A bicycle odometer (which kh89t skbc+fi+pw95 omeasures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens i+8+ 9kcf9ibk otw 5shpf you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angu1vkwi(qh g j)g,g pt57lar 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 tangentialgj5i(wkq71 pt,) g vhg 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 -a,.-ne*ai o ycxtq6 m/gm8;h*iup pjvelocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Exp8bxv(yy3h+8c*;yzp 1hml cf( yr 7 seu .cv0wglain.

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 handmrvwqa 6h)0kg r-hc n7(m,.lns behind your head than when your arms are stretched out in front of you? anh,mm kh)n.r v-l0 gcw(6r q7A diagram may help you to answer this.

A 21-speed bicycle has se-afg- k g8 ,bp1/qkg7s lzqz7iven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to p/- kqpfqk-zg7 78,a1lzibgs g edal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower le yv.ujvkvi31 w epekb sap84u+ 93p.*zgs 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 is98e1vzj a+i3bupk4ky.p pe*vw 3s vu. advantageous.

Why do tightrope walkers (Fig8t4 je1r4 gmk m;lozb*. 8–35) carry a long, narrow beam?

If the net force on a systelqd6-rz1yl b 6m is zero, is the net torque also zero? If the net torque on a system is zero, ir d1- yllqbz66s the net force zero?

Two inclines have the same height but make different angles with the horokc/7z7 x/ gyqg7*e ubn/ egy4e2ft3iizontal. The same steel ball is rolled down each incge7 iog7et*xzn7yb y/2eqgkf3/4/c u line. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simu6nj z9 t6wscp8ltaneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at tsj9p 8zt6nc6whe bottom?

A sphere and a cylinder have the same radius and the same mass..)rljvg 3xn(p2 v1 xvk They start from rest at the top of an incline. 3 1jv2 (gp.)vxkxnrlvWhich reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserr :)/odmnbq4 uved. Yet most moving or rotating objects eventually slow down and stop. E :r qb/4nmo)duxplain.

If there were a great migration of people toward the Earth’s equator, how ro 7 +o34oywkk 5azlg)would this affect tr okzo35 gaylw)4k+7ohe length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rj9eri*x 5:d pwotation when she leaves the board?rdwpi :ex5 9j*

The moment of inertia of a5jq7l j+q2rp a;: 2nra-h hjah rotating solid disk about an axis through its center of mpla a+:ajq 5-7rh2h;jhr2 qj nass 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 onk:rj (5g eik.q a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drjr: e.kqk5i(g op the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical andw +w h)fllp7 2)w h2/y6rhmugf have the same mass. However, one is hollow and the other is solid. Describe an experiment to determinew)mh+w/wh 2ug)r7 y6fllhpf2 which is which.

The angular velocity of a wheel rotating oomlz (/y 6fgv.n 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, descri (z/fyvl6mg .obe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a largxd tcqtljy.. m) 442f0+ etolge freely rotating turntable. What happens if you walk towartlg0d)m2lq.ytx.+co 44etjfd the center?

A shortstop may leap into the air to fz -t-nap4ig+82emtv7 y bd(p q 5q:xi4kin8m 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 legz+tnxepy-7i5fiqdviqnk8 8 m 42 -:( gapb mt4s rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservationo-pcrem 1; *qn of angular momentum, discuss why a helicopte q;no*cp erm1-r must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in raxgpq exo/3*r: dians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing v-nytk2 (gk4) esvon -w)gpu8 coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen n4)n g-pg8uy(esk o)vw2kt v-on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Ear iupul,oy4 (s:(i0fgsw ybs4:th. The beam diverges at an agsiybpi4uw0 ,ufy((:ol: ss4ngle $\theta$ (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 t1 t()4q2.ichweyzk+kmcl pr :he motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration a he.2kq(lr14ki w+zy: ct)cmps the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ba6( aveyce*t6 php- ,ih u+gp-nll makes 15.0 revolution +i -vy-u p,6tghc*ahpp n(6ees, what is its diameter?    m

  A bicycle with tires 68 cm in fnkq,mia1g o/wt6v c02/pv7 sdiameter travels 8.0 km. How many revolutions do the wheels kc71/mv antv ,p/6qw2si0go fmake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angulkdujrck8ch5*0qp -+l ar velckjhr80d5+ k pqc u*-locity 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–erdc,ryw/d i1e(c 0fz mq):( c38). (a),mq:y idc(1)r/wc(cze r f e0d What is the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its7d2d wx.iga-+lw:uik p9t k)h orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed;ah rr f,k8fwvy.if8y9)e+ a(a) kuyj 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 p1i qns6hkwq1 1sd1e5 nt-+folarticle 7.0 cm from the axis of rotation is to experience an acceleration of 100,0 iq tf+5ss1hnwe 161kqon1- dl00 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpmo,(rai;dvrs /n,)z*q gp, tqx to 280 rpm in 4.0 s *qsnxqzt,;,p)ig ordarv ,/( . 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:pbvyx 6 73mlrs $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put themoife l 4zy;m*ipoc; faei7n/ s.6+jy-selves into a slow rotation to distribute the Sun’s energy evenly jl*e ini4. + ;sycfoaey/miof-6p7z;. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniforim+8iz0i( ::mbpft-p7i wlz imly from rest to 15,000 rpm in 220 s. Through how m:0mppi iimizw:8tb (z - lfi7+any revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpmlb4 q49ev(mrq/az e(u 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 highspeed jets in a whirlins daux37ku. ;1s q,hfhg “human centrifuge,” which takes 1.0 min to turn through 203. ,h uh7qau sdks;f1x 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 uniformly from 240 rpm to 3 r4sorwsdh3)m2 f5 ke060 rpm in 6.5 s. How far will a point on the edge of the wheel hw5 23r hdsm0rofe4k s)ave traveled in this time?    m

  A cooling fan is turned off whehmaxb,s f3 6uekr**:gn it is running at 850rev/min It turns 1500 revolutihk6fb*amx use: ,g3* rons 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 revoeleybs g 6t.uc 1*q+c2mk; dq6 0iity+lutions as the car reduces its speed uniformly from 95km/h to 45km/h dylc *t62sib 6+; mu1ekei.y gtc+0qqThe 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 spe6 qege1lgw; +wed uniformly from 95ql1wgw;g6e+ e km/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 wh5iz76 4eyap:u nly6- gglxp. ven climbing a hill. The pedals rogi.peu576lyx 64pyv anz- :gl tate 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. What is the ma aimi/cld( z,-gnitude of imd(zlc-ai,/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 i7hl8k g jg 7u2n.9snfcm y,pt+n Fig. 8–39. Assume that a friction +ygg. 27nk fl7stph9cu n,m8j torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, arp1eql -;ynvwe30 oq*2bqm9z he attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and directionp;mb vnew oh2e39q l1-zy*0qq of the net torque on this system.

  The bolts on the cylinder head of an engine require tighteninge; yk/ guz-,h f*bqs9a to a torque of 38ask q; h- z,*u/fbyge9 $m \cdot N$ 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 sph.b +jkac.mg7h,1jage 6 m:l gwere of radius 0.648 m when the axisjag:1l67mea.+k bgjg wmc, h. of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertiaiwz (eslv w ez9s4hy;0ou+) .lw2siw; of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combine+z; 2)w sh;.z(4yeu0ev9sio llwww is d 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 e0n2g)m*9, vo vnee tjdnd of a thin, light rod is rotated in a horizontal circle of radius 1.2 m9em)g0,*vv n2j otdne. 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 angular speewd )zdp6ws (m.m+3wjkvn6qr 3 d (Fig. 8–42). The friction for dj6zd3 3wv(+wwms. mq6pnrk)ce between 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 th wwfj0y:jb5f3mcs86 xe array of point objects shown in Fig. 8–43 a:5mxfjfj06cs y8w w3b bout
(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 ezlq*j8 v7sqn k30-sbof 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 cylindrix;slp8ufom,6k*e w5 y wc)m x/cal satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force ,w se85lxoukp wm*6/)c;f mxyof each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8 * 2ncrpk-mehtq54 ob(e80nyo .50 cm and a mass of 0.580 kg. Calculatp2e08 n5qo (o4m cy*tbekn-rhe
(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 0x.4uciq7xj hzrru+(, 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 tangentiallyems;bv y 6w 7pdk-6jc* on a small hand-driven merry-go-round and is able to accelerate it *mjc;sd eb p-66kyw7v 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 the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm ikr 9bbf 54qvbqk zn 1lg6ei3+v6(b u9fs shut off and is eventually brought uniformly to rest by a frictional torque of5r i1g vze6vb+bqqbkun6flb49 k9(3f 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball atjf;: bf.ho 4a(3yrhw a 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the foro; kn,v). *zm*67w nbc mrt;ap6h chuhearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is a;*;r)b*h ch6vht,w npauno m7z. m6ck ccelerated 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 rxby7bd*)p iee .a*qv 5od, as shown in Fig. 8–46yed*b p5)vaq x*7ibe ..
(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 consism1, 9u c-8w*jbq+t ohxs1gf zooqp ;0zts 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 from rest within four ful j2k8)okh0st bl turns (revolutions) and releases it8thbkj)oks 2 0 at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a momenv:z69y .vk qjet 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 a b7cfu :t5+o8yy z yoy2torque 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.d.7weuehs.0zho 7t 7c 3 kg and radius 9.0 cm rolls without slipping down a lane at7st.u7 0ceohhw.7 e dz 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with res-/tmsn8c- 4w6ha ify ypect to the Sun as the sum of twoi t-8sywy64/afh mcn- 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 1640 kg and a radiu:p.f* bed,ew cx)+t jzs of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolutionzwbtejc,+)e x p :d*.f per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm 4+e a*l1k)9u s. u.ukornnavdand mass 1.80 kg starts from rest and rolls without slip+k.udn.4)* ur seao 9a1 klvunping 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 *4jj**xnoyp a to fall and its lower end does not slip. What will be the speed of the upper enojxp* *a4j* ynd of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentodw:2zaiwaynuf .j*q7w- 7;s 89s dvsum of a 0.210-kg ball rotating on the end of a thin string in a circle of radi zaw.w 79q27*dsss:8fj;w- and vuyious 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 cylindrical grinding wheel( 8:r4ssdjj 8dfawn 5x of radius 18 cm when rotating s5ddj4f w8jns 8:(ar xat 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 a)ce)1q sgmx :platform that is rotating at a rate of 1.3rev/s If he raises his ae)am ):g 1cqxsrms 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 the one shown in Fig. 8–29) v+ ql2/zr0:1mo 2v rqjkiaf* qz)pqn 3can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck rz0qvqrq 2iplq 2)ofa/ *j :31kz+vm nposition. 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 increahxbw,9 .7c xaeuitv(og,ap6r s/ 2ab1nam3; sse her spin rotation rate from an initial rate of 1.0 rev everw/ a973ax hvu to,e sba.2; s( gp6iac,mnr1bxy 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 rotad/ nwz 7ljj-hx-y/ q:hting around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximnl/xq7/ w-jj h-zy:dh ately 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 momj(nfqk7dy4t:8 (s mu,a cet 9jentum of a 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 mojl3q; s6t yk-k5sxms1mentum 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 /;cza9vpoec (moment of inertia I is dropped onto an identical disk rotati(ac 9cpe/z ;vong at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4al,e qqom4i,, $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round playlej l7g 7g1)htform of radius 3.) hgye 77l1lgj0 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-mp1isu8h+ wm-: rixh( go-round is rotating freely with an angular velocity of 0.8 -(1i8hh :r+xp sw mimu$rad/s$ 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 ha50 mw dr* 1gjopl3w/fxpm275 z, lkaiplf 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, whjimm3pwkow, 5 0a5l fl*1d7 p/x zp2rgat 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 129 duvvuu0 .jflvd7eu-w 9dx050 $km/h$ 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 d4zy,rz 1ls,*a h nfr.$ 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 resq;cao *.m2 0xtj *arkzt, that can rotate freely without friction. The moment of inertia of the person pluj;a*zcr qa0 xmto2. *ks 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 diameter m z hbkqm h-br y)hcj9sm2,c+)*erry-go-round turntable that is mounted on frictionless bearings anr mbqz* cm)9+hh bk ,h)y-s2jcd 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 theg:pz k7 mc5+lr0ey2ht ty7 2 5erz0k l+h:gcpmtop 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 unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same sfsr ,b.xg x ) :9xarq6*mfyj)yide 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,rjqx x 6mrs)),gx yfa: 9yf.*b treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a r-fzcbqv a0:94 xk d8vrate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acquirelt2-q o 0u5jyos a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calc-utq2ojy o50 lulate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of*w :le epn(26azin:dr two solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and deprlw:*e 26 nd:nazi( iameter 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 rear wheewa74yrz fv1 :vl ($\omega_R$) 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 massfhk2e5 h1 yuo0 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 1ekh 1u0fo2yh 51 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 low-pollution automobile is for it 3/d hhnb5i;h eto use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a unhbd hinh5/;3eiform 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 illustrates an ywa+7: +fluhn lt8mpcg 9zx7 64a2zz d$H_2O$ 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 (hoop4lxoju0 9b *rq) is rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we igni4 kk:l.oqwg 57clzm1t ryps:d,u;(xore 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 gravitypuk:zt1, ;ol7qg rywxk l5s( i4.d:mc acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius Rtr h;ei4 io1o7ox3vx7p -nzk 6. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle eoip6 niov-xk;73 r1 x4h7zotso that it will 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 making 7z . u-nwh/+kskny.kh5 q1b1fpf8 emka turn with a radius The forces acting on the cyclist and cycle are the normal fo11wb -fp/ kh+suqh k..yzk knne7m58f rce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 1.58xhn(6v76gw x ,uy pca 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 achieve this feat, and where does the torque come from ,(p acw7gu6 y8h6vxnx?    $m \cdot N$

  Model a figure skater’s bod-x2aa ah2 f0fdy as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning h afxd2a2 fa0-skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clja4 215s3riu .pcbpqf g*m8klutch assembly which consists of two cylindrical plates, of magi5uk8sp3c pbfr2 a. ljq*4m 1ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 roihes c6dzr ,al61c6 8;c ch6nl8h+d nylls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble 6 c8 1ihy8sd6ahcc,n+z6;6hcl rnle dmust 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 t sfnpmz:3g++ not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions a3e/ usmi) hul 5r59bpys the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration5msrl )i5 euh39pb/yu 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