A bicycle odometer (which measures distance traveled) is atta k+(.d *xmfgdlched near the wheel hub d*xdkl f+g(m.and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. 6)cs g otx0*vmDoes 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 actm0 ) o*v6xgcsceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described bvefmho,etad,q . w:7gn-a2 +am q ;cd-y a single value of the angular velocity $\omega$ Explain.

Can a small force eve.7otqvk+mk1do, e0+3vj qvrp r exert a greater torque than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behind your head than whfk7 )v, ihd/y.c0p 2 pn,qwrnten your arms are stretched out in front of you? A diagram may help you to ans,ct./,w v d2 fhqrni 7knp)y0pwer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pedal xy - n12y bl /cmdb1c1p9qbp4bcranks. 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 frol9 1bp- xybb1bd/c 42pcnmq y1nt sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fa cp8g1xo36jq0 zp+p nmst have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distributio6po8nxpgz1 p3m+jc0qn of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow l7ysya1d ;yzt,f7b j- 18pkp bbeam?

If the net force on a system is ze+c96 gco e6rk6it5mrdro, is the net torque also zero? If the net torque on a system is zero,6gkd6 r+t59ei or6m cc is the net force zero?

Two inclines have the same height but make o cxh. sjp9ceu ,c j:/:10pp:t0os mfedifferent angles with the horizontal. The same steel ball is rolled down each incline. On which inc ,p:o sjpoch me:ce0x9s f0ctj.1u/p:line will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneouslzruqdg l(3- y -xeje79y start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline fird zr7l (xueq j9--3yegst? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same m)23oho yr0;xy5t zoe 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 ttohmx 3y5y;e r)2 ozo0he bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserveeo .;qah ),nv k-ufg/m*lkk5 pd. Yet most moving or rotating objects evv-5*qouk /n) k klh,epafg. ;mentually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equari,ed 63jhc rhoat: v54 oz8k00k if6vtor, how would this affect the length of thv,:6ktk8 h a5e3 h4idz ocvrorji6f00e day?

Can the diver of Fig. 8–29 do a somersault without hav9q0+ p * 2(fyljvoi3znkszqw+ uolt**ing any initial rotation when she li2juk(tw* l of9*ql3*q +s+yz zo0pvneaves the board?

The moment of inertia ofcpcv 0vujg 2:7g5g 8pt a rotating solid disk about an axis through its center of mas2gc0pvvp8g7j5 :guc t s 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 t9c (4yh4lcin5 6pmsx rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decreaseicc46y5 4mnh ps(tx9 l, or stay the same? Explain.

Two spheres look identical and have the samiy n-r3p z ,caw0.j7ire mass. However, one is hollow and the other pnzi,j. -3r7y c0raiwis solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizob6y3cj2.m izmjd1 hh s.t,5wqsa m9* xntal 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, descriq ,y.xj.dmbai3h*5 9 1sm6 h2tjwczsm be 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 freely0l)jnm0po b y; rotating turntable. What h0 nlypj)o0;bm appens if you walk toward the center?

A shortstop may leap into the air to catch a ball and thra67rx+0 gug9xt a(qd low it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explai7xg9( gua6 dlt0r+aqx n.

On the basis of the law of conseq0c 3zsy4 x(p3h7 3ttvyen(o4tz1 xdf rvation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propelltct oe431fsxqz4 z3ph(y07td (vyxn3 er can operate to keep the helicopter stable.

  Express the following angles in ra*mz:ul1e1 d aadians: (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 amazin c( ou-y5wqz ,bongu/-g coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of thb (zgy,/qu -on cuwo-5e Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km fr0vi+s1vev5j g( 3caswom Earth. The beam diverges at an angle vv 1cswv0e 5(ia+gs 3j$\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotahnqt s -b:wkt66x -2aqte at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slowh wnt--kbs6xa q 6tq:2 down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the 67p jze9rd9xwc-+j:d,ev(-*rjk s wj os)vef ball makes 15.0 revolutions, what is its6o jv+cv7 xs*ewedwjrj,jd(9ekr-9 z -)sp: f diameter?    m

  A bicycle with tires 68 cm in dcui 2*b8h :flfiameter travels 8.0 km. How many revolutions do theh* ufb8c fli2: wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate vgtq/ dq pq .ll97,d*zits angular,9pqdgtl v.q7zqd *l/ velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes oneku080( d8d v7zqhzqmx complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m fd8z 0uq0d( v78 qhzkmxrom 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 orbit aro*p;9/sfa m; 4xfm7y ad ,vwbi6jhq( jtund the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed o q;zf:gtkbf xz1)7iq *f 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 centm/1sdxi;o jmj;jk + 4nrifuge rotate if a particle 7.0 cm from the axis of rotation is to experijj /;;x s+kio1dnm4 mjence an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 w28 yxz/ ,besjrpm to 280 rpm in 4.0 s. Dex z,be w2/yj8stermine
(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 a0:xb ez9emn4 2;v tum rpa)co9j.4ks$R_1$ 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 spacy a uoagb--)0f3ga r*iecraft put themselves into a slow rotag-0 baa*fraigo3 )y-u tion to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft 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 uniux;u lt(2e)zr zd97eoformly from rest to 15,000 rpm in 220 s. Through how many revolution2z9exr7e) u;ul(dzots did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 120,ss ,f nw+z:kl0 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 hqxnj79ffe. r5i .ky f*ighspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speef .q5i.9 ykfx*ner7f jd.
(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 y)rf(i c ur04uaccelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this )(0rfry4c uiu time?    m

  A cooling fan is turned off when it is running at 850rev/m0.l6jc* jbhryrv zx (;uzh f0/in It turns 1500 revolutions before( ;0lhzbvz cxj*0/ ju hr.6yrf 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 unift nei ,p)hnuv((s0 gt xkp92*yormly from 95km/h to 45km/k p0)s t( 9*genu,v(ytihp n2xh 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

  The tires of a car make 65 revolutions as the car reduces its a (278cdpd qfr kpne4mlop32) speed uniformly from 95km/h to 45km/h The tir73fd)k4lcpqpemon r (28dp2 a es 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 nggu+j hg p,ar-p6bwua3 80m(bike puts all her weight on each pedal when climbing a hill. The pedals rotatgnp0,r-h p(6g3u8ag w+mjb au e 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 force6 tjej mnjw..)*y cal2pfc1;y8t l;vd of 55 N on the end of a door 74 cm wide. What is the magnitude of the tl8) av.2ft;mle cy6;d* jwjy.t 1j ncporque 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 abouquuvy88h 1c)q) c o(oft the axle of the wheel shown in Fig. 8–39. Assume thaq8v coohq8()uf y1 )cut a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to thezntv)vwj 725h ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and 5 )jtv wnvh2z7then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tighti wn,dr0 qex),ening to a torque of 38iqx,,0re wn )d $m \cdot N$ 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 sphlew0 khh .a7wh-tm3*tere of radius 0.648 m when the axis of rotatioe7w k.3 lht0t wh-*ahmn is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia kyoy;d-ef*()r0 t7bu lin xh, of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of - lhy fb iy0o*ndx(ur)e;tk7,1.25 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 is rotated in a horh nubv4o .**kq ;0yppbizontal ciru 4k.*bohny;bp*vq 0pcle of 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 bowl on a potter’s wheel rs (3yy2oxt2j4 gnfj /rotating at constant angular speed (Fig. 8–42). The friction force between hy(2fj 4g otrsnjyx 32/er 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 object/;,0ces,e :t/zbtihsl :e4tv wi8cursq2h0 ss shown in Fig. 8–43 abous,e:c ;8tw 4/ic,zqus :0tv0/rtlshse2bieht
(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 oxyge.-hxl pwa(/;p vn utwoqzv /6:n 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 cylinbo2yl0kjl g8jc r;fd7laz;9.drical satellite spinning at the correct rate, engineers fire four tan7z aly k0 92dl;bgjol8fcrj; .gential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a unifor 2-kt 1pwib0z b24dzkam cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calck4za1dptzwi2 2k0-bb ulate
(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 baqkov+-q-gapw. .f2f mjetx4zkw :; o6t, accelerating 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-dd 8ax8x1x -cnpriven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume xd-8nxpa1cx8 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 10,30 xlbzkxdd:(53da i8 8os1a9bm0 rpm is shut off and is eventually brought uniformly b91olm5iad38(a8 kbdz:xs x d 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. 8–45 accelerates a 3.6-kg ball /4ajio k :sv)mat 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 actioncwovxu 1y.;o36gn z/ f of the forearm, which rotates about the elbow joint under the action of the triceps muscle, o/6fg1v y; 3wnxu co.zFig. 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 k: knc v/ecg tf/qc**bn s7su;9oh6a*n in Fig. 8–46.gcsqksaboe/* ; nt cu: c7h*n* 96k/fv
(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 two5r/cthi-x0 2 pl fxnr/z*ra/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-*gqdauj5:ks rest within four full turns (revolutions) and releases it ak ajg*udq :5-st 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 has a moment of inertia of g:r(+mkt-1(hw zl vpz0ysaj4 $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torqu6 20fzi zxoux0e 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 rolls without slipping down-hxwfx, euut zcyb6)x// 9jp9l2md2q a lacluz) 9jb/x 62pw /q ymduh29xf-tx,ene at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to t;5sjrbkd7;tx wzb;/ehe Sun as the sum of two terms,;dk5 j;e/xwbrb;zs7 t
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How m g g;cpl7 6*.y9 mrvwo-r+jonvuch net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8 n6l joog;-+gv v7yrwp*.9mcr.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest an:bu.m )ss9 x6 tr8clmgd rolls without slipping mgu s9x6.b:sl8 c tm)rdown a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It 2a+ )n2pneedn t2xdf5starts to fall and its lower end does not slip. What will be + n2ax225d ndetp fen)the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentumld ie*fta9d48 of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed d48fdl 9ti* eaof 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding whe1a2 9bf zkhq4188g of8dowbnf el of radius 18 cm when roo f h8o8dzq1n2w4gfb 91akfb8tating 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 si(x 2b logs. dk/3s32yva 6dtujde, 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 speeb63 ss(.dyo2 3xa ugdljtv/k2 d 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 inertia nz n 0 bfa)b.k,sha;w*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 he *s ;awfk bz0nn.ba,)hr angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotat+z z b(5qj9g cch5pwp fa2+rk;ion rate from an initial rate of 1.0 rev e2zqrk p(9b ;c+gcz+w5fp5 ajhvery 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 vert,5l vppar2 +)od+ k7nbz -evwwical 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, )w7 al+ b-v2 v+pw,z 5nrekdopapproximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning a54ehmz q+lk0ltqoh/+ t 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 momen:*pff x9i esw0tum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is droz:n8wgsb(l:(ji t j)y pped onto an identical disk roj(jgwn l::s b(zi8ty)tating at 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 3.v6dmm9y b biskc 3w/$rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round p1( kg5ctvkc c4latform of radius 3.0 m and moment of inert v45(t kccg1ckia 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 freezy/tkf ea1)):9fxg jo ly with an angular velocity of 0ja1 z/g9exofy f) t)k:.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 even 4dtsac0a+f3 qtually 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 ra+4ct s3 aafqd0te 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 wi lv;6k f27rms unmbimym+f 7ltr 59:q;nds 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 a7pj1hvx5f 2; skje5z.mvb. q$ 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, ini,-m3fbm xykn2 ysz)5 gg ,bx)qtially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platform is mn)kzx, 2)b,3-mybgxfsq g 5y $I_P$ 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 ovi9r(8iy rqokvs7wkw8(w9 cg::c2 ja f a 6.5-m diameter merry-go-round turntab wq(c ikig8 ws:( vj9rc8yk:voa72wr9 le 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 gxgvnt(go-pwkia+-q86d; 8 qthe 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 behi-p+ xggq ;gn88dqk(ti-a o6wvnd 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. Determ;7uel m :e )4)stgcjbz/1ufadine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbitalzage7 ctm)f:/;4lu 1dbus j) e angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from v 2:e,jcj3 zzjrest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radiu9km*n8 :rhqmns 0.20 m acquires a rotational ra89rhkm :nq*mn te of 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, each of mass 0.050 kg andy )g+z1toug5g* :jtxv 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 string, if it is released from rest. y+z)* 5 jt1gt gu:xgvo   $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular * zk..z3 :ag5ktgv grp7m3xrx 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 wcr6s0 kd)gq(u ith mass 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 wog rd(0qu 6kcs)uld its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy stqmmj lw,3ss1ytgd4 ro ,.7lqu,j *g +nored 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 agsj. ,1yr qmgdsmq* +73uwj4nolt , ,lble 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 t1 +hi,ufte;4;4p 8lcnb5 n+nkfrtz wan $H_2O$ 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 su8xcrqm+a/k2, r gx* mlrface 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 ignore fr*mu+l +fgo1vimup4v +iction) 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 forc+* 4uvoimpmv+ 1lfgu+ e 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 stande( 1/ zd3yajbding vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a stepd/dj3 e abzy1( against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with sm4 o( 0yvabd 3+utxk0cpeed v=4.2m/s on a flat road is making a turn with a radius The forces ( 0 ub+ 0dyckmatvxo34acting 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 rock into a sling of length 1.5 m and begins whirl8loq2 n-sge 9ping 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 fr8e-n p2qgslo 9om?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms w8p4u,6 . vaytpev)omg 1pqn4 as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretoa.6 pu) e4y ,nmp8w qtg1vpv4ched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consista 8-uxu b2hsp.s of two cylindrical plates, of mas8p -h2uusbx.a s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 roytx9 mtc/j w7u1xk ( /yaq9 *ekm9c0pells along the 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 1at9qp/xkkcmw m 7 e/uxty9 e(yc90j*the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not a r f6.qbg,fx3ek dx5r 5hsg*c:ssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reducesi8rp rm 1z;*zt its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the mr 8t ;ziz1*rpangular 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