A bicycle odometer (which measures di q0 *ejk 0je u).70mw+v8m-ybizkjg isstance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a qv.0gm*ij sz0-u iby8)e jkmw+e7jk0bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a5d7 zl ,tuozs k47h3f e*vow/s point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity incrl5u,3os7zzksw d * 7e/4tfvh oeases 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 ve2bb unbu.heeswg 7hzd k(6.7(0* dxhhlocity $\omega$ Explain.

Can a small force ever exert 8 xck0j em;d(ka greater torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your headkt ha: hlr t0:2).pz:zsjrh q2 than when your arms are stretched out in front of.zhljt qa:h tphzrr2ks:0) 2: you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at eyueya-d)a *4 the pedal cranks. In which gear is it harder to pedal, a smal- 4*deaeyayu)l 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 legs with fleshjjjvg 7z2,dt8maul) 8 .x4ds t and muscle concentr78gxm 2dtldjusa 8,j.j4 vtz)ated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrn:ag,;f i g(8a7clfvy :5v6w g5xrev zow beam?

If the net force on a system is zero, is the net torque ti*nx0v 88gt8psvr8 ualso zero? If the net torque on a system is zero, is the net forcit88n8gv*st 0 uvpx8re zero?

Two inclines have the same height butjk6n;ho3 i u:t make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be grea;j u3 tn:ok6hiter? Explain.

Two solid spheres simultaneouslys hi6d1:epyxyk08jle. 9,g hgme*ht: 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? t:. g ed :j6e*g,1klh xy80 heihm9sypWhich has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same ma0i a;eimsjn,oho u6 1+ss. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed asmiou1+ o0,ai6; nje ht 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 ar:/b .zqqymdtk05f wp+9 (vfsp e conserved. Yet most moving or rotatingdvbms/ p9ft.z:q 5q0k(+ypfw objects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how would 7o6i.ryngda 6hw4 v7 3er 8uwq1 m,qtcthis affect the length of the day?t 7yw1w6q3q46,h cmor r.nia uv8egd7

Can the diver of Figshsy;juy)5- 3q-vmeq . 8–29 do a somersault without having any initial rotation when shvje mq -hyy3);s u5s-qe leaves the board?

The moment of inertia of a rod;p5yhxj ujz . k*8fhfj1:kz3tating solid disk about an axis through its center of ma.:z1z*hdh xj5pjj8f y3f k;ku ss 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 zh/o* 9bzoxog6z-n 8un g+-dc holding a 2-kg mass in each outstretched hand. If you suz6 g o+zuh cbx-o-9n8o gn*/dzddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have h,67bbr eap /zthe same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is whichrhb,/ pz7b6ea .

The angular velocity of a wheel rotatin +m1x3w8wkv he) 1k(tih2-2 r ujzpvqg+dneq7g 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 t7+x e viw2j2kk qd ev)+nwuhp(hrgmzt - 13q18he 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 large freely rotating tr3)pg g 6j8ewfw i(4n c.qx2kourntable. What happens if yo24xgw pr. cwjie6o3g)knf( q8u walk toward the center?

A shortstop may leap into the aig)e:b1 fryk11v:tc*ng,zba 3 o pt;trr to catch a ball and throw it quickly. As he throws the bz1 rt ,gk: *y)an1 p1br;tft3c:goeb vall, 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). Explain.

On the basis of the law off2 g) zrmyc1 f27z y2l-(omcmd conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). dfc21 zgylzym(7f co m-)m22rDiscuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a)wb5 zrx xg4e/, 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 coincidence. Calculat-y kr z sgp:v)d/19cvie, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, pvs :1 v/zi)ckyr- 9dgas seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The be ( xt/rg,,s-cycl1wwx : f.rokam diverges at an angle:tg oxk( frlw. /-y1s c,cxrw, $\theta$ (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 oe2xl8sp 0o jq1f 6500 rpm. When the motor is turned off during operation, the blades slj sp qxo021e8low to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a l* v5ugje3h+g zevel floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its d u5vgj ez+*3ghiameter?    m

  A bicycle with tires 68 cm in dj;cm/6+4u x 9n tacwtmiameter travels 8.0 km. How many revolutions do the wheels 9;u mw/nt6cj4acx+ tmmake?    $rev$

  (a) A grinding wheel 0.35 m in din67 /v ,wcuoujameter rotates at 2500 rpm. Calculate its angular velocity in 7, 6 ou/nvcjuw$rad/s$ $\omega$ =    $rad/sec$
(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-l og1m/p pz1;lround makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the g;/ol1lzpp1 m linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around the Sun ,y9a:,wsyq.stt5 t/ bjg wty0   $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of(n .j0srcj9 1cw qw0w5;vuf lh 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 7gz) wnu5/ 6 s ;lffmq0sy0pjlif a particle 7.0 cm from the axis of rotation is to ;f5mplfg) 7 zlq06sj/swu0ny experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm t0 p nlshym,d,cii6.6mo 280 rpmim,hcypms 6i .0 l,nd6 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 radius b9wphy5)2zhfoz4cm5 $R_1$ 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 themselves/z: b 5x 3yfffjlapq(6 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 3(qyfzab/6 :l5xffj pcan be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest t,u 8m)ql zbb+ga8jjl: o 15,000 rpm in 220 s. Through how many revolutions did it turn in t)jj88a: ,+qgblulb mzhis time?    $rev$

  An automobile engine slows down from 4500 rpm ton5xb:a 7yyhaop au wn pm 5):qrq)6n.6 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 whirgy8u 8mb ,rma-h7rcg5ling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching g u c58b,y8mm7ragr-hits 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 afy1 9q l5 inwt9wl+rynh3/kwz)7ck g 9ccelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How r fint9wy9cz n9/5h g 37kk+)lwqwy1lfar will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned o:gup z xmun6svfl .,4fc*/gf6ff when it is running at 850rev/min It turns 1500 revolutions bef uxm, * 64fns6c/g.uplgvf: fzore 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/t :inxlw g8olr 5b+czmj:i/4 9.vzry reduces its speed uniformly froml ni45bjcx: zl/ vr+:/ 9twzr iyg.8om 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

  The tires of a car make 65 revolutions as the go, hh8iy*ho 3.*jphf car reduces its speed uniformly from 95km/h to 45km/h The tires have 3j8o*ph y,h fg.oh*hia 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 climbingiwj e 1pj;n,(j a hill. The pedals rotate in a ci(;jew 1 ipjn,jrcle 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 wid4h jhcyc: 7+wue. What is the magnitude of the torque if the forcewhu 4:c7 hycj+ 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 torqeka/sx*30p+/ kdm twkue about the axle of the wheel shown in Fig. 8–39. Assume that a friction torque /+s k*k/a0wmd ekp3t xof 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attacjzv,pb fs l).4hed to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the z 4)vjs pf.l,bhorizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine requio9zs9t : kwy 4lttb2 rtd3gjj8o q- vc;wu80e8re tightening to a torque of 38owtktl38-8vczdq w or40 ;:yj ju etb9ts98 g2 $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.644.9m, umphtf cek5(bo8 m when the axis of rotkf, 4o( thm m5.cep9buation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rim av ;7o j xd.z51la ,o3aghu5utand tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?avtd5ja 5 ;uu3,o7o .zl1gah x).    $kg \cdot m^2$

  A small 650-gram ball on the en8y, .nq nuhj2-z qd:gqd of a thin, light rod is rotated in a horizontal qd,h.:yng z ju8-n qq2circle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s w:na23il/3vi rups0 qtheel rotating at constant angular speed (Fig. 8–42). The fri irp3qns/auti l23 :0vction force 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 the arrah)x,s b w ba1tp +/jrw.8 rdqs83ge1 dkt6mj/vy of point objects shown in Fig. 8–43 a,w6g1 r b 3d1ted/pjwjvs +xb88)sm qh.rt/ kabout
(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 2cx/ cycvo1r/pz rf)(2dj9* ,zhitdytwo 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 satellite spinning q7xmzv4vyo0x,s igp +7m x4(uat 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 th7+xqxyizsgm ,p0 xo 4(m4vvu7e satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder w8ne( xc .xb6fnith a radius of 8.50 cm and a mass of 0.580 kg. Ccx n 6xn.eb8(falculate
(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 from :da4z-*6p s b)doyypncl -v191hle ierest 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 o-ue: c/o:d*, n9f6gq rqma b8s uckpf6n a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 1kq6qn9cm:p: /a ous8bf6,d ref-*guc0.0 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 is shut off and is eventually yr-bdg* ( 8 5knv1z .pwlirfx+)5kerm brought uniformly to rest by a frictional torqu5p8(vrlwmkefz.*1d k5ib )g yxrn+r-e of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kglnwh2q ltc-rau)kw r :ji0402 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 the forea fglru:(bn,k uaz0.g+rm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. Thg(r0u+lzkbga .ufn:, e 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, as shown in Fig. 80:n: vn/dggsrv g;9jw –46. ndwsgn ;:v rgg0:v9/j
(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 o. -kjpo h3oo+xr7 1uirf 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 ful1x-nk2laus jw+fa) n 4l turns (revolutions) and rela w s-) k+jnl2nfxa1u4eases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inego* 6*js oe+oq6ntd f(rtia 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 tords1ztl(p 4f0 ique 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 withou18o 0jksun0 ko69u;sdylk m/ht slipping down a lane at 3.3 kmsko8kn9y0 ;l ouju/61ds0h $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the -zx -v *t.3 ar7xo6ii s7dufkqsum of two ts fq7 6t3i-v.u7ok-ia dr x*xzerms,
(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 kb lcc9n9bc e xmn7zi;lje 591/g and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation r7ei951mnlb bccxjl c/z9 n e9;ate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg mi/5uz)4dz z:9 cotjtstarts from rest and rolls without slizt9u4zdct zi)/5mjo :pping 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 oh 7,ojqu/ al0 w:ds0vsn its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conse,swjh u/sd 0o0lvqa 7:rvation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thin st p9f ila-act,1t5k 6p fqz mmvs;,zr2/ring in a cilrq;msat/ i6taz, vfkm f,92cz-1pp5 rcle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum oo rd.nd-axd v2 yo9f9-f a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when dr.-oxo dfa92- dyn9 vrotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform nh31io7lkav /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 decrease3noia7 1/ lhvks to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the on,.ifn56y5 t pz6sagvfe shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 r65pvinyaf5., zgsf6t otations 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 spcqdsi n21xf/ leis 46*in rotation rate from an initial rate of 1.0 rev cdis4ni *21/6xqse lfevery 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around aacpxh 2.p*dld lu/saq; 3w;y5 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, approximately shaped as a flat diskpddq*2ll; ypausa3c5 wxh/; . 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 mobwx9o- +2;hixvcopwt4)gmg 6mentum 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 moment9: s27;c x nf mcsld7eiwfr)0ium 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 dropped onto an lkhn5 r 6*a*oaidentical disk rotatah kln*ra6*o5 ing at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns.qd7y0m2:baeefrkmbx.c 76 o( dzc a 8 at 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 aax:7)5 ow)btqsmi1 dnt the center of a rotating merry-go-round platfor 7dq tmbw )n1)5xs:oaim of radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating free tjqz47 )vs)uterq kmpq4 +4-uly with an angular velocity of 0.8 sk4meur74jzq-tv 4q q ) +u)pt$rad/s$ 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 ; gusu06 hk.swinto a white dwarf, losing about half its mass in the ps0uw6 hguks.; rocess, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the 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 win-7s5 t2 rk6nqc:vrrtxk/ru- ids 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 zpf)4qy h0ex) $ 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 , a-p0wgx(zc*p3wx3 ngm8r kbrotate freely without friction.r , 3g3x0w awbxg knczm-p*8(p 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 oyj)dl ;k5(vu i2eq4qrf a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearingj5;ye rq4qlui k2) (dvs 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 61ui ,d, uaz9xkeym2nthe ground with the end of the rope lying on the top edge of the spool. A person grabs the91a uk2ny,dz, iuxm6e 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 side always faces the9nq)jgs w )r5z Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a pa9gzqns w5j)) rrticle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from aq1das 6 3 ml5y2k/taerest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylyd-2y :55hv: zuyrog;g9w vj rinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acy-zy5 :2ovg wurhv5d: ;yg9j rceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical j p6s2)6v ezyzjdm:u 1disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the lin vjmz62y s6:zde j)pu1ear 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 angu(xrscj 1+4a 0fodv 5pclar 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 Sun, but with mass 8.0 times as g64mocnjkmfr c a/*6fn7lpq+ (gh mh;4reat, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a n6q4+j pa;lnfnhmkfh*(gr 4mc6o 7m c/eutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automo z2tf 42tm5vtv (gq/5 eunbz3cbile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1v4tfve3bztq gu2(n25mct z/5400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustra4.) zma vji9fites 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 speed v=3.3 b 6-1 sawzgioh*7 x,ek$m/s$ 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 zzq7/: e giyp:r5 3(iv/ mynh q:zt1ri(i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass g/7(hnqi vm : ziyq yrr/3pt1::ezz5iof the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and ,m;.qcb alhn-we want to exert a horizontal force F at its axle so that it will climb a step against which it rests hm,al-nq b .;c(Fig. 8–55). The step has height h, where h

  A bicyclist traveling wi9i s(5rjbt4w.pn va2mth speed v=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 wnt bp9.s5ij2mrv 4 a($\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 intoq)(x naffkm37f 8p 6wp a sling of length 1.5 m and begins whirling a3ff(7fp 6xw) kpqn8m 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?    $m \cdot N$

  Model a figure skater’s body asn-uyn kqm8y d2zg ;*i,y9 bmu8 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 8n d9i*8nygy;q2 mbu myu,kz -skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which cz9h3h lzw7xm *:hjpv02b7tgc- abq 0x 87o bugonsists of two cylindrical plates, of masszobz37bw0umj-lg *7:7ta x v0c g289pxhbhhq $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fig. 8–58..v1dry m)0 - yst-aonjcb/f h- What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of hsrj1-/y c- vo- 0daf .ntyb)mthe loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but d:afmbj,;t 3rekpw 4h (r5n xm6o not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car q4xx h5 9ta/ft.kmq d, xr3w:qreduces its speed uniformly from 90km/h to 60kmq5x.9aw, /q txrmf3qkd4 :xth/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s