A bicycle odometer (w)7qe92rsn b akhich measures distance traveled) is attached near the wheel hub and is designed for )2saqr knb7e9 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotateqpah pz 3k ,51rg+ks/es 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 component of linear aczak/1,kgp5rp eq 3 h+sceleration change?

Could a nonrigid body be described by a single value of the angular ved 9k hyb*fgrpe.d/:euf749 o elocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? h 5nliz7 q9q55c vbh3zExplain.

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 sig); pd1b djhwibw;0b 6t-up with your hands behind your head than when your arms are stretched out in front of you? A diagram madpb;0b d w)b;hj6 iw1gy help you to answer this.

A 21-speed bicycle has seven sprockets at the rear )3n o7gv u;nz,ffj(ejwheel and three at the pedal cra gff,n;(jnz oue jv3)7nks. In which gear is it harder to pedal, 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 slenue, 4bc,(jz( vey6m oqder lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynyquz(,bo ,6cv4m e(j eamics, explain why this distribution of mass is advantageous.

Why do tightrope walkerscz01 * kmit7kc (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torqq+c lk :mnsp.3tofr48 ue also zero? If the net torque on a system is :nlq otkc4p3. s+rm8f zero, is the net force zero?

Two inclines have the same height but make different angles with the horizofr5vj1.p u 7lbntal. The same steel ball is rolled down each incline. On whfb.7 vpj1 5lurich incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an ;9sffg12 vbm zy, q1aqincline. 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? Whizq g2sa1y9vbf, f qm;1ch has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. o9a5:ui cc yf*They start from rest at the top of an if:9u c5ioc*y ancline. 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 the greater rotational KE?

We claim that momentum an 8szfmm p5qth1uxz1wo ka/-oiq g-2 h51 k2zp4d angular momentum are conserved. Yet most moving or rotating objects eventually slow down and st 5hqw/141xf-gh-ikktumszza oom5z12p2pq 8op. Explain.

If there were a great migration of people ihgxr r r-peo) 4s:8.wtoward the Earth’s equator, how would this affect the length of the day-wre 8 i r4gso:rh)p.x?

Can the diver of Fig. 8–29 do a som-zy78nw nn fz+jjtj7* ersault without having any initial rotation when s -yzz78*j7j +nwnfjnt he leaves the board?

The moment of inertia of a rotating solid disk about an axis through its centexwft0 : ,) kb,xtcj1pur o)tu,xkxpj10 c t:,fw bf 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 n6jdja,gg 0e2mx di4vrfl5-5 holding a 2-kg mass in each outstretched hand. If you suddenly dal5 4gfe 0dgmni-x,rjj v62d5rop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one g v6 ww 0.j-fcuf29rjeis hollow and the other is solid. Describe an experiment to determjj6- ewf92cu0 wgrf .vine which is which.

The angular velocity of a wheel rotating on a horiz18sd/rtodvt;/ ; g)af6deew bontal 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 acc aret1/ed d v6)s/f;w8ogtbd;eleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on tz-kgdi, 0f lz+ tpvl.1ho;b) mhe edge of a large freely rotating turntable. What happens if you walk toward the center0vgbzizp.-om)l ,k+dh ;ft l 1?

A shortstop may leap into the air to catch a ball a uhf r-t48g;dz .yl1jlnd throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposi;1.-z 8jhfg ryt4l dlute direction (Fig. 8–36). Explain.

On the basis of the s a6 wsr+l kl5hdbh;07law of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or mobd7rs ;alh+lk 6hs5w0re ways the second propeller can operate to keep the helicopter stable.

  Express the following a;yoh/plqcac fcf383 yeh5y ,g de,;)w ngles 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. Crxoq g9n :gdq4/8w m,walculate, using the information inside the Front Cover, the rq,9q/xdg wm n8 :4wgoangular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Eeky91*q:p yog:-q xh3szo+ue arth. The beam diverges at an anglo q:q1-so3eg zy:y ehk9p x+*ue $\theta$ (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 motocdw/uiq) ybg19 p4u i7,rn u(ar is turned off during operation, the blades slow to rest in 3.0 s. What is the angular accelerationyqd 7u rbupcgin(/a)4w u9,1i as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m tnoh9fb2/024cvymh jg ori b,;o another child. If the ball makes 15.0 revolutions, wmry2,/h ic 2oh fjgvb;b490nohat is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many (9 sv,/ab:1vw0snnmfpg xssuj5vl .; revolutions do the wh1/mnl9u v0(v.5sg v,njspswbfs;xa : eels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rp-oj fl1,ai+ 8dnwcz h-m. Calculate its angular velnoi8azw+f-1dcj, lh- ocity 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-rn m1hd(4a-bbr6sp9 q found makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the lineb( 6hm9-4dqn ar1pbfsar 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 v(ibs*opa )j s1mc9p9e j)7p dvelocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed8lmkj 80f/,3tf -rgci l*mwlt of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm-pu+d siy9ugcj / fha0rc17 *n from the axis of rotation is to experience an acceleration of 100,000h c su+1ydrup9/ c*7ifg-n a0j $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center fromn2s qbsttfl0x69md 546eb 3mx 130 rpm to 280 rpm in 4.9m4 0me6x56ldqtt bx2s ns3b f0 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 3tfa - tyrc+c.dx8i-b $R_1$ 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, astronaut0cgn * yvdr-r/s aboard the Apollo spacecraft put themselves into a slow rotation to distribute thd 0-*vy ncr/gre 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
(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 to 15,000 w4ulbjrc73ni 9(ei w; rpm in 220 s. Through how many revolutions did it tu( wl;3bwii94ne u7jcrrn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpmnz.g4+xa2zh 3i1wz f m 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 n0a li0pt nk)im31w i1:als1b in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions beisn3m0) t11alw1ia kl:binp0 fore 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 frokruw 2s l(qc34m 240 rpm to 360 rpm in 6.5 s. How far will a point on thuqcwk34sr 2l (e edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rr cgf4.6vw:zc5p /x iyrf31b fev/min It turns 1500 revolutions before it comes to a stop.3xfgz cf: f.1v6pic5ryr b/4w
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed unif*zy-puwd*c + r99pou formly from 95km/h to 45km/h The tires have o-+ pfp*wyd9uz*9 cru 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 revoluti1 akhl3lo*y+0:nqmvq:0 vaa xons as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameq*oay+hqaknlx300vv: :alm 1 ter 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 climbingmn qty3i1va2xg;(:)ybue7 ic- on 2vl a hill. The pedals rota 32ey 7b)2(oli tyxnmu1v;c-:ingv q ate 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 7 (yngf*9i8 )p muawxyl;hb01b4 cm wide. What is the magnitude of the torque if th)l(yy0;n 9gb8pxh*a1mfw i ube force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. xzsw a yslw6+-;w ar2;m)mapl95hp p6 Assume that a friction ar;m xs6+asawzmpww)6l9 y5h p-l2; ptorque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of adw*e*h/ 2y)av kze r;c;o2m da massless rod which pivots as shown in Fig.)2da*v c oheyk*med r2; ;a/wz 8–40. Initially the rod 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 reqvj:sgn1i* : yquire tightening to a torque of 38 :*vjyq1s:ngi $m \cdot N$ 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 6b(ak; 2qhxocgtp o0e gy+l. 1of inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its celoc;+g1pagotqhy (6bk2e .0x nter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diame -zzg2s0hsr 6rter. The rim and tire have a combinrr-gzs z 0hs62ed 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 end of a thin, light rod is rotateq )u *gqxtnoj 4t h,h7/i8r*gxd in a horizontal circle of radius,tho8x**rqig)7/ uj x qt4nhg 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 a-,eg ),gicftzz3d+a bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force be3gaga,f tcd )+ez-z i,tween 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 arra 9g5/ cb*f b4bdgpr)zty of point objects shown in Fig. 8–43tbfb 4 zg9r)p g*/cdb5 about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total masshhee 3zk,avg 73wn/9k6(jgq r 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 satellitebj1u. ) pzg4w6((ab5fq zv /zsnfwr 8d 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 sr6z8f w( ab1z5 nzp4(/jfsvg.u)w bdq teady 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 a uniform cylinder with a radius of 8.50 cm anhun p/ofovhtkf9qw*p7md5 9: ; 5 2tzgd a mass of 0.580 fu95hmh2 /vf; qkptpzo: o7nt*dw 59gkg. 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, acceleraturgls,2i*kk 2ing it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and ism:se9f4ii jw a4xil30+ +azde9:jf zv able to accelerwlaje iz0s: i499 +xvzia4+: fdfe3j mate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate 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 event57/l ;;*w fhlk*yappgd wj *hyually brought uniformly to rest by a frictional py* *h7 jl ;aklf;*/py5hwwgdtorque 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. u+:/e yh4 qlill2by*8yfwnsph6v 2 6d8–45 accelerates 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 thrownd* ;y-kycwl h5umu 9(p solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated unif(; u yhwc*um9py5 dk-lormly 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 bis)( cvy 9-txuzo)n o5e considered a long thin rod, as shown in Fig. 8–46i9zy5 )v(s otox -cnu).
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two masses, (nt *1opd x9wgh(tc h:$m_1$ 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 accelera gwgu:mp 15g. n;9qptttes the hammer from rest within four full turns (revolutions) and releases p t;5:g.g q1upg9tnm wit 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 /5i nme-8+s i0tu orltof 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 azx -7tnfxtn/pj4/ r, n torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping doi)6kr, sb 8ylfwn a lane at 3.)b,6ly8k sifr 3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the*cx z un1u2t2k Earth with respect to the Sun as the sum of two termz2kc2tnuux1 *s,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7a xh-o-i c/8sa.50 m. How much net work is required to accelerate -ai sxoa/-c8hit from rest to a rotation 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 rest7 egzma h/c-s( and rolls without slmhz (-a/csg 7eipping 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 stgbn a-6t4 nk*varts to fall and its lower end does not slip. What wi-ang 6t*nvkb4 ll be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of i xhozoq7whc3g z ( h(ht2 3u: n-/4xi5rplzo:a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed h:x3rxz-hnz5(qzh g4i/ 3:(ip ot o wl2hu7c oof 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding whee kif,d6(, u,wgrxw6 wgjqdj) 8l of radius 1g86w , , ik)dxqr6(wwuf,gdjj8 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, hands at his side, on a platform thav2rp i 0l8kht)m-8 cyct is rotating at a rate of 1.3rev/s If he raises his ytvpc lm -2i 8)ck8hr0arms 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; wo7a49 xc2ovmua*rd one shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changingwa9o; c2 r7avxo4*um d from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can inc c): ol)82ooj5,dxhral4f e/m lamd:urease her spin rotation rate from an initial rate of 1.0 rx))d jah /lmaf mll 4 285c::,ouoeodrev every 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 arm ,vmw z1s+h-8ig/mnx6*cz 3 kj q z7c2b5mwreound 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, approximately shaped as a flat disk of radius 8.0 cmzckm 7z1 3h webirxm c/j*- v52 86zs,mqgw+nm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinna92reilucd b 0l:lp:, ing 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 momenay*j/cm 9c)jr(ow, pn1mi+z rtum 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 odce;.6b75v :d l njbwsnto an identicadbj s7b6;5:lenvd c.wl disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atxla5:9jgh x kzn91 s9z7upwq/ 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 :q-2xelvln i0 at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia 9-l :v0ni lqxe220 $kg \cdot m^2$ 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 angul,acnm9cpe+;w)m d 5ye ar velocity of 09 w+ )cmy;emcen,5apd.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 wu* w 6h(lc5aaqhite dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass ca hqca (6ulaw5*rries 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 excess 3azko7tpjc ke9w+97tof 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 jl p7 +t2hcmbwg )7kc2$ 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 r mw:)6jhum/dd ul w80iotate freely without friction. The mom6h)m:d/u wwu j8ld0 iment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-round x0 nmznl.2bplc +(1sxm.a9ew turntable that is1+ zmw0nxxsellp9c( ma2.nb. mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of tcc.fav7x3 0 nche rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig.cvx fc7can3.0 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 samin*3q-hwrur kcs6++le side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angul*w c ik36- nh+l+rsuqrar momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ratbxf9 i7 0n xvr6eh(vd2e 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 radiusuar* )31sqm3,gtlinq 0.20 m acquires a rotational rate of from re1, n rgsqi t)m3au3*lqst over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solj5osl,( +vr*fps (s aons; mmsa:w0t.id cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concen m:wv5sjs ;0s+.af, mls(n p(tro*asotric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how i(pxhqc zad ak*31vf 2h9lt-k3r/cm q)s the angular 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 times2h0 e7 0b gszvytei5;w as great, were rotating at a speed sbg0zv25; 0e t 7hweiyof 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution auto06syx7;e/ +n n:cw.ucw wgsqimobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mas:cwn0wuixs;/ w.se7 ncgy 6+qs 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 ie-ruzoyp/rchb 0 wo 2j4k82e ,5r-py$H_2O$ 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: knabezg 70se4f+7 g d34assy=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 lengzk wi u2mq: x/9ib7n5uth L can pivot freely (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 ruknu mw25z7i/i:bq 9xod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically o ib0*vp,dq8m nn the floor, and we want to exert a horizontal force F at its axle so that it will p,i0q 8bmvnd* climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed vw78v (cn cefj19j1l.xez:zc w=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the non. cc1f81:ex9l w jevjw( cz7zrmal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and beginsk;k-0:o8 bvwzzn hw /s 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 rvkw; o0hsz /k: wzn-8bequired to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body asl sx(dp1ok7l(qyu -3 r 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 skater with outstretched arms, and witkdl(sl(r p 3x- 7yuqo1h arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical,)09kdws +gr bfu ,5tw jpoxtqo +ao:* plates, of to+ok5s:ftgo9j*w)xp ra dbq0+,, wumass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 loopld+ z+ghn 2b;bed rough track of Fig. 8–58. What is the minimum value of the vertical height h that the ma;+z2n+g lbbdhrble 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 ass(ba:16l /th6lkyt1 7 yqxkfk eume $r\ll R$ h =    (R-r)

  The tires of a car make 85 rsf1h 3jye et5x.bfz z )--r0dqevolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) Wh.1zbffq 5r-0y sh)z 3jxedt -eat 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