaneously start rolling (from rest) down an incline. One sphere has (n d ogvzctpwkrejokjc c3: 5 )5c,m1+0v7p0w twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder ho;p1s xwthoz7fr55c* 8zjs5 have the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greateo5zhj5xo sfs 8 5; c7p1*thzwrr rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or 5oxurhl2 o*/nrotating objects eventuallyr hn2uo5x /lo* slow down and stop. Explain.

If there were a great migration of people toward the Earth’s );1h tky xwfr)equator, how would thisrh kt1) fx;)wy affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having an( 63gctu oom/ x(hg0 go)j.njny initial rotation when sh ctoj.u o(g ngm/6nj)0(o3 xhge leaves the board?

The moment of inertia of a rotating solid disk about an axis throwk+-k(u-fc v wugh its center of mass isc(v +-ww-kku f $\frac{1}{2}WR^2$ (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 holding0 9zesmci:l*ro w*bjor31 ;ii a 2-kg mass in each outstretched hand. If you suddenl0o9e bro3rici*z: ;wis *j1 mly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identicagjp ua2woe.a,*a icmfs(3k; z/x6 p:jl and have the same mass. However, one is hollow and the other is solid. Descri,/*ju;gcwe6mpjs3fa: 2.k( aia pozxbe an experiment to determine which is which.

The angular velocity of a wheel rotatingaw 0)/b1 zocvbha0gmrrxv7(v0 o i8c 2 on a horizontal axle points west. In what direction is the linear velocity of a point on the to abv m1wh0go)c/zba (i8ovr 00crx 7v2p of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely0y/ k6cvs dlr-+r-tcv rotating turntable. What happens if yol ysr-dv6 k0+t/cc-vr u walk toward the center?

A shortstop may leap ic+rl5w (+wbvento 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 t+b wlv5(ewcr+he opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of obe i4df;5ypo gmz0;0angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to kdz 5ibf e0;m04;g opyoeep the helicopter stable.

  Express the following angles in radio71qy9 d suxuy:meg7u 6 7.npians: (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 coincidence. Calcz zahazeqwls8;/pgza *35 yf9 4bw 2z,ulate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon,,wz8e9za3ab/ y sl* zf gz;w 4ah5z2pq as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Ear45fqhfm h k9v16ws ,dtth. The beam diverges at an angle vdf4w q tkhm9sf51h,6 $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the mot5jsay rwd5qi0 j9h4m:21jy74 bm r czmik,xf ,or is turned off during operation, the blayx 4 mwbmr,rsf0hmjqj91d:, 7i5k52yaz4ic jdes slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another chic yhh 8)w1wx: vjdn4ws m92ux:y)aqt*ld. If the ball makes 15.0 revolutions, what is)yqws8 h*uc4 xxww ::9d1 yjvh2)mat n its diameter?    m

  A bicycle with tiresx p:lm13-* 6bmckxefk tkt:;o 68 cm in diameter travels 8.0 km. How many revolutions do the whct3;:-*kf lmokx6xk: te pbm1 eels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its:bv8 ;gb 3n4+g(vpmdw t50xpj.hqck k angular velocity inj4 dm0gbh( p 5nkkcvq+ pw;bg. vt8:3x $rad/s$ $\omega$ =    $rad/sec$
(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 revo6js47fz ij(2 gcrle(jlution in 4.0 s (Fig. 8–38). (a) What is the linear 4lj7 ge2jr(6 zji(fc sspeed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbt3ke,/wuz: bz2 yn 8 1mfqc8ekit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a 7syp;r p3, gskpoint
(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 rota8 y /+g dgauko0,a kvp,cs6bj.te if a particle 7.0 cm from the axis of rotation is to experience an acceleration a,so dy8pvgc,k.j6 0bg u +/akof 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates8gpmnydk9t5v4t/np0 , t foq 0 uniformly about its center from 130 rpm to 280 rpm in 4.0 m4nttk0ogn pp /d,tvy590f8qs. 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 ;oh wx6t ,.3biuy*tcv$R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put themselve/hb37ib sxrso 28) ymys 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 timyrhso783x2s)yib b / me 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 ht6cf4 )i 34yl3easgyl ow many revolutions diy3f syec )a6l4 4gtl3id it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to,s k+qk+clgr- 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 i drnz0mq8 , qv*ct(y/oibn+ d*di/-son a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolu sn0o/ r didn o/vt,qb*-my(*qc+z d8itions 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 rp3)4dozmy y/x6v w ggf8m in 6.5 s. How far will a point on the edge of the wheel have traveled)yzx8g6 3o4yw/g vfmd in this time?    m

  A cooling fan is turned off when it irf 6 , ezp9eobt3aobud d1(74j5s uuq4s running at 850rev/min It turns 1500 revolutions before jer(bou 1tz d5q,dup4 3uao4e 9sb 6f7it 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 0iqw r*m/8sno as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.8ns0wm *8oiqr/0 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)7fal qgv/j4 p reduces its speed uniformly from 95km/h to 45km/h The tires have a dil/f) p4gjq7av ameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbinqtlb;)lz 1b ( vjcp:a4g a hill. The pedals rotate iptc )a 14jb; qbll:(zvn 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 lv*1esyv- r7ethe end of a door 74 cm wide. What is the magnitude of the torque if the force is exvly1ser 7 *-veerted
(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-w :+m:ev5i6t2jtocbajvbo) the axle of the wheel shown in Fig. 8–39. Assume that a frictione-:cjj+6 wv:a52vombi) b ott torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of oribisvx)t4 /jw63p) q h6;hq mass m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torqxwhqqb4)s 3r6io/h ivt;j6 ) pue on this system.

  The bolts on the cylinder head of an engine require tightening 55owoj;y bu+d9djc5d to a torque of 38ou9 c55 ;w 5oddbdj+yj $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m wr;p5oxkqz 8l -hen the axis ofx 58l k-;oqzpr rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diamlqw i-w. f-v/mu 1nei3eter. The rim and-/f. wi ie1-ln3uqv wm tire have a combined 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 ywo d y86o8kh.of a thin, light rod is rotated in a horizontal circle ofohwdo8 6y.ky 8 radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a box56at8slhgmd) i 86:ov5htn fwl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and th5x6hgtvh n so586)ma ift8 d:le 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 shownk +9pkp0dgh ** /bsoezxhlw80 in Fig. 8–43 abk/w e+ 90pokg *80xlz *hhbpsdout
(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 whose total mass is rhei.l,: i;n1p iix. o$5.3 \times10^{ -26}$ 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 raujw-9 *dym ,nvhj+ 3grte, 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 the satellite is to reach 32 rpm in 5.+w9j rud*nm,-v gy j3h0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cyli gg1zw q5gbmjz)kqt( 9.,pu, dnder with a radius of 8.50 cm and a mass of 0.580 kg. Calcudqkpg,(z gq5u9,zb)t.g1w mjlate
(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 i g0e0lpkck34bz/s 5- * u2tnwsj sf0xlt 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 tangentialk;h*m ny1/dfoe3yk3vxd ztb8q - 9rk.ly on 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 tw */mk.3z1 fnkx-o tr3 8 yyv9qbd;dheko 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 rotatint ja0p, z7mi7jg at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictiotza7ji7pm,j0 nal 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 accelerates a 3.6-y) ,i/mccgu sb*z j1q+3(waenkg 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 aca/ 1h usqr06-gvzens6jk b9 w7tion of the forearm, which rotates about the elbow joint under the action of the trnrwvhj 106-79sbsg/6 qk uaze iceps 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, as show fnn kuun4ldb 37(49win in Fig. 8–47l(uud kn w bnf44n93i6.
(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 con1/v * zm 1eyr5k2gwt4afybt)isists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates*4ev+g ob y0y;uusi9x the hammer from rest within four full turns (revolutions) and releases it at a speed of 28 ;xy9vu4beoi u+g0s *y$m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of ine;u b7oqdram0(rtia 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 3efgkv8 ,uz5zm1j; y6cytml* 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping downi,x3j( ynex2z a lane at zxe2n3 (x ijy,3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with resp zbpe a-k-,0 +7t5uzudjm*dz eect to the Sun as the sum of two terms,7-z0 ub kzead t ,d+juez*-m5p
(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 anm pi4x 03saus9d a radius of 7.50 m. How much net work is requirex9p mui 43s0sad 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 8cg*vhwl (am/ *,2i8 vfomeszkg starts from rest and rolls without slipping doc w ia,(l2ovs8v **hmezm8g f/wn 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 it7 jhc-p)x76 9z7lp2exiscl:ld0qkd s s tip. It starts to fall and its lower end does not slip. What will be the speed of the upper endc):qizl j-lh20 76p s 7xspkdde97 cxl of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thiep9;m6 9kn/zeybok q- n streyk/nm9q9 ze pk;b-o6ing in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angulrm g1gti/:s mkpyrik133 bx .0ar momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 rsg kpi1 3it.m/b3kyg0:m1r xcm 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, handy 1k,6 q/k;sqhhpwjd+bq3ug6s at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms1qh/ ,qs +ywk6jk3hu;g6bpdq 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 Fw,1 rggq e 7d-:vks8 vz1s6pouig. 8–29) can reduce her 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 posi evs8,qrkz wpg7-ougd 61s:v 1tion, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increi3b4dh,lovd2 c4enskf0. 1 prase her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of o vp cei.krl4d1bn3dh4,s2 0f 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 verticaur 9hkezf7qdi38y g:9 l axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the cente zkrf u99hqi387ge:ydr 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 tsgd 8, m7)zm vhj+(0obii 4kmskater 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 mome ck pv*r zjz1,hr.* h-4:ed vxkrq1z2tntum 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 cylindrj *sydz1g6t m trt-tf5 q.,wo+ical disk of moment of inertia I is dropped onto an identical disk rotatif,1wt td+gst*q6zrt5yj m- .ong at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns fv: 8e2 (/rzp5nsyy yhat 2.4 $rev/s$ 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 ceyxl-yb zperf* tz 6hpp(i:59 be58su,nter of a rotating merry-go-round platform of radius 3.0 m and mome8bt*9z e,:iyesh6b-rz5yulp ( ppf5x nt 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-ro bn*)4f ri:b l10awpzbund is rotating freely with an angular velocity of 0.8 w4 0rl fbi*1ap)bnz:b$rad/s$ 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.r +w -cl0hr:e nh4tmg half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mr 4:ec+m0nwth r-hgl.ass 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 excess of 1m,9sri0bl e) k20 $km/h$ 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 g:lb 8kuvmmlm50 / bw5$ 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, tha(al /hi9kbv: ft can rotate freely without frictioi /9lhk:vfb (an. The moment of inertia 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 diameter6fn flav:1d .y3sr. avlx++q96 a wlnvoz.lj 4 merry-go-round turntable36fzal94xv: l . v .ydllfoq6nv +rj+.asa1nw that 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 end of the rope lyi q3kx)x gn.u-v u.gicz30o qo.62m4c ffnqv6lng on the top edge of the spool. A person grabs thc646. g -uxxm.olfu gfnzoc)vi 3.q0nqq k23ve end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Eartk uxo1hw,x0,j5 jw/s5rg 8pwzw/3 c 1sx/hipnh. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Eart1xh ,xxz8j5csp1wu /nkr w g3w0os,i j/ p/hw5h.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 mdk)1xevv q 3y//$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acquirt w80g8fryqyx2fe7 /jl*fe 9o es a rotational rate of7rl2w8y*yf e08e/gj fo9 qxft from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, ea 3:xbi;hriqta 5;jx r3ch of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thiij: ;hi;3qxatbx 3rr5 n 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/nma/qevb/vxch 366oh*l 3xo is the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with massvvkv0(xar;n : 8.0 times as great, 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 no angular momentu;r vn(kvv:0x am.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy stored inum+ w+8ezj7 i7a c*spa ag-(/gewvo ,y a heavy rotating flywh *cm/ezw+apggwj 8,( ao7v-uey7ia s+eel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, 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 illustratri;t )tz 9rbvj(*sj*aes an $H_2O$ 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 surfr *qk1f00ttq mmr2- k dono-chpi0+-oace at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignorv: 3;tejvso g2al q48ie 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) the linear acceleration of the tip of the rod. Assume that the 2l48i tvvgjo;qs a3e :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 radim6dot/ kk (d-jlrzf2 6)6otjymqyt;4us R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that i2;dlt46mjy)kyktmq - 6/rfj to dz( 6ot 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 makingz(jr*5p3 cx1xrxhn7 g5 - ztmr6of pp7 a turn with a radius The forces acting on the zmx-1onj( cx3f67*r5 zt rp x7phr g5pcyclist 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 rock into a sling of length 1.5 m and begins whivsp2cf p0+nt4an) z .ra* wtz.rling 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 feat, and where does the torque come from?+sn* za) t t2c ..04pnprvazwf    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and herbt z 5-u9s3q*v1/6 doywuuo.fmfj)he arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly agaiu ej) 1 z/96ot3*yo5 .db hqs-wfuufvmnst her body.   

  You are designing a clutch assembly which consists of two cylindrl2z ttm y,-*u:xmkx,gduo ) 2dical plates, of mdz,ug :d-y *x ,)m2tmu oktl2xass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 the2i co2rk i3+bp looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the higheprci2okb i23+st point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, bdhvtqq;pd 7b 4 4um-/-0rksrtut do not assume $r\ll R$ h =    (R-r)

  The tires of a car maqpcm+o 75i5yojkv *6cdec:0fs, s 8szke 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of easoo*sjpyv m7: 8z,defsk c+05cqc56i ch 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