A bicycle odometer (which measures distance traveled) is attachmn u9tw,ccda:r x 73jra3 :mpk9u87 dfed near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a ad:ra9dtn8f 33urj cpx,mc wk797mu:bicycle with 24-inch wheels?

Suppose a disk rotates /usn,n9:v i27ofni luat constant angular 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/or7v2nsni9 ufluni /:o , tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value 3g q1dvyvfwth 6( 5+spof the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explaiw8y21y rlq0m2u:*futy2)bj bdfaf+ in.

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 doesu 2kyeeqp (2o) y8m;* e4pac6w e*pr a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diya s**(ee eep)2r;y64 puk2qe pw8omc agram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rearbjqd.2g qyw fe2iy97+mou)(k wheel and three at the pedal cbuok j2mw gy729q qi+)f(e .dyranks. 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 sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lowe)s.z:yja p :wq-g0lp6zw:s jv r legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotatioq) pzvs:zw6g0jyw.- : pasl:jnal dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walke2tpzomp) k:ba3;pr3c8p lu1e rs (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is ;6u3p3cbs f n 8wiw5zbzero, is the net torque also zero? If the net torque 3s;inwp 86b zc3f5uwbon a system is zero, is the net force zero?

Two inclines have the same height but make differe qv t) n:e*e,mf6txi/lfrh).e nt angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at v* ttlfm.,)/fi enxe)qe:r 6hthe bottom be greater? Explain.

Two solid spheres simultaneously st 7l)wb5 vt:/1y+;gw/ytatrz wwf;m mhart rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has thbt;ww1 ;) 7w/mghfrtlaw:y5t+zv m/ye greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same n3bym xvnog09 v.yg-+ 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 greaterg g.n xy+mo-nbv9y3v0 rotational KE?

We claim that momentum and angular momentum are conserved. Yet most p43qkg k3au12)6kacu ;yop meos*g+j moving or rotating objects eventually slow down and stoc 3p2kkk+;um6gysupj g4e)a3* 1ao qop. Explain.

If there were a great migration of people toward the Earth’s equator, how wo.*(s 1t3f( wcvatptq )tww+tq wuzis/cc** 7fuld this affect the ls/(7w*t v f.3*t(twftcpqiw w+z1)tuca*sqc ength of the day?

Can the diver of Fig. 8–29 do a somersault without havi,.:sqh s hg4dong any initial rotation when she leavshd4: sg,hqo. es the board?

The moment of inertia of a rotating solid disk s .vp9+gldfm* about an axis through its center oflg *vp 9.+smfd mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holdin +bbqu(mm4sci)o0 9yt. 3 pssxg a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the sa s)mtq0. xso b +i4csuym3bp9(me? Explain.

Two spheres look identical and have the same mass. However, one is hollow io 5sv ap6-97l ma+pyxand the other is solid. Describe an experiment tovxopl ia56+m7y9-s ap determine which is which.

The angular velocity of a wheel rotating on a horizontal axle p s6rb./gcn) dmoints west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration poinbs /g6cm).n rdts 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 gi+s3r1p /8kvkx l4bg a large freely rotating turntable. What happens if y3pkkbrgsg +1v4l / 8xiou walk toward the center?

A shortstop may leap into the air to catch a ball and throw it q 8ovv- jmh8z5d( vt2gluickly. As he throws the ball, the upper part of his body rotathtz8j2o85vv(v mlg-d es. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the la*-ph6 e0 wqyxq3oedq8w of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate tq 0*epqox6q we y-d3h8o keep the helicopter stable.

  Express the following abv h9fhyc8 x2 0+jpna2ngles 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 because of an amazikqr-osu4cj7hn u +1,zng coincidence. Calculate, using the information inside the Front Cover, the angularsqcoh kn+z1-,u74u jr diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Mooz)dke*x)0r y;lu fem -n, 380,000 km from Earth. The beam diverges at-zx reel)mk )dyf 0u*; an 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 j6urqnr8 dq(4at 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 acceleratio6n( jdr4qu 8qrn as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 mcrw q vvv+r6.r hh6q;9 to another child. If the ball makes 15.0 revolutions, what is qvr 6vq69rhh.cr+vw; its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolkt)qs0v p4c/t j/v9q8yc9k wk utions do thcvp8q0/qw 94)tkky kvc9 jt /se wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at /f2sr/vstd d72500 rpm. Calculate its angular veloctfd72 //ssrdv ity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revoluti *yylt:8l9t j31fafupon in 4.0 s (Fig. 8–38). (a) What is tht3fly*u8 1j l a9pf:yte linear speed 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 orbit ar1ag3p,y)ijg n ound the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a(:yn z sl7gme, 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 partixp0mx)h:tr)ryr adu ad5: l96cle 7.0 cm from the axis of rotation is to experience an accelerax9a 6xaru y:)pm )rd5l0:rdhttion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about4vf pe vqu+c71 its center from 130 rpm to 280 rppv7c u4 1v+qfem in 4.0 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 radiusm*zyo:300)sfgt1yb , fcy piy $R_1$ 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 spat76 2 sbc0nw:nh;k+olvh d h-kcecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trils- 7ht+:kvn2o 0knb;dw6h chp, 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 220 s. Throug/lf4 d4iucc( rh how many revolutions4c/l i(r c4fdu did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in j4ozbu* acz glmscy 18s6a:/52.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling “hu umcbmc496 lxf z;-g0fl rl2q7man centrifuge,” whicbgmqu-mz; crlf6 l4lf2x9c0 7h takes 1.0 min to turn through 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 a 3*weeu0 -j pwskuc.fm)*fp )occelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How faroc0 -suwuee**j k)f3)p.pfwm will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off h t(6lmmh+d3l when it is running at 850rev/min It turns 1500 revol d63mhlltm+ (hutions before 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 reduce:i ol*pf c;u(fs its speed uniformly from 95km/h to 45km/h The tires fcu* p(;i:fl ohave 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 speedkatnb(a5 ;mwoi)j :t5 jgmu60 uniformly from 95km/h to 45km/h The tires have a diameter of(mj bj:0 an)5wi5o 6g ;tkmuat 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 we.(nlf eodc-j 2mto5z3q9w0qdt ca/(j ight on each pedal when climbing a hill. The pedals rotate in a circle of radndej0 d35cl2ocq -q t(a .j/w9mtf(zo ius 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 5dre d,e9lmc/a door 74 cm wide. What is the magnid9m delr/c5e,tude 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 of the wheel shown in Fig. 8–3mw7 j ,c.jdwk:m1x y1g9. Assume that a friction tor7xw ,cmk 1.ym:gd1jj wque 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 ends of a massless rod whic(;0xpx1tgj mq h pivots as shown in Fig. 8–tpxjx0 m;(1qg 40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an e* vdzksoy .)5tngine require tightening to a torque of 38 o)d k s*vtz5.y$m \cdot N$ 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 0ola(pv3l: 3 ue.648 m when the axis of rotation is through itov 3( p:3lelaus center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm n9e1 ru,r7ars w(yi/spo5 bmlo+c8 b8 in diameter. The rim andr+l nirp/178 8e o9s(wm5 yorbua,bsc 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 of a thin, light rod is ro3atl84 0nfyl05m kjprtated in a horizontal circle of radius 1.2 m. Calcl3a 8nl05ytrfp mk0 4julate
(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 u/ +n q3ybu2rzrotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay isb3urznq y+2u/ 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 oo+hh tj7p97*oe txc p;f point objects shown in Fig. 8–43 about *ht h7o7jeto9 +c;xpp
(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 coes1btxnno p j+qv ;,a) y8eg4(nsists 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, uniforcfz.)l+ eg .3bp/x zjjm cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius ocb)xepjz.j/g.+ lf 3zf 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 cylinder93ni3ot 2j2x:dgaki w with a radius of 8.50 cm and a mass of 0.580 kg. ai wnd29:ox j2k i33tgCalculate
(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, acceleraip-wiqmr qwqfak8ul 5yn lf+4 j3/(75ting it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and is ay2h*azmboz:)(/s8j l w yz n; wqu-e2kble to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform ew2*)q nuozyl/8zs2hb:myk w (;jza-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 eventually brou5 1x, h ((ncc3+nwwd5-lidgizbcb );3aykh kdght uniformly to rest by a fricticl yb d x(c,ak (dh-g; h)3nni3k+ zb1wid5wc5onal 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 balr4ue1n yf0 g54q by;pvl at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forst h1rjnqm2 xn-h79om6 z-z f)earm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is acceleraxz7 tqf mhz2nn--)jm1 or9s6 hted 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 8qb /,85u4wz /kc5mel fyyieq be considered a long thin rod, as shown in Fig. 8–46.i/c ezb/l,q8e45w y yq85f mku
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two masselpk5:1 h ;ce ;yijhit1p .z7-z*oxojzs, $m_1$ 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 four wv lpu7 mhni5 b0v v5;wh5*9kb,gisj )full turns (revolutions) and releaseskms 5j, bwh0pi uvhi9ngbv 5)*7;l5wv it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a momd(ecy +1+ihy w),tq;e jgtv (ment 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 do +ioco ;d 3a4+fgmq8develops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg a5rkbqs+2t*.ilxi7*ebhkb (58(n1skqg jxp b nd radius 9.0 cm rolls without slipping down a lane at. rs qs8l(b5q ih kxn7*2 ke(bkgb5j1xi*pt+b 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy ofz muatv41+ t2k the Earth with respect to the Sun as the sum of two terms,m +uz4kv a21tt
(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 much 2. zn5x1cj cet/h6f hrnet work is required to accelerate it from rest tot5f6 1 jc.z/nr2hc exh a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest a*0 f u2f:srsrbnd rolls without slipping0sr2 sf:*f urb down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertical(vq :ass6dgd:ly on its tip. It starts to fall and its qgv ss::d 6ad(lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momeuei8d, k) *x hdnbex5l ygx)1i(n7* gxntum of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m hi7nd)8x* ,dliyxen*)x(gu1k5bgxe 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 cylindric(*g)kh seibem6 ( 0gztal grinding wheel of radius 18 cm when r(*(6bi) sg zeg 0etkhmotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at c4)jhkzyy.0o a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation 4k .h z)yojcy0decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shc;- ej, zr2g+twsylm-own in Fig. 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 position, wh mylz;cj,r e g+-stw-2at is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an inn)mr9 nu v*j/5u bkzg;itial rate of 1.0 rev every 2.0 s to a fiu )5/* bgumz;9nnrkvjnal 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 ve *moov1f2/yr vrtical 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 center of the rotating wheel. What is the frequency of the wheelo21/ o*mvr fvy after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater5iwoap :;hothnacd ,xpd24kr mgd. ,.8 ;v7va spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Earth:b/gcu q dks+(
(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 dismo ;+osdznp2ejz/f7x4,f )ug k of moment of inertia I is dropped onto an identical disk rotating at angeo74+,szf mz;/ g do 2n)pjxfuular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns j0w zpqn ;nu+v94sxz *o7bevy9xol -6t/;skgat 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 center of a rotating merryax1ciz;s ir 15-go-round platform of radius 3.0 m and moment of inertrciizs1ax1 ;5 ia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an nfhq-p w9hela 69nn -6angular velocity of 0.89lnnwfqapeh- h66n9 - $rad/s$ 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 whf 5of dwdkb+,+gg9the 5o;a 6qite 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 rate be?(round to the near5g+e,aoh gfb5;9ko+6dwt fd qest 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 invol sb5jot+)rs+z 8pjw*eve winds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass i35/oqqj (see$ 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, +x qmdvfyz7n4*e gn+xfsk5 1, that can rotate freely without friceq,kzsffdng n +yx* xv+57m1 4tion. 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 diameterz-(ohzr qql 7ymyi/9 , merry-go-round turntable that is mounted on frictionless bearings and has a moment ooz qy(/hli-7yr , qzm9f 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 o mqncv sqp, k6f+d3n/(n the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig.qndnp q/,cvm(f6+s k3 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 sa d4fvo , .//mmcxdzcv+me side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular c fcd. xzmo,d/4/vvm+momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rx2xg7 r4argh 6est 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 p 3e0i au0t8qicylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-ip0 ieu30 ta8qs 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 b3 pox mp-73btln:(vhdisks, 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 string, if it is renpobp:bm (t- 3hv3lx7 leased from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wheel (;7snje73dbc4. , x/ a2zoq6wmp:ciz c*ggoij$\omega_R$) 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 wit .bgn(, y/mt7ffqi* ewpk9i z8h 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 me,*i8tf9g yp/ n 7bwzmk.(q fiass 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 automobile is zyh,d+ral.k6 + gnv -wfor 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 trave+a, h w6r-+yk gzd.lnvl 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 an *w8f(rdnq)lcllb ; )-j- r vrw$H_2O$ 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 horizon9ey7i ;lngvter1j2*i tal 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 pivot freely (i.e., we ignore friction)j ew9,;kp,wk u 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 force of gravity acts at the center of mass of the ruw k k9e,;pw,jod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, o5c(km xkh(k.:z (kse and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (F(kc (xseh .m kkk:(o5zig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s oneqy7a (:e(bzn i zj +c(k/*znj a flat road is making a turn with a radius The forces acting on the cyclist and cycle arbnyi(zek7 j a*n+:e z(jz/cq(e 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-kgmolh6s4w +5v b rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from res6+5l4vm bhows t to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s b4bs tt,p p3s(nc -ps6gody as a solid cylinder and her arms as thin rods, making reasonable estimates for the dib3 t(cspnsg-,p 64 tspmensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindg: wx(f0kcxvq k x3mh3jm8ru( 6jg :6krical plates, of:33qvgx6(6jk0h 8rc:mmw( kx gk u jxf mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 of Fig. 8oq3j prblo 3tx-*wqa.h1 0n f,–58. What is the minimum value of the vertical height 3 1pojqx-3 o, r0tlb*.ahqfnwh 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 pzr ::f; ff br6ebk4kr) val965angabw-3, dudo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its spe3 wjh wk pv75vrp ig,c2d41z7wed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. vw2pvkh i, r1d 5gjw37pw7c4z(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