A bicycle odometer (which measures distance traveled) is attached near +88fprod zhss. v4ahl8t t*+uthe wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle witt8 + 8ds.spvz*+aho4 hru 8lfth 24-inch wheels?

Suppose a disk rotates atv5f;k1 cx,ni6za5n y/*vn o at 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/or tangential acceleration? For which cases would thea 56,f zk/5*vn yvnc nx1ot;ia magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value 7ghbll(knr.: of the angular velocity $\omega$ Explain.

Can a small force eva2b*, 2tsw2lw xnf0 zn:tfc 1zer 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 y4-dw 60nq4(iy umhtf qour hands behind your head than when your arms are stretched out in front of you? A dia q-6wm (dy0itnuq hf44gram may help you to answer this.

A 21-speed bicycle has seven sprockets at the reark mi4ygi;yb(r59 ay(b wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or (9k gby5rii; ( amyby4a large front sprocket? Why?

Mammals that depend on beipa0 ml ,mu7du4ng able to run fast 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 distribution of mass is advantageousm,7d a40um upl.

Why do tightrope walkers (Fig. 8–35) carry a long, narrowsw fa.upt*(/6s5t e bu beam?

If the net force on a system is zero, is theayrtb-aqsfbeb: ,2n 9w-ei7a)r4q 2 o44y zgb net torque also zero? If the net torque on a system is zebq b,4s-ria 4b9nz ayq:r2eebg y7aw)4o-2tfro, is the net force zero?

Two inclines have the same height but make differeg-clp6iz m h2f nyy74)nt angles with the horizontal. The same steel ball is rolled down each incl )fm pyz7cyi-4 lh6n2gine. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rollinxayn ig0bawl m/,7; *yg (from rest) down an incline. One sphere has twice the radius and twice the mass g/bx;myawl,y i0*a n7 of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have xu6am vaa4)b9 the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has ta u) x4ava6m9bhe greater speed at the 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 conserved:j da*-1ngbauhy71pwu /w3z)ci zd a0. Yet most moving or rotating objects eventually slow do d :0g-awz ) hdp1ajcyi*/1w7zbuaun3wn and stop. Explain.

If there were a great migration of peoptw9. 1x97 eeum g7vnvjle toward the Earth’s equator, how would this affect the length of the dx7ejmtg9w7 u e .1vvn9ay?

Can the diver of Fig. 8–29 do a somersault without having any initial rotatil8 xkfa-.0gf mqrv4la9 m(1bzon when she leaves the board?xf4br qagf8a( ml0m9lv1k.- z

The moment of inertia of a f0ji, 2q.yphs2b6be x8q67r:vgey u krotating solid disk about an axis through its center of massx06 2:e7qgyyf 8bpvksu.hr2qe 6b j i, 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 sittinguq q14:dv,vmk on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain dvq 1,kqmuv:4.

Two spheres look identical and have th)lxao5x vcsco v );)z3e same mass. However, one is hollow and the other is )xao);vzl)c c5o3 xv ssolid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a hortwrv:coi5 x:pb. oe 8et4-3t2 v e6kdnizontal 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, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasicwnot3 tkbx62:o: ve-reit.dpe58 4vng?

Suppose you are standing on the edge of a large freely rotating turntably85lsb py2 w6up(nmw;mi+4( t* mcfxwe. What happens if y;86wymn(42xm(cbfsil+ *pum 5p y wwtou walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quicklxk 9*kvhv e;a0*)o-j3iz p+cz4 q ojwhy. As he throws the ball, +;ao w) ev o9z*4 p*xqjckhjvh3i-k 0zthe 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). Explain.

On the basis of the law of *z7t3dhtp-axe +3o kf conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one o-* et7 p+zk d33foahtxr more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 30a,9f 4eh/ce,jt1udti $^{\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 Ear+ e-qv slj7f8z5;nxeyth because of an amazing coincidence. Calculate, using the information inside the Front Cover, the7f-e +e5 s8l;nvqx zyj 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 km fromv*fr 2h lxp:6hgw 8npi.;u3tw Earth. The beam diverges at8 nh wuwpxi6:3 .tlfh v2r*;pg 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 rota+aloqjo7jvz l6 1i+/ate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest o6 oa7i j/lv+l1zqja+in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor ;.jgvx n;ve 03tj (mkm3.5 m to another child. If the ball makes 15.0 revolutionvmv j;mk3x.; enj0gt( s, what is its diameter?    m

  A bicycle with tires 68 cm in qony4by5x loq60w 3g :diameter travels 8.0 km. How many revolutions do th0lx3:gowobyq 654y qne wheels make?    $rev$

  (a) A grinding wheel tz9 (s tfs3i9iy(+g * zbf,com0.35 m in diameter rotates at 2500 rpm. Calculate its angular velocityym bt9(g zztf( f*oi,3s+csi 9 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 comple64dh fcyv7 l-yte revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the centec6yyv4l-7 d hfr?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of thenz7lqr j/ jz9dy )m99h Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spe gmgs 7 m3se.7w8g-nuicnmkw 6, 9xa*led 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 amqtclhmy.wbl 5 k2:z ei 32j/3 particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,lc5 /.bkwym2 qz l:imj3eht32000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center nk4; c87y,cw1zmv,qo/zl prk from 130 rpm to 280 rpm in 4.0 s.,c;q7yzwkl,ocvz 1 /knmp 48r 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 .g7+qmj/omqa $R_1$ 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 A+ho andl( r,6rehyv65pollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameth,n e hvy 6rdr5+o6(laer 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 8 fi 1wo;fmmga3am((hrest to 15,000 rpm in 220 s. Through how m mmfh1gm a(;( 3wio8faany revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpamsdg.)+cb8 cdoq i;.r*g:1 afmjsq + m to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses oflh55 1vi.aa pj(n58:m xaoq -(z tbptc flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions befa1jp p-m .iqt( 8(lvazobx 5ht5nac :5ore reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6 qomuflna09tv544q3q2ma3 bk( rfm e+.5 s. How far will a point on the edu+0qafae4tm 3 rvn5f k49m lb2om3qq( ge of the wheel have traveled in this time?    m

  A cooling fan is turned oftofbl/+u 08v; t+dkbjk9z1ipf when it is running at 850rev/min It turns 1500 revolutions befkp f ubt+o8v+ ikjb;zl901t/d ore 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 m.rt exxtei/l 0w* 7k5hake 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h Thee/ie7 h5 ttwlrkxx *.0 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 sb:b 9 5ukv;jnv/)u0bwjrp ttyxv 0+ a5peed uniformly from 95km/h to 45km/vuvrb9aj;tj5: y )+knwu5 b /v00txpbh 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 cli4e rzftq//m/i,+ ctzumbing a hill. The pedals rotate in a cir fi/mzu/z ,+ e/tqr4tccle 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 zo,.l:4x7 z ;rntaranthe end of a door 74 cm wide. What is the magnitu to;a7ln ,:nzx.r zra4de 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 b3brc:-rz-m a:.d mn7*y :. jorknmroFig. 8–39. Assume that a friction torque of 0:n r zc*n7bo.-3.o:rak: mrdm-jr mby.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 nglc.9yr 5z9 cwhich pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal p 9cg5zr.n9 cylosition and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to aor) wgg/y 48s txv+t,n torque of 388w/n+ggo xs4rv ty),t $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m wh;xlm)how/xgc dus;3 /en the axis of rotation is throulh;;cs3x /dm/u)x w gogh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle5)nutb ;(v 0fyom d*ag wheel 66.7 cm in diameter. The rim and tire have a comg;0)bdyf m*(v5outn a bined 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 avtp h/x aame o307.j-thin, light rod is rotated in a horizontal cirajx03a/m o7hpavt. e-cle 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 rotating at constant afj4(wy9z9 v +ueyn6owngular speed (Fig. 8–42). The friction force between her hands and w yejzu9nyo(+vf94 w6the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown 6 04ptp/m-kkm9g;c irus pf4 iin Fig. 8–43904t/i6f-u i rkpcmkpsm;g 4p about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total mas5 zz1lgj* t; v9hfrv3qs 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 a5h8zv3 *bj/bqn k;xfm-+ c /e eq,rgqqt 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 of 4.0 m, what is the required steady force of each rocket if the satelliteqx8mj*3 e;qv,+en-q/h r/bcqgzbkf5 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 masd-ht 2 o3ox9ia vi/:uxc*jggajz+, m;s of 0.580 kg. Calcula9+v 3xh/g uaj;m*tod2i,:zc xoj-i agte
(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 b wygxo+qpns*fl 5bs)1p57 bdc.:zabu n* -s)pat, 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-driven merry-go-round andsfunw1dfh):7+d3ensw76 he, ui(jx b is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform de hh fnjx6( nw b13d+deu)ui,77wfs:sisk 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 rotatir x7,fd5hq *qax lq/:ing at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torqueldix, 5:qxqhr*q/a 7f 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 accy/glw7.jtx eza3lbyo0g* ./alm1z x 3 elerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solt0h(ldb mj iz+iq.y a 64;0wmaely by the action of the forearm, which rotates about the m6l4+;d(a .izbmw ty0jh 0a iqelbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade du b,xtqgl;8 ldh: 8+pcan be considered a long thin rod, as shown in Fig. 8–46. ;x ltdg h+:8,pq ul8db
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two masses,r3) xl 4ppp/.acz:ney $m_1$ 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 full ts1 2sug9 t*uhmurns (revolutions) and releases it at a speed ofum9gss t1h2*u 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 o c-yl4 aqr22nm9o8ijcf $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torqu,nv*54m go.(,cyu fd4 sirx rpe 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 kont7+ 4zyio+.go.ah6gy9gz ik(qgt1 g and radius 9.0 cm rolls without slipping down a lane atgz+.9iyh q( o.6ogznkat17 t g+ o4giy 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energ+k) rncktgz2- b7 pi5oy of the Earth with respect to the Sun as the sum of two po7g+rt-k) 2ck5nbiz terms,
(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 164/,jc6zdgzwo1l : lr(8 s* qqcr0 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Ass6ll*qw/d,qc1rz : jc s zrog(8ume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts fry pp w6;f602m pp2xzdtom rest and rolls without slipping down a 30xp6mpwt2zpyd p f 2;60.0 $^{\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 sa ux dj0fj,;;jtarts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conserjdu0;j, jfx a;vation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on theu 1aqn4:beq und7e*9c, 4jco m7r9e zi4qix6l end of a thin string in a circlodn4*69zilmcqx q bje4 a 1 ie u4q:nu79r7,cee of radius 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-k*b2pyrl gb5 .ig uniform cylindrical grinding wheel ofr lp2i*.5bygb radius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform thatd-w/xg)z;xx2zwcs; da h p*. s is rotating at a rate of 1.3rev/s If he raiswpxw*g;s.s2h za )zd;cx -/xdes his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as theb8/y1ff o6u2rzp2bh5h hdno7 one shown 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 makey/fdhphnz62ub 1f5 8b2 rhoo7s 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 spin rotation ratec:3pbb+e,,ny;; g*bgladr1 dk kjk2 a from an initial rate of 1.0 rev ean2da * rebb: 1+gd3;j,l cgbky;kpk,very 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 freq2,*yj cu)vy mduency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and dd jvuy 2)c*y,miameter 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 wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3 r qc8k-ip;*nq.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 angula3tvl0hbn,0q nr momentum 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 momen5pzalwztmjxu xt+-8(5o2 f 1st of inertia I is dropped onto an identical disk rotating at angular speez(j s25zx5t8+fmwp oxt lu1-ad $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at :ji(b9s 3ggqkr +ig.j 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 u85aa: ufouam6. ka8yof a rotating merry-go-round platform 8f.oa: auu5yk8a6u ma of radius 3.0 m and moment 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 freely with an angular velocityf)avu/u2serix 6op vl3ybw;gu2: ( z/ of 0.8) /rxp2wu(z l2usfbv:io /a6 v ug;e3y $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about h4tgez*u. -ubhebpya 89 n+4 uqalf its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuminte+y4 ab.ebg9uuq- u8nh z*p 4g the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 1p nslk5 og+2.j20 $km/h$ 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 + ty3g5rs nw2d$ 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, initialfrd5j5 nz.yhf4m ;,v ely at rest, that can rotate freely without friction. The moment of inertia of the person pny 5 z ef4frd,h5j.;mvlus 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 thsdltt 7 riwe+ 75s4s4d4+vbtbe edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless beaitb7v4bst wsedl4 dt 5++7 sr4rings 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 roll fvvbv ojc-0d * wr4tgy.z7/;gs on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a dista/7gf dw*c 4t vjyb.zvvr-;o0gnce L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such tha.w nb1/c 8gomst the same side always 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, treat the Moon as a particle orbitco .8 1/bwsmnging the Earth.)    $\times10^{ -6}$

  A cyclist accelerates a+,fq-cze*y w from rest 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 8zu+uz)r mr69u4ik hjaual:0 in 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 torq zru86 jrz4haa 0u lu)muk9+i:ue delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, eac 3ov;45dc,nf y6 wluq g)7ukuwh of mass 0.050 kg and diametg5)6ucvlk37n;w qdy u wuf4o,er 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.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rearm.3u f6sjlf 6j wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mag/ut/3 ts87 lx ioo/u2 -sfmpkss 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo grav fmo 7t3s8-/2sulkt ugop/ x/iitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a lowxh4*ge. vech )-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car hac.e) xe*4hg vhs a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrateswf2swf/q.6,d/rbc khmq8x 9u an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal suro,mlcz psti0o9nrw ; *b44 n(i1bgvls 803h fvface 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 Lqy*egw5(x w6e can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (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 centeq (wyx5 w*eg6er of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the flo7 ke6sh72ag cfj5j::dgv k7e gil;4fsor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, k; 5:2cg gfj gf7k:6vi477alsedjhse where h

  A bicyclist traveling with speed v=4.2m/s on a flat roa 3v8st0qmw,l wd is making a turn with a radius The forces acting on the cyclist and cywms,vl308wqt cle 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 pt o;moq h.e306 c2+qpimax+ xof length 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 ach2 36 cq+oipq0p+t ae hmx.mo;xieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin r(rp7 bg+2 bb8nb31 * lyb 4amdygitp1rods, making reasonable estimates for the dimensions. Then calculate the r71i*+ gybp 3b2arltmnrdg18 ypb( bb4atio 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 cy4+qj:ll.sdwqv0 z3eu2 0yiev lindrical plates, of m03s jq0 uq:livdy zl4ve.we2+ ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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. 8–,ex-e9 nmwb ius,.o,g 58. What is the minimum value of the vertic,,emsuwgxnib ,oe. 9 -al 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 not aszi ua2ottej .l6pe8( 3sume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformljfb6nn5xgtrq:,nn8 6j wg y6yz (.ao/y from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What wf, yq jntbjngx6zy 6o6gnw 5:a/ (nr.8as 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