A bicycle odometer (which measures di2rbykbx* / (pl ecpef**j.hy(stance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if y*ebr cf(p*keb2/(px lh.*y yjou use it on a bicycle with 24-inch wheels?

Suppose a disk rotat h;st.wv4e xy6es at constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either componentx 4 v;6ys.wteh of linear acceleration change?

Could a nonrigid body be described by a single8/ m5+ d/ng ndlkqovla3po ,.b value of the angular velocity $\omega$ Explain.

Can a small force ever exert8y 6i e8ic5ymr a greater torque than a larger force? Explain.

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

Why is it more diffidf2,zr nqy1mp,u )lt 0cult to do a sit-up with your hands behind your head than when your arlt 21)pzuf nd0y, mq,rms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has sb: qi- ;0fj g+(ll 0yll;zlejfeven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear spro-eji0l l:+; gq0fl(ll;fj zyb cket 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 slfk, mi9ub0o/o ender lower legs with flesh and muscle concentro,ui9bfmo0 /kated 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 walk z0 jy0lapzei-8y8x :qers (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net99tcj vmwiyp7l) 2g7c7xkp1 t torque oc7) 2y719 mic7lgwp txtkpjv 9n a system is zero, is the net force zero?

Two inclines have the same height but make d27z dqa5-d hs.nz0 mrhifferent angles with the horizontal. The same steel ball is rolled down each incline. On which incznm2 as -r50z.dd7hqh line will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an inclin1 :fmjd7f6t ttmjx f)so:79 ege. 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 g 7: t mj tj7esf6fm9g)1dxfot:reater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and thebg ap yk;(i5o4dz(vf5 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 (;o54 aibydzpvkgf 5(the greater rotational KE?

We claim that momentum and a8z ,tl t*e4 w k:(6:kox1hukfflecpg2ngular momentum are conserved. Yet most moving or rotatin(6:h,fxl4lf8 wgkete1zo:c* 2pku k tg objects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equaudcaj.gt jk5 i8j/,bi,vte pi 1 s0)o2tor, how would this affect the length of t08)a b2sc,tgiu.i d i v1/ep5to, jkjjhe day?

Can the diver of Fig. 8–29 do a somersault without having anyyfid snol 6j0(ppq-4w0h8 b+o initial rotation when she leaves the board?fjpy08+o hd6i s(qlwo pn-b40

The moment of inertia of a rotating solid c6q4f5hzbo k3 disk about an axis through its center bockq6 4hfz35of mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mash-bp 5we9 u 0jku,ti0is in each outstretched hand. If you suddenly drop t- b ie00juwp,k5hiut9 he masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have thewx h31/fo,tvt)my4y i same mass. However, one is hollow and the other is solid. Describe an experiment to w1h34/vt y)o,mi tfxydetermine which is which.

The angular velocity of a w+fsd9i7lwo.r s3 3xq*yarkl) heel rotating 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 linear acceleration of this point at the top of the wheel. Is the angular speed inc.ld +ry7lw*ksfsa rx qo)9i33reasing or decreasing?

Suppose you are standing on the edge u fxmi7gh ofscs,iy)0(7a7u ,of a large freely rotating turntable. What happens if you walk toward the centeu) u0s7(gf,f 7 symiaih,7xocr?

A shortstop may leap into the air to catch a ball and throw it qui(-vqy3p i3,grz 6thg yckly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direct6h(3,zg vr ytgy- q3piion (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a5v d -; (upfvvc9d ttdzq;-a uz0m,xc7 helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the9tzv;-;u (c 0zvdqt dpc,fxm ud-7av5 helicopter stable.

  Express the following angles;z:ds0 h7xmgv in radians: (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 coincidence. Calculate, usin8c+dsih 0h o2fg the information inside the Front Cover, the angular diameters (in radians) of the Sun and d 0h+cos f2i8hthe Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam divez7 qz +pbc p1p z*n: )ooz5m8ilpnz7s6rges at an an7zo*z mqlp pzn+7z6cp1i z)os p8b: 5ngle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor ivdym)m;tto;i r/ ;i t/s turned off during operation, the/o iry ;mt d)tt;/m;iv blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball ,al3zp ovat n6lm8 t+z0zvo *ys 6l,ecwq; i89on a level floor 3.5 m to another child. If the ball makes 15.0 revolutionvn i60w+3yozo pq*,mes 8llt6,zlzt9ac;8v as, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions 4ys44 (s vxoczs6y(w9bm evq8 9sl/zb do the wheels (mbb vv(zql yo c/s89wy4szs 6944sxemake?    $rev$

  (a) A grinding wheel 0.35 m x/ t,;vgu*v/uekhk6t in diameter rotates at 2500 rpm. Calculate its angular velocity i/tv*u/6uegk ;vxt hk,n $rad/s$ $\omega$ =    $rad/sec$
(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 re:c6;ukm f7*neq8w dc c. s4rr 0sg,sawvolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.nc7sk: r*rs,uacm w6 d;swc q0fe8g4.2 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 i18y pl m*qv5l,qjzz8f ts orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of aq0,i*norvd xjx5 ;5aw :j1dxqx9q ep1 point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm frnudk83vvzxd;6* vu;z om the axis of rotation is to experience an acc zku;*dn;6x vvd8v 3uzeleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from xziva7ds 4+s m3/u0c x130 rpm to 280 rpm in 4.0 s. Determi0 vca7i4 xumsd/3+xsz ne
(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 qw4i 0;qqa 7a u7hd.yq$R_1$ 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 4 -(jj/kq +qj n.jm3cqdsz k/kthemselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine k3s4j(mnkqd.qj// j c q+jzk-
(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 zc9c* e i/ urzd6ef,v sn)r::oto 15,000 rpm in 220 s. Through how many revolutions did it turn in this time? z6::eesi)zdvr,no * 9/ cucfr   $rev$

  An automobile engine slows down from 4500 rpm to 1200 r6ztp;xv4k u3 j. n3 ,au,rukq uulo18jpm 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 fly 5ap p6vncvt3.(4 dfk i02:8inq uvewsing highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to tur6 s0pe:u( ia ipv q.w8t45n v23ncdkfvn 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 uni+rki;iok *2wrformly from 240 rpm to 360 rpm in 6.5 s. How f *2;riwo rk+ikar will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned pi b((72dcs5k1am 8uie * lkbzoff when it is running at 850rev/min It turns 1500 revolutions beforzpmeb(1ab 7(ids *8 kkuc5i2 le 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 c)m ojbs/sg4y m/0pef *ar reduces its speed uniformly from 95km/h to eom mb/* ) gs0ysf/j4p45km/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 reducesn.8ymvs o/v7i its speed uniformly from 95km/h to 45kmv .sy87nivo m//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 climbh5wx uz*fpc;s5 / k /ap-pyp9ving a hill. The pedals rotate in a5-5pyw vzp*sp/ /a 9p;xkhf uc 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 4pe*f8fcxfj4, (vfk kp (r(zyN on the end of a door 74 cm wide. What is the magnitude of the *p r fj(y4 ff ,k4ke(p(v8zcxftorque 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 wk t:x(tk9 5mc0j0s*lks2its bheel shown in Fig. 8–39. Assume that a friction torqk2*m c:0ltx 50 skt9ktsji(b sue of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, pfxh* jcs 2,s6are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the ro*jp6,2fh xcs sd is held in the horizontal 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 require tightening to kakbcp8n s*v3+njia1 z 2f0 :ha torque of 38 3*+k ihn0fcjnka v18b: spz2 a$m \cdot N$ 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 rakp:fs+1: lduqdius 0.648 m when the axis of rot::ld+1kp uqs fation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diamet,1cdb ri33 lwger. The rim and tire have a combined mass of 1.25 kg. The mass of the hub cadlg3w1,b i3crn be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, l wf)xq8a-s,hpight rod is rotated in a horizontal circle of radius 1.2 m. p) ,8-aqfxshwCalculate
(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 consta//j3 s9 xwg cs*budj+cj8j8 mqnt angular speed j q9gju8 dwbs3c/*c j8xm+sj/(Fig. 8–42). The friction 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 array of point fyijt)n ak :d4(hu:db5)uqgy + .b*kc objects shown in Fig. 8–43 about af)d+icd*k( uqygb) thj5:u4:yb.kn
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two o 7-/3no. lgp5, ylzzd7;rggvp rs emn:xygen 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 at tyb)wjn hn 1;*i f8* pxdnk/+i,od9 zkjhe correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass oh) jd+nf9 8jxy* zwii /ko;k,np*n1dbf 3600 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 ap(bz t+ks38nst3r,i y uniform cylinder with a radius of 8.50 cm and a mass of 0.580 p ky,tb338ri +zs(snt kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest t8yafpw+,2al q 1wvx l3o 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 tangt f3 4fq*qio4nentially on 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 qn of3t44 ifq*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,t xh .90- nar:mngsnu rpm is shut off and is eventually brought uniformly to rest by a9n. hnuxt-gs0: ,nmr a frictional 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 accel6pd4uxez0d9j erates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm,ij 1vyjhr2qu n2h:j44 which rotates about the elbow joint under the ac4iq4 j 2j1jhvurnyh:2tion of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can -(py abl7/yra be considered a long thin rod, as shown in Fig. 8–46. y/rapa y(b-l7
(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 two9cr9ixe+z j1 i tm1v)c 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 accelms *(d8fz y-bverates the hammer from rest within four full turns (revolutions) and rels -z 8ymv*b(dfeases 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 inert to( wvb1ibeky( 6w9tg9.bo3eia 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 tnmz t1192w r,vm0bjlijhjh aw22 18or orque 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 radiusvnx) ig 99xrc:5 +cwdw 9.0 cm rolls without slipping down a lane dvcx :)iw5gwcr+nx99 at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of tzk:edrben5j0 x ,dk z0rg bsj y:y7-:9: rnbrbk-jz7de9j:xe gzdsy5y0k: ,0wo 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 yd (ki+do*m 0ca mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a roi o0d+dykc m(*tation rate 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 starts from rest oiu/r t 6h2 sgbb+r dkj2jd-5:and rolls without slipping down ju+52-r rgth6 :s/bj2 dkdb ioa 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 y:p/3 8c sn3j m9js-.sbjzyfetip. It starts to fall and its lower end does not slip. What will be the speed of the upper enej33yzpfs. y -8j/9mjn :sscbd of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotlzp1y8h9u 2yf8+,gko ( bc sg0al-i obating on the end of a thin string in a cir o(2g 8ca,9i-18kh+oy0zys lbpgluf b cle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular m5 ;lxefc9k;o5;qniso omentum of a 2.8-kg uniform cylindrical grinding wheel oq5;f;5ko; 9ec l nxsiof radius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, han ,ufcj 3kxo u4hyc-2-a e7e- wgwe*;kxds at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the socug4cw ,f w-e k-ah7xk3yej;e*x-u 2peed 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 redh,l9x tb+ 6zw6wymz/duce 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 rotations in 1.5 s when in the tuc+,dlztz6 x9ymhwb/6wk position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial ra smgo:7n/4 lx y0pe5late of 1.0 rev every 2.0 s to a finlpams4oe :n 7l/0xyg 5al rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its c) yamll sl9 -tsvdq3/9enter 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 disk of radius 8.0 cm, onto the center of the rotdlm)al-9qsvl9s3 / yt ating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figteo3l6 1 +priyi. tgc/ure 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 mn 4bpa/y+qul031t rlaomentum 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 :/upa diw1: 1x dcc0v4rjvlm(inertia I is dropped onto an identical c ic0dxa1m( jpwdu/:rl vv:14disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at fe b50tl:*gnh2.4 $rev/s$ 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 c eyrv 3 74fho:yd.ynp y:x3/rkenter of a rotating merry-go-round platform of radius 3.0 m and momr npx:3: rh4yfedv7yyo/ k .3yent of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocitc57(4cfgb 3inngzv(h o1(bi m y of 03gc5nfz bc1i(7(vb mogn(ih 4.8 $rad/s$ 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 av 1)z3m +7rc/nfsi c2we .lziwhite dwarf, losing about half its mass in the process, and wi3wzc12+me f)ar /niisv z7 lc.nding 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 winds in excessivesfsnn 9(p ci,2))o 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 j9ln gso :7ecvlu,bbjuc0142aw :k +b$ 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 mr w vw hxc1lss72:t,6pa:s8jplatform, initially at rest, that can rotate freely without friction. Th xswsrlp1h ,jvt7::6 m2scw 8ae 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 stabo d;jp *67bvv -jssj3nds at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on fr6 bspojsd jv7-*v; 3bjictionless 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 4p)beirybwfsoo5 ;g; 0ua +i4 the ground with the end of the rope lying on the top edge of the spool.4pub+gri o0fi;w boy s) 45e;a 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 side always faces the Earth. Dee2b7o 152 1yx6v4dfh sgqx mqptermine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orxg1 mq5 esqxb2h6 yv f42o71dpbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from bow4 9 qyh2ua2rest 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 thexgs;2d57k+ aglnntv*3t5 hm b shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of fromnxsh237k;d5v+ mt*5gg a nblt 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 c /zjpnch*e;vwpj .(f w h(*n/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 dianhnv ;p*c h/jw(* (pf/wc.ez jmeter 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 thec+nzzdo3r2)uwm 7v z 6 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 great, w8 :sey2gyq nupkmwhj6 c2:*j7ere rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collak yqu: 2ynsghjp6:c *2 wmje87pse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy storedo8li8m ru7b kz-f99uf in a heavy rota7u9zr8 ffb8okml9 -ui ting flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without 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 f4t,fx8( upea$H_2O$ 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 kehow4gf/m: /.ojt y c-ty2i)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 lerf 2 ig,k/6jgcq:z7dvv2s /ywngth L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, asy/zvs/q 2w, 7c2:g 6vkf ijdrg 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 of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertical :je7t8ylb;cgly on the floor, and we want to exert a horizontal force F at its axle so that it will climb a stb ;l8ejg7:c ytep against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on * 3e :n))e0dhzbz+ gpkc8gdl ea flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal force 0)):ezk ldgehnb3 +gzpd8*e c$\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 ngr7:e , omfs0sling of length 1.5 m and begins whirling the0,oegs7fnr m : 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 as a solid cylinder and her armsydwk*f 4-bxd*fs0 l +e as thin rods, making reasonable estimates for t4fyxk s+be0l-dd*f* whe dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of 3 ldv ks0wb *. kwo-4q3kmm:wdks5vp/two cylindrical plates, of q4b3 ov.k0kswkw3:/vl*dk 5md-m wpsmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ro0 d/p* ok 7w ;m2-aumz0unr3nsq l8qecugh track of Fig. 8–58. What u zpsnc q0m-n2*a kwe o/8r;u0md37lqis the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not s w0*c:cvmr 0qskgmg0c)wvp7qk: (a 0assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolution)b fzd 6;xjv;p9*mo2/ndenips as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diametemp e;6 o2;djz)v*xdi pb /f9nnr 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