A bicycle odometer (which measures disteo iivg qafni8fsz 541.;.lk)ance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens ioig qne.1l i5 k.48zs;ffiva)f you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poycdgsttsr5n 2, qz6bfkl+un2x2 d ;.6int on the rim have radial and/or tangential acceleration?zc2ftd s nxg+btlks5yu;2 d,q6. n r26 If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described dd.+u6zzy f .qby a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a gbz2ga c d,o/ne :ib -txg/v5e,reater 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 wit awkjk,4d 5)zxh your hands behind your head than when your arms are stretched out in front of you? A diagram may help j45) wzd,a xkkyou to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel 1-pyb ev -pt6- dqie6zand three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocketp6p qbzeyidt-1e-v -6 or a large front sprocket? Why?

Mammals that depend on being able to run fast hpj*,3 rfjes h4atw /b6swai01ave slender lower legs with flesh and36/ s w0ai1wbhsrjt,j* a4pfe muscle 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 terxrru8wch uy-n6 ) a53.nu mp0/j*ua long, narrow beam?

If the net force on a system is zero, is the net torque .ltt9 s,tyi( s*z;:kj 2 gzyvcalso zero? If the net torque on a syst.syct ( *ytvszlj z,k9 ;itg:2em is zero, is the net force zero?

Two inclines have the same height but make different angles with the horivf(s 62 an1ri-qkzil;,b h-qv.ehx9 gzontal. The same steel ball is rolled down each incline. On which incline will txhv,zi g.1 2;6bkl- 9srh(eva-n qifqhe speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an inclivl o/10hhioicm0vv( 5v 7jh6m ne. One sphere has twice the radius and twice the mass of tho/i 5l0hmvm0h6 o7j1ivc(v vhe other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same masst*i+4 r:a t9:tr rdklo. 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 r dio:a4 tktr9 +r*:lthas the greater rotational KE?

We claim that momentum and angular momentum are conseimxdyu4ag*f bkmbtl +h :1 m7942eg ;hrved. Yet most moving or rotating objects e hfb9i7bum l;:*m mh4+g1y2x a4dektgventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wo3a)kw z8( hdyfuld this affect the length of theazh3( k )y8wfd day?

Can the diver of Fig.a*hq5gizt t86a3r4lbeg) u+m 8–29 do a somersault without having any initial rotation when she leaves bri h+ 5guaztq 683gmtea* )l4the board?

The moment of inertia of a rotating solid disk about an axis through its cetai0f*s -j.ct nter of isf0. -cj*tatmass 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 holding a 2-i*c 6x,f(l)z eqqp k0qf;z,dpkg mass in each outstretched hand. If0*,l;dzk qpc q6xp) ( fzf,eqi you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is xmee/dhgbb g7z337b. hollow and the other is solid. Describe an experiment to determine which is whic e gdbme/.z7 3bxghb37h.

The angular velocity of a wheel rotatingl8xalby bp-*s;r 0+ s c/ddc1f on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If t;8x * pbfrd+scsllb1a /cy0-dhe 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 freely rotating turntable. 5/w 6g:)jy cwfq 3fqlsug/ +zyWhat happen)5 qg sqfwy/:lzgycf 3/6juw +s if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As he 2,vjnpd8qd5mb4 y7 ndthrows the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the oppd84vnp2 , d5nbm j7qydosite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angu+yskk3oq- imisl7u: +lar momentum, discuss why a helicopter must have more than one rotor (-k3k iiuys+qm+7 o:sl or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following a-u d .-s9,ppbgju,zcingles in radians: (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 be(yq g1 (mj3ysucause of an amazing coincidence. Calculate, using the information iny3g1 ujmyq(s( side the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 np .w1zpz-;p akm from Earth. The beam diverges at an zppap1-.nwz; angle $\theta$ (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 f06 jwlz6ljc 8rate of 6500 rpm. When the motor is turned off during operation, the blades slow to 86 06jz jflwclrest 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 q,8 2lq hep6c** vpkrffloor 3.5 m to another child. If the ball makes 15.0 revolut cr*fpe,8h k*6v l2qpqions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 kmc y,vu-kj..um. How many revolutions do the wheels make?vm,y-.cuuk .j    $rev$

  (a) A grinding wheel 0.35 m 1hc y 9b8wcf5hs al);)zkwp5b2e8ps xin diameter rotates at 2500 rpm. Calculate its angular velocitlsb8 h5s)baf51 2h cw cye98pwx);zp ky 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 c.sql e-lu *jx6/ jf2(uonzpp7omplete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated jq7 /.us-x l2*p(njol fe6puz 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 j)vpd qw*dzs c*(( b3lywp /qmj-y a1go2h40hthe Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spee :hvd zq.j3 e-7c s(:+ummjzpod of a point
(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 a 6+t(mfh s)n sb2/xtvfrom the axis of rotat /vxshtsna2t)m(6 b +fion is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates unsy -tr yfm4cc4 ms24d(iformly about its center from 130 rpm to 280 rpm in 4my 42 -scf4s tmc4ryd(.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius 7dem3fhyi i:) $R_1$ 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 aboardat*d k k/zvrci.-)u-i the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start ovukt. )z dai- /ir*k-cf their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in eg5hb* w wkqi34le,rb a,- ak-220 s. Through how many revolutions did -b-wl4heak3ria k,q *e5bw,git turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calc j+3 *acmgyvao7p m:-uulate
(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 stress6lj3 bbvym/ 30lf s3imes of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn thro s3y0jm6biv3l/f lbm 3ugh 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 accelera 0q2 ex,ppr)l ldfeu/s- mg -g;ousl)7tes uniformly from 240 rpm to 360 rpm in 6.5 s. How far wil,x p- de0)/ or-lg)sfue7lu 2lgp;sqml a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when igyo.igbjfq tj1tt) w) ;8fz55 t is running at 850rev/min It turns 1500 revolutions be o;8 )5wibftgt jfj)1.gyzqt 5fore 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 trwcr+xacvu-5u*k0 0/xw pl+ jhe car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 lw rp0w+uxr a +5x kcv/u-j*0cm.
(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 ezqkcawzjys 1*qe.qc)96 :9 f as the car reduces its speed uniformly from 95 eyq )z cqkw .6sejfa1:*c99qzkm/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when 6onm8 j /ts*hcclimbing a hill. The pedals rotatj6/osnt8m h *ce 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 ae 13j4yj dd *of )1vgy85zafbj door 74 cm wide. What is the magnitefjy8v o 1 4ydjf)a3j1gbz *d5ude of the torque 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)lw jtq.ssru +w th;m-p5schop 1 1+c4 of the wheel shown in Fig. 8–39. Assume that a friction torque l1) 1wqpjcr ot-shm;t4u+s 5shp+ .cw of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the l7w;7xhvj n,d ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position ajw7;,7 lxhdnvnd then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine g0 :sln: e74 cszgf.ldrequire tightening to a torque of 38 ls40edc g:fgn: .s7lz$m \cdot N$ 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 0.64 eyznncny.*km2kz-c * (m*vw.8 m when the axis of roy.w m*-c(zkmny*cz. evnnk 2* tation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diamyr42psf dklv7/g: 4smeter. The rim and tire have a combined mass of 1.2dsyflp sk:4mg/7 v2 r45 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 is rotated in a hh7h3qx k(j;o horizontal circle of radius 1.2 m.hox;7kh jhq3( 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 wke bm fzxe8 zmq( h5-9d+;nfukkpn *om76/(k pheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 Nkf ud+b eohnke9pxmq;m *fp5zzkm k/n-6 ((78 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 in.*gy)*v uubw/ djgjo 2t(,tka ertia of the array of point objects shown in Fig. 8–43 * *(.bokt/g)2ua gdjj, t uyvwabout
(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 consa0 ) b3eqbu) l29oe.z;ixfmzxists of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, eo jb * 8jzo0+n7yl,jurngineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a8j0 rj u *,+7bjzoonyl radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a ma d 40*vl, p,bxhk7xybqss of 0.580 * b hpxqy v7d04b,lx,kkg. 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 reigq,9d1r8 f pfst 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-go4j0; p3q(b jzhuvw hn 4ud*g8q-round and is able to accelerate in8*d4ghhq3b0j;pu v 4 jzqu( wt 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 rhx z89w 6+gx)tvy-ke eventually brought uniformly to rest by a frictional torqueg 9wzt+ehyk6v r8xx) - 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) :;gh vf,m +yh*rwmob;trp5j 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-kk *; w;k; jg)9 l2+rpqtkgauqeg ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. w 9)klqt+p ukge2* q; ga;jrk;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 ldjm uz-.j-6dthin rod, as shown in Fig. 8–46j-l d 6-u.jzmd.
(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 twoa4 hn2u.z u9lzamw7ro aq:*.v 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 the hammer from rest within fourgtw+t1orza4/ full turns (revolutions) and releases it aa 4otgz/r wt+1t 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 haswim,l;m.uf i+ a moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque 0 exswb 3 *fpot(49bgjof 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 rk yth1 *+ix:4pw:lqagolls without slipping down a la1 :li:gak4p+*yhxqtw ne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earagskk/t61 h5rth with respect to the Sun as the sum of two termah 5 /t1g6kkrss,
(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 zk.o wbj226ub a radius of 7.50 m. How much net work is required to accelerate it from rest to a bk6w jb2.ozu 2rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 c 9wp rkyshjmpz)ye61ek(3p*,m and mass 1.80 kg starts from rest and rolls without slipping dow 9jskee6p pm3yr)p1z ,hk(y *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 itso e6/0cu i/emh 5s0c pb*z. awpy2oea4 tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole js/45cup o*y/6b 0ea 0 eihpmce .2oawzust 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 en57q(xqfxc pzww91tk/6 r ggf3 d of a thin string in a circle of r fck6tw/q w5x1r9gfq7(zpx 3gadius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cyli 5xfc8uh)x-qgndrical grinding wheel of radius 18 cm when rotatingq8c f xxh5g)u- 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 side3ts/ *qftc gez )vk c8 orj-uzj9q9 zr(6rt:3n, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8tjzqqgtc/ 9rs u33 t( :9ckrz-)e *6 jvznr8fo $rev/s$ (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 inertia bnh 3 7gvkz8g) ol+cd-gy a factor of about 3.5 when changing from the straight position hogl3)zng7 8 g+-cdvkto the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her o* a+q0l(vynbspin rotation rate from an initial rate of 1.0 revvy+ a*( b0qoln 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 around a vertical axis through its center at a fryr(l0 naeg 86xequency 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 l( 8e 6yr0ngxaclay, 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 spinnipbs5ts(f syqw584s; :ii5jq sng 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 Earth avxjcn;4j6b,ct/ biga v9 /t3
(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 ident:m1543furn,swl xvj iical disk rotating at angular i,sn:54lvr xwu31m fjspeed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4an 0 hx- (-xhgide58qp $rev/s$ 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 cenyn, unr (gf0 7v-ayw-gter of a rotating merry-go-round platform of radius 3.0 m and m-vfg(au,nr wyn g0-7yoment 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 freelgl 5daid4 vmf8- j/7tbs:3upzy with an angular velocity of 0.8t8lp 5v 4 m:b7jd -u/iagfsd3z $rad/s$ 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 eventual 3r r; 7soom6l9hjw6lyly collapses into a white dwarf, losing about half 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 ratl6yor rs9ojwh;6l3m 7 e 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 ofwfz) .nh ac2o pk4f2d7 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 p0eletv9d i1y/l j4 b:$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freely withouta1blb*ql i );t friction. The moment of inertia of the person plusltb)qb1;il a* 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 ege)73 8z +jc.zjxu;-utpoacr-t qq k*dge of a 6.5-m diameter merry-go-round turntable that is mounted ojp.g)u+ ;tc er7ok38tq -cj zxa uzq*-n 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 groundkmmp;dv7 nfvi/6h *)q 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 L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How f pm6m7qk*; nh/i vv)fdar does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side alw.ws k;1mvbw3en17tk g.rey 0yays faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, trea3; s 7beegkwv. 1y.n tymrk10wt the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ratm2wbdp ; hkadpy7a. ;*e 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 1ryi*uef9ec9o 3 vw /bin the shape of a uniform 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 delivcei 9v*3rwy1be9fou/ered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid fov)f/ufk 6 h(cw tw,-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 its 1.0-m-long stri-)o6h v /wfkftw f,(ucng, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the (t jto-:) ozacangular 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 oy ,icje9k-x ,noh.)va f our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapsek)j,-v e 9xhniya, o.c to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobilk,hubo dlec/v9y:f 30e 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 mass 240 kg, and should be able to travel 33/ l:chd,ufob9k 0yev 50 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 illustra2ztdey ;zkhp*v5 h/:ytes 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 +4zqb 3/ozvd ezt;9zcon a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivo)wo.j fe7qt jie kygdv8-d)i6 +ktn, )t freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and theng)v)k8kjitj, .qifoy7 ewn+)6ddet- 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 vertica u:r ham9ozj8z( tjoq61s 3b.zlly on the floor, and we want to exert a horizontal force F at its axle so that it will bsa83o zj:r9uq1 m6 zzjo(ht.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/szz5 4ke74r(br8 6(,riwznb .jrttdjz on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal force z7zr8jr dn (zb,w t.(e rbk4jzt6ri45$\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 lengec+-sa ;pphn ;th 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 required to achieve this facp- h;;pse+neat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solidbk.-toa. m4i)jglh j 7 cylinder and her 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 t h.a.m4j7jbg o)i-lk tightly against her body.   

  You are designing a clutch assembly which consistc+f; 4:d,eivnrc5 r )ovqit5i s of two cylindrical plates, of ri+tn e5f cv):oi;5 , crqdiv4mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track iqjy1/ca,2 q zof Fig. 8–58. What is the minimum vaaij/ 1 czyq2,qlue of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not8-,vajqvw h ,ohp.osb5hp 6)a assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the c kfpo0(jk9 ng0ar reduces its speed uniformly from 90km/h to 60km/h The tires have a diamete(gp 0k9j0 fknor 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