A bicycle odometer (which measures distance traveled) is attached +o4-o+dab, e3gqjig o near the wheel hub and is designed for 27-inch w3ig geqod+4+b -ojo,aheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular3k53 rf +snu x0kzug7h velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s auk0kzxs+n 35guf3 7 hrngular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular velo9c9sv1cqyki5 city $\omega$ Explain.

Can a small force ever exert a greater torque than a larger fo1*;fjbx4zk2rdw1k 0:zcrk mt3z fmw ;rce? Explain.

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

Why is it more difficult to do a sit-up with your heg124 zl2 ajxzfr7dtmht8 r91ands behind your head than when your arms arhj872x 1rmedt9fg 2 rtzza1l 4e stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle ha,;oz7 jxce2so s seven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprock x, ose2c;oj7zet? 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 hp +2sufat02v * m9irhoave 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 a*+9m af2rhvio20ustp dvantageous.

Why do tightrope walkers :rsmr*jbq 4+r 5m8nvf (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the nejvub+6,-igx ygr 0zy )0fr5e lt torque also zero? If the net torque on a sysi+jf6rge -0by) xy,rz gu05lv tem is zero, is the net force zero?

Two inclines have the same height but make 49 th;hdrog5-5fip gydifferent angles with the horizontal. The same steel ball is rolled down eachhrp fhdt5iy9o-5 4gg; incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rollinb;uq/*u2 t acp*srop) g (from rest) down an incline. One sphere has twice the radius and twice the mass of the ot rpuupo*)s t;b2ac*q/ her. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the+wr 6aid 6nd80ne- qk4r(zicu 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 greater total kinetic energy at the bottom? Which has thekq8idinr0n w6 e-cu6r d4a+( z greater rotational KE?

We claim that momentum and angular mk2bj xv+tr m5:omentum are conserved. Yet most moving or rotating objects eventually slow downvxj2:5 mb+tk r and stop. Explain.

If there were a great migration of people toward the Ehd f/6gc2gbi3uwah,i2g1 by 8arth’s equator, how would this affect the len gh /i,y82afiw6bg321b gcu dhgth of the day?

Can the diver of Fig. 8–29 dw2c 9nao6us2c/k l- cjo a somersault without having any initial rotation when she leaves the b9/ u2o clcsjk2wn a6c-oard?

The moment of inertia of a rotating solid disk about an axis through its cent jkswz8 ox0nks9,2(rx er of w98(0z2rxoxjkn , s skmass 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.r +8chjk:fdx;,tlijo tb cc )b 817bb a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Expla+8;bh.cf j,kldjtixtbcb7c r )b:8 o1 in.

Two spheres look identical and 44t o3nbal7xz4pfvtz* 3 z k fkq5zu+*have the same mass. However, one is hollow and th3zkz+47* bz*o tvptfqak l35n u4xz4 fe other is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotatin jtdq)g,p+ lw;)ckm5 tg on a 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 linej;c ,lmk5tdq+ pwt)g) ar acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely ,8 9l.n: uzy(s dwbjyzrotating turntable. What happenzdw89(snu,z y:y. blj s if you walk toward the center?

A shortstop may leap into the air to catch a)xkp2ir: k;k h 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:phi r k;x2k)k legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular moments)y3yy )ef 0t(,i.iwm hrl 7-m yr9kayum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stablemyyi9 w-f k l0ht(y)m)ysea.r7yr,i3.

  Express the following angles in radia pfd8))r;t :kk l.m sn*x/kmfwlyv-+ ins: (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 Eab6 fu+ asdhk2)oef5g-o3k vxh 55 uql0rth because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) o )suhlqkhooa 55ux 5fde20 fkg+b 6v-3f the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges 31lxaw2y.:ys p mm7ii(mg d:xat alm(.3 paxy2 1m: 7is:g yidwxmn 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 blende v5in,sq*g6b4ouv4por rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is to 4 i4*6up5 ,qsvngobvhe angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ba7u ui2ltw25ie 3a( dhall makes 15.0 revolution5a iu7 al(thd2weu i23s, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolut-j/l k9sydc6ff 1z cs.ions do the wheels maz9s csk/f 6cy.lj1df-ke?    $rev$

  (a) A grinding wheel 0.35 m in diameter re6u 9f s.fo9 :opsjd3potates at 2500 rpm. Calculate its angulad.6fsspo 9u:p9oe fj3r velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 8–3 idj, .h:)p tpdtf)xa78). (a) What is the linear speed of a child seated 1.2jp.),7tthfiadpd:) x 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 *x2u1ul/irr rayr,8j u6( 8f jodv(drEarth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spee7z9c() wicpzvx,uh/z vo0wl6 d 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 particlhb3lb ( g0q1k/l s,yip0 es;nbe 7.0 cm from the axis of 0bi0/le;pbhg1s( k synl ,b3qrotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly aboutciz ef/.*rhs - its center from 130 rpm to 280 rezc*r.-s if/hpm 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 radiu(kqo0(dupqoa q6*8nvui )4g cs $R_1$ 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 Ak4v.qcew g7v) pollo 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 tho v)vw.cek7q4gught 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 frombpz1wo./ b jrlk e28y.1xw*m p rest to 15,000 rpm in 220 s. Through how many revolutions o*8zlwpje 1mk..bbx wy 2pr/1did it turn in this time?    $rev$

  An automobile engine4 jznr83 bsj* ms i7m-ex7v5th slows down from 4500 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 sd5imzry e2sh 2;m0o/atresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 mi ;0oerm2za2 sid/yhm5n 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 accelerates uns7mi pprjfc5 5k(b,kyx4k z(1iformly from 240 rpm to 360 rpm in 6.5 s. 5kbj 1,m(fkp(4rxpc7z k5siy How far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev4, kq*e8n6reo6hp s(r kkj fi7/min It turns 1500 revolutions before it comes to a stopp6 6skj7( kn*ek4q fhre8,io r.
(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 ma8x k)rhy1qw,zsnus /w- y9h:bke 65 revolutions as the car reduces its speed uniformly from 95km/h zrks wwh/yn, s)x :u91h-8byq 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

  The tires of a car make 65 revolutions as the car reduces , (x 7v9hlfxcse bc:g;its speed uniformly frgxf:v9c;exh s,7lc (bom 95km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbing a hrt c+zw,a 4rfh4ct7m3il,c4a+7 hwtmrf zt4r3c l. The pedals 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 df,k38rfx3ep*rvz( y loor 74 cm wide. What is the magnitude of the torque ifx8 f(fvz,3 l*rkr p3ey 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. 8–39. Asuun05b ml1f4usume that a friction torque bu450lnufm u 1of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attac qa*m-xz.k hynr9gc .dz 2vc71hed to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal pos1-2m cgq.*7z kcnv xdz.hr 9yaition and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of x6xp zy.. +nv3mudn+gan engine require tightening to a torque of 38unz p3x.m+y.d +g xv6n $m \cdot N$ 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 radiue3ylnlt6t mdf r,u6s2wb2 2*us 0.648 m when the axis of r,bllte tu 3d2mruyf 2w *66ns2otation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. Thfqgw/d3 :)q2*l lxl5syn/gyyg,v d3e e rim and tire have a combined mass of 1.25 kg. The mass33 xw/yl :vgfsggy*d )q5qlle2n ,/d y of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, lighxz u,r*(ac7q; m jfv)vt rod is rotated in a horizontal circle of radius 1.2 mau v*q vz,fj(r;x) 7cm. 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 bo; im6+1s b:bdhi,su mlwl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force bhsbb m,m1ul:+; 6di isetween her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objeco2gb4 .8tr cgaxck e91ts shown in Fig. 8–43 aa. cktgb94oe8 12gcrxbout
(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 consist c 6 kznw0 k*i,tuis83ucjx0-cp2 xk3is of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical sa5p6ra ss);fp g6er if:tellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 360f6fi):r5g s6sa; p rpe0 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is 6z y 6rjj,nt3xa uniform cylinder with a radius of 8.50 cm and a mass of 0.580 ,6j36y nt jzxrkg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it froby7(l ejh fs+vt.y1foc-(mr1 ivoi *+m 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 oaei00)vd -flvn a small hand-driven merry-go-round 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)0vd ve0-ilaf 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 rpmx yx wi1//6s e*mhy0ubgb8 ;ac;qs/befzd 44e is shut off and is eventually brought uniformly to rest by a frictionae/y0 xa//yu zb cbq4s4 feb x;ie*6w g1;s8mhdl 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 0w tug hxh-g3:,twz1zmf7ef/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 solely by the action of 5id.auyou8n w g21dx2the forearm, which rotates about the elbow joint under the action of the triceps muscly81n da.dxgui w 5u22oe, 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 considere +0gi :)1211 z fcfozokxjmt/g1tziuhd a long thin rod, as shown in Fig. 8–4zo+k t1ut1c)f:ih zfo2i1/j01mzgxg 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 consists of two massesaemiou oj s:+e/:gc5f ya: 01p, $m_1$ 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 accelerat3 ;tsy/ol 2ogv :yh( 8fysff3les the hammer from rest within four full turns (revolutions) and releases it at a speedfl yl/s; o 32gy8syhfv(fto:3 of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia ofx3x3hw cpl*8e $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 2l4l8i7:rs xh d80 $m \cdot N$ 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 rolv- oc2 / spl pbu1+pbsyx/m9g0ls without slipping down a lane axb/1c9bp-/o myulv0+ sps2 pgt 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the E y3fafes (le/-arth with respect to the Sun as the sum of two ee/-(f laf3ysterms,
(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 net woc ev)lonsm0,/ rk is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cyliscm ev0/), nlonder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls without gtgclj/4z8+3s*ulv m sliplgczu3sl*jm+8/ 4tv gping 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 vertically on its tip. It starts to fall and 6nmqd8djlim(ji.: paz5 w. 7u its lower end does not slip. What will be the speed of the upper end of the pole just before it hzmi:d .7a u5wjn.6q ild(p8mjits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rnb6x2i:n4 ff 3j nq,gpotating on the end of a thin string in a circle of radius 1.10 m at an angular speed o,2n 3g bn4:i6x fqfnjpf 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular mj unl/kzg mos*6:p z ej7o-o00omentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating an-m*okglo670zp /:u ojej sz0t 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 platfo(5h eopgr fsg.q2 2(/cpo. xeorm that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the spfrsog.5 op2(oche.2g e (p/xqeed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can redb sduh+4:fly)c ky47o uce her moment of inertia by a factor4ykc)u:flhb+7oyds 4 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 increase her spin r3).fb x2**w ,dnquzo( xuozptotation rate from an initial rate of 1.0 rev every 2.0 s to a final rat zbw.xu3*(,)*xzd fu2qon p ote 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 axisu* iijlpf. 6n2,ot(vs through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg itfl*jp vnu2oi 6,.s (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 a figure skate,+ 5d0tbva*kztqk l0u9 wv5umr 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 t1-ks4t 5c hz +kd8j xd(fky4fli/uj7 bhe 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 m)vfv4i..l8duu5vqt; cii7 w eoment of inertia I is dropped onto an identical disk rotatv wvqd.)t8 ; 7veiif 5uliu.c4ing at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2wnxstwy / e;i-c0 .0ma.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 merry-gokg b k21k,e3q8pp pn7o-round platform of radiuskg,p pk q178 ben3kop2 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 freeobcra;56r t0fly with an angular velocity of 06 5a;rtob0rcf .8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a w-.26ot9d7b /iqhaug1 xr wmlshite 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 the1d2mih r xl6 sqwgto .bu7-a9/ 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 windq9t2 9c5j x+o+ata / bk5qpdwqs 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 p h/rpbd7.)ef$ 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 a;9*b avnd6y ubt rest, that can rotate freely without friction. The moment of inertia o9b6yan; *bu dvf 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 athx2/f8eh w0 y4xdlf3jemc +m 5 the edge of a 6.5-m diameter merry-go-round turntable that is mounted on f3j+m whf c2d/h8 xyl5efx4me0rictionless 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 rope lying on t6 8:dj5y oyiwphe top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope di86y:pj5yw ounwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that th/c3hr(f e+i ;pzz(,zs yqui y/e same side always faces the Earth. Determine the ratio of the Moon’s spin /( zsz3p+ qi(/ yuyircfze,h; angular momentum (about its 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 ofdu7 )eey,qf7 m 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0e *m7ebdik;sl15cvnnh( v 2) h.20 m acquires a ro*72 ()1bhkev5h ;iemcvnsdn l tational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 k7b;j *o3ut pnyg and di* py3bju; ont7ameter 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 spej or. 34h9ridrudg -4bed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as .ecsdyumx* n49f q1*z2-hsa9o 1 szfkhz 0f y6great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost my6xfsk0-c4 *m9.oz *fs sy2f e za dhhqu11nz9ass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-polluz,niq:/ yxe2f,boc a 1tion automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a unif o:c/fyn2 bq1xi,ae,zorm 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 illustratesuht9jnuader 3e;35u0 gv; qp8 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 surface at speeoaumk9r (zl*ur/ - i;ad 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 an59l;dlv2+gxw ukg cv9s7rcu 9d length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 85xwv97 +gdl vcs9ku2 l ur9;gc–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 rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on3nmgu 3g qk rmz :;4mss/i1dm0 the floor, and we want to exert a horizontal force F at its axle so that it wmr 4sugznm d;0k1iq/3 mg3:msill climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is makingcii 5(b/lijp0 ,q,ijl a turn with a radius The forces acting on the cyclist and cycle are the normal forccbi pjjl0,q/ l (ii5,ie $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begins sr9(-wk h+iityy*.sp whirling the rock in a nearly horizontal circle above his head, accelerating it +* yr.w ts-9i(pyihskfrom rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body a id,nie (tv )gump2o7.s a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the raid). i2g (ovup,ne7tm tio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assemblycs bytjkri.jxf)-je 31 e t3nu: 4/9lz which consists of two cylindrical plates, of m4ln t jkt.jb:s)fej zc/y3-9rixeu13ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 try:n*n d+jfzl ww*s -y6ack of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop with +d*6lsyfw-j:n*nw z yout leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do neft8xxd99 0 ptot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly fr 03uua rf.hc-yom 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the anguac3fru.h y0- ular 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