A bicycle odometer (which moxf 3va5g*:*yr ami k-easures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What hapx *:argkma5y i-f3v*o pens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotatekk4j)om 7j8,bpj5ozutm grr8* w4tt3s 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 casto4jj zpo58* gr,ru 3jk)4twtm m7kb8es would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the ang0g 5) c l9r,jxpkxv-h)gk 7z4 fp(47ygiomuawular velocity $\omega$ Explain.

Can a small force ever exert a greate c iwq dk443f)f5+fvwvr 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 x.cq(1 wc4h0l 9gs hgcto do a sit-up with your hands behind your head than when your arms are stretched out in front of y hw01cl (4c9qg.cxgs hou? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel anz.rrjiix f)y971 8 axfd 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 if)jifx r179r. 8zaxiys it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run f3shg 4i-+w;yd jqav: mast 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 massgs; m-w4h:a yj+ iq3dv is advantageous.

Why do tightrope wal 8ibme.9a 0 -sl-mtgrdkers (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zerrxs8r 02ayvv4m*x0-mgc+tqf o, is the net torque also zero? If the net torque on a system is zero, is the net gvmxc xq8 s2t4afr -* y0rvm0+force zero?

Two inclines have the same height but make difx8eu*c j/4d hv kwjs c0czw-/+ferent angles with the horizontal. The same steel ball is rolled hwue c4jc+ z8*d/j 0v-/sxwkcdown each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an2gef((je ezg v 1 *mmp2idb.e38vqwo- 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 *ee2e g vdwvoef1(3qib.g2z -j8 m(pmgreater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same onwao9g56/iwpks vss8)t 2n+radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the gr)wsa 9o+s5s p og2wtk/n68nv ieater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular mo*ml9fkzdv-:*og ng e;mentum are conserved. Yet most moving or rotating objects e z *9;kgvlegf:m*o-nd ventually slow down and stop. Explain.

If there were a great migration of people toward nq-j8 y2o6/egrt 2zzlthe Earth’s equator, how would this affect the length oz- /jl6g nye2qz82ro tf the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rota;n , d(yu +mjfv5,rn5mbvwcl,tion when she leaves th(vdly;,n5,bw f ,v nj u+rmmc5e board?

The moment of inertia of a rotating solid disk aboutc 4f*wme).n hl7x,zoj an axis through its center of mas )m *4.exnw 7olhzfcj,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 rotating stool holding a 2-kg mass in each outsw :l d:3o mstki+ec6l)tretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the +6l wkeo i)::tcs3 dmlsame? Explain.

Two spheres look identical and have the sam 06v+ -xrx,amy p*-fo0lboma pe mass. However, one is hollow and the other is solid. yma- m0a0 pvx,lpfb6o+xo * -rDescribe an experiment to determine which is which.

The angular velocity of a wheel rotating on al8 7 f8ew.qcio ja7zvajx p(r-4, yv(b horizontal 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 thlp 74 ,fqr-oa7y ecjbwax.( 88 jz(vvie top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely 46vv( m enqmb5rotating turntable. What happens if you walk toward the mmenv 56b qv(4center?

A shortstop may leap into t* as3f( /fxbeex; zp.pf8 3benhe air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). E *e83faf( x n3b/;zfs.p bepexxplain.

On the basis of the law of conservation of angulauy m;xcypng 5ng1q (+a/ch6/tr momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can ope p1t6cg; (anynh mx+g/ cuqy5/rate to keep the helicopter stable.

  Express the following angles in ra - /mij*j/,swhlx ct/y-v1pzbdians: (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 becauseqs+rp00e 8 w*ns j.lmj of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) omwjp+. * 8ssnlj0req0f the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,00v;:,qs;5hgqtd2 jwk x0 km from Earth. The beam diverges at anh kjxv2:q ;5ws t,dqg; angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the moto3hq/66qc tc:si5ld, werk q k.r is turned off during operation, the blades slow to rest in 3,s .:klw5riqcdhq 6kqc/e6 t3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another cmy8 8rvjnfu xx /p76-dhild. If the ball makes 15.0 revofjd x8-67u/mn xvr 8pylutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolution+gr7jwl) z o+ys do the whee7)jy zr+o l+wgls make?    $rev$

  (a) A grinding wheel 0.35 eui(qv7icln 5:lh -2s m in diameter rotates at 2500 rpm. Calculate its angular velociei- inl h(72uq c:s5vlty 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 revolutior 8f 41ua96cr3ordgjh yriu8)y.; pvyn in 4.0 s (Fig. 8–38). (a) What is the linear speed of a chiu.h ) 4r3r198f8 vj gd;au6rcpiryy yold 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 yri4. tkb 4h9dits orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear srpyy qy+b6, r8peed of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle xkzxc, y7s )vzjo6ll c/e *56l7.0 cm from the axis of rotation is to experience an accelerz7llk *yc cvxe lsx5jo6),6z/ ation of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm6qs;a*lbx.kjm ;hyzm9u r q, 1 to 280 rpm in 4.0 s. Del 9m,m.khyu;1j *qr bxzq6s ;atermine
(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 radiu,cb/sqt4b.n ho 5+br os $R_1$ 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 aboar. irvbjny/47ln4 w,mk7py:gf d the Apollo 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 b/7m. :g4 7nfwjvri,nlyyk b4p e 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 rest0flnsii 8(1m q to 15,000 rpm in 220 s. Through how nf 8isil(10mqmany revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 450vr 5,uhfs6latrf; s42 0 rpm 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 of flying highspj 5+.e uj3-ipm)gzcq cub g40wqov.p( eed jets in a whirling “human centrifuge,” which takes 1.0 min to turn throug.g+zm-b)ipue copc5(u. qv wj g0q j43h 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;f6 l/eitm s(h accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a poinhl/fes; (ti6 mt on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned0: va;a2bo+nqfa-y mhjx- 3k +axhf3q off when it is running at 850rev/min It turns 1500 revoluti- yx+h;3haq q-+vxbn2aa3o j0 mafkf :ons 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 reduces its speed unkn *pzc64)z9k fuv(y liformly from 95km/h to 45km/h The tires havz( zk knu4vfy6)*l 9pce 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 speed uniformlbz/l3 p36dsxfb4 )qru6o4c no y from 9bx/u3 d6rnfo )4bl o3 zs4q6pc5km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weig9i4r mvm, f tyj/vh)9uht on each pedal when climbing a hill. The pedals 99mu /rmtyvh),4ijfv rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. wm t6hggdz9r :sqvs7c/(et,+ What is the magnitude of the torque if the force r( mvct e,q9 hg+gw /6s7d:sztis 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 whee lceth( m7j9i6l shown in Fig. 8–39. Assume that a friction tor e69c imjh(7tlque 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 massl9lj,c/ep37)w eb7rorz wc dw; ess rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and7bjw7d ec,zw9 ow/lper3;)rc 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 a torqued.gt8m2- fmj:c; rura of 38 .m8t2jacr:;r g -d ufm$m \cdot N$ 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 3 957nq ttv3xokb jyz*0.648 m when the axis of rotation 35* jttb 3oyqkzvnx79is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of af(ybi6g5f s 8q3iu e92. bjmde bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass o (j9ys b65 g8ebiiqfem.d23 uff 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on 0o*rbclmj0x 6the end of a thin, light rod is rotated in a horizontal circle of radius 1.b6o0rcm xj* 0l2 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 pot:arqrcz t f. f/uv2vug-d2e;.ter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1t2qg: euvf.r;fd -c.u /zavr2.5 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 inertix vnu t. 9fe0og39q 8w3soh8mna of the array of point objects shown in Fig. 8–43 m q3wnf h90v 8o. 8gus3xet9onabout
(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 *phvd, ywyb+8 mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellitej7rk0r+,-9k iivw t kh 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 of 4.0 m, what is the required steady force of each rocket if the satellite i+ rki w-kv7j0hr,i9 tks to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder wcg ;ydts 6v ol97/ 5ie7wt:pvrith a radius of 8.50 cm and a mass of 0.585/etg7 v:l9o yc7 dw 6tvpsri;0 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, t y n7uya7*c6vk-nd-qaccelerating 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 l64oirm o(cwe/0h: ru7:uxvx and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate th ui07vxu:ohe womxcr/4lr:6(e 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 i2 r5edr6 a martzf.+j7s shut off and is eventually brought uniformly to rest by a frictional tt .jdfr2rer7 6za5+maorque 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 acbg z f ;,shawx4 i(388o8iwvfmcelerates 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 +c*z :zozc)kc*ode*xsolely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle:dzkcco*x o ce* )+z*z, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, aiqbfg ly aj,t8-p,5k; s shown in Fig. 8–4,g,f i-jpkqbtl8;5ya 6.
(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 cons9mevp 6jfa/h0 ucq7*iists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer (dsylt c5l x1yu- t c5d)pee84 from rest within four full turns (revolutions)ycdtl t85(leed 5-)p yxu1 sc4 and releases 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)loq; dyrxb,5 na *-bbt(zm*k f*qz(e a moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops:qasan5*+ tzodqg9f. 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 and radius 9.0 cm rolls wul t xln*7sg55ithout slipping down a lane at 3.ull5s xn5t*7 g3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as tht,pe6cbc z i1wn d7j9,/ua*yre sum of two termsytdc,1 w/nia9jp*b 6urc7ze, ,
(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 iwwmnu n(u+xzg0+ /twnb3 7(xkg 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? Assumw (z3u/+7(iwg nn0 xmx+utbnw e it is a solid cylinder.    J

  A sphere of radius 20.0 cmxk-durt2y 9y/ and mass 1.80 kg starts from rest and rolls without slik y-/ur92y tdxpping 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 verticallirkkl -ue.,wl o1x7qzub 1,)fy on its tip. It starts to fall and its lower end does not slip. What will be the -1 1qzo7r,uu) .ek,lkxlfbiwspeed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 2fax c +hki7/vh.;hq 1fy+qiv 0.210-kg ball rotating on the end of a thin string in a circle of radiu+/fyv.va ic1 hi+2 h qh7qfk;xs 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform 0a(i+w j r,)k.thpogpcylindrical grinding wheel of radius 18 cm when o ( a.pk)rth+ig p,j0wrotating 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 at7d a0grpldt0m g3quf hg8;58p his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.80up70hg 53ar dfmlpgt8q ;8dg $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can re)te,;rzv ;h/u9k s cydd7d g0anwzr29 duce her moment of inertia by a f9n r7)d,w; ksu0dzeazc yt ;g 2d9/rvhactor 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 her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increasi r4lre:j2 l(oe her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rr:lei2lo(4r j ate 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 ft k4v. a52ibrorequency of 1.5rev/s The whe54a .2iovk rbtel 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 wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of ax1zcw:7en- twz1;nv5 x 7 q 5g:zjhytf figure skater 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*diy2uin82n flsmetfjy 4/r v (n26. k 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 moment of inertia I is gh9rbiu33 my( dropped onto an identical disk rotatiy 33( i9rhbugmng at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ath63tanq4 .w)fka y 0lc 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 mt0q;e6z077 cxek axb(pd 7prgerry-go-round platform of radius 3.0 m7qp0(arz;pedetb kx 0 7c6x7g 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 k uro9uk u pa y:gb3*6)7az6icfreely with an angular velocity of 0.8 b7ur p azu3y goa*:6uk)9 ci6k$rad/s$ 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 dwarf9s +;fgmdg ,ed, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radi fg;sd+9, dgemus. Assuming 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 wtd )p7 2nincs:lk- b,xxv)gi; inds 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 -3s 5ylau mq+l$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate;.qivx./ z8kr31sb(x f wxucpn 5rga4 freely without fric3izrrcgp1/5su fw.8b k4na(.;qxxvxtion. 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 diamet9wbe/vbp wat)ayhk3: 25m;gzer merry-go-round turntable that is mouz;avt 235we bpya wh)/9mgb:k nted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the ropl8sn0ueq5zec+ / b+s fe lying on the top edge of the spool. A person grabs the end of the rope and walks a dista/5n lbue ssq+cf+0z e8nce 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 sss k*6bxx.( rim*4o yguch that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its y*kog*r .4 6bms(ixsx own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 mz9clpoqwk1/*i ;vw 5:rr rqa9/$s^2$ 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 raddi8c w:8mn x(p0u wm;gius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at cons8c;uxm(w w80gim:n pdtant 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 and d gnvl8wvny0 bg:-n.m4iameter 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 nvv4g0b:wnng. -m8l ylinear 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 angula +tmod1 +y9wxpr 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 u g z/rajq(anw*am/5e - 8mc7lSun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its m( /a85rmqm l-/agn7wu aze c*jass 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 for it to ustg:qxqz:quw, :u f p40a4ln.se energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needin gq4x sqf::puuw :t0a4 l,.qnzg 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 5g;2 dmyhx4ytkb xn)m/* bqmq7x n7m.$H_2O$ 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 surfctrgd jc2t/6crz2 0a 7kwl r -.: 00ffbgq5ufcace 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 ignordgiud96utauwbj,0.b r/pz-s + )gd4a e 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 thezasauu td)d/ 04,uipgjr9 +gb-6bw. d tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R w34xwx.4tv e0:vosgexfx5a8. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will clfx x4w83:s4xxawg e0.ve vto 5imb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=hhhi 0b s7;mz.kw.3hr 4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal force . h7m;0si h.zw h3rbhk$\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 int b67t-tn mgd tycxy579o a sling of 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. tg6t 79myc5xbt7nyd-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 body as vd)lx 5)6rjkh il pfnqis d-02hi1j67a solid cylinder and her arms as thin rods, making reasonable esti dn20jvh kp7 xl)iqh-r5 d616)flijis mates for the dimensions. 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 czt3k/zq;+hy j lutch assembly which consists of two cylindrical plates, of mz ; 3+tkzqyjh/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. s2)xdchuo6 9y8–58. What is the minimum value of the verticaox )6u 2cs9hdyl 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 assutnc6 r66oso2b88 ifyrme $r\ll R$ h =    (R-r)

  The tires of a car mae *8hy/1d-jph h ed c-pizo;*xke 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) W1e;jc- hop-dh/ex*d*y ziph8hat 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