Angular displacement is usually express ;(m9:x*m v n, gvdgzfoi5zs(win units of

  Angular velocity is u5ldwvn; (g +vexpressed in units of

  Angular acceleration is extq9yv 2+jjbps3adx 3+ pressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a con4 vmt;4duvxr4 stant rate. The boy is near the outuvr4 4dx4v;t mer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a consta2h-zp;jyfo s: nt rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular spe- ;2 :sfyjzhoped?

  A boy and a girl are riding on a merry-go-round which is turning at a( v:.)egbttofdmd r2: constant rate. The boy is2)mv tef:bo drt.g (d: near the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constanfnegrzll3( czf*j*5: t rate. The j35:znf zf g *(lcerl*boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a medzz9.spk-f 6ykk - yjw.a9v )wrry-go-round which is turning at a constant rate-kf)k ypyk j9z 9vsaz6w.-d w.. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of 7(5+quji+akkt9e 3h)xttyfjthe following is an accurate statfi yut j7 h)(+5ea+qkjt t93kxement?

  Rolling without slipping depgc* 8bjzm-6-ey1 jsve;/tjl xi i,x3d ends on

  Two equal forces are applied to a door. The7ab gnd- *oeebg) ;5yepaw 0,t first force is applied at the midpoint of the door; the second force ipagn w)b; 7-bat *eyedo0e5g,s applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. jmg mj9w2y6 li67sy 7nThe first force is applied perpendicular to the door; the second force is6j js6 img72wly7mn9 y applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the d,c,lz5 dryd dtq 24cg5oor. The first force is twice as large ast,ydqg5c4r2d, lz 5 dc the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to chm6l9x; 1zedw :z qtl.manges in rotati69wl;1t m lqe zdm.zx:on?

  Consider two uniform solid spheres where both h uw,pf.uyow8pn f0 84fave the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to thatw0pf.,uopw8 ufy48f n of the smaller moment of inertia is

  Two uniform solid spheres hav wq.2 w2fhlo0o27jhfu e the same mass, but one has twice the radius of the other. The ratio of tuoo 7wl 2 q2fj0h.f2whhe larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the 1hta1zy c s0*.xy i6oxdiameter of the other. The ratio of the larger moment of inertia to that of the smaller moment ofxzx6 ya0o c1is*1hyt . inertia is

  A uniform solid sphere has mass M and radfvlfitst1+70j8ip, f2se(h t ;p8- x+jqpg ddius R. If these are increased to 2M and 3R, what happens to the sfs pft+8ds h pl +iejtdj,8 p;xvqtig21f-( 70phere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, thac;n+3 u x3li9yjy 1sb:qg1bkyt object will

  The moment of inertia of a zckuc0sdcfhiwh2b )( 1jc6n;hm ut9hx) 6 3-ssolid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kiz))mc j1hbx9;hc6hhid2 utf( ssnk0uw63c- c netic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass e ai+0n. g*bkd7iin8n of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to thi nnkb 7 +in*ig.0d8aee total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere ,y/jg lg0n/jts5 kam.7 a( z*psvwpx3of mass M and radius R rolls without slipping down an inclns,pvj 7y*kg psal.3x/(t0 a/zwjm g5ined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M89e6e nxx )22zxl hmkf and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bot ke2)fxn melhz96x28x tom of the incline depends on

  "The total angular momentum of a system of particle 7gifpnstf:3 3qw6xt9 i 2pux6s changes when a net external force acts tifi6x9 n:x pt63 qf2gwp73suon the system." This statement is

  In what circumstances can the angular velocity of systedt o 2j2x1n,stm of particles change wit2od, jtn t21sxhout any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any fric 63mi hkk s6aqed*x:1ption which may be present. What happens over time to the Earth's angular momentum about ka*kdpie: 6qh31 xsm6 the Sun?

  The Earth moves about the Sunyr;f4i d9rcjlvkdtxg 5m9)5 5 in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about59c4 y rm;idg vdxt9j f55k)rl the Sun?

  An ice skater performs a pirouette (a fast spin) by a6j7q z-h-e/fi sl2d6qciw.c pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rota6waq/c d q js.2c--ifelizh76tion?

  An ice skater performs a pirouette (a fast spi/q g7vd5a r(azo(xd .nn) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the ao/d5d qx.avg7 anrz( (xis of rotation?

  An ice skater performs a pirouet5-gsogp; epqf*7p1ic1;w tke te (a fast spin) by pulling in his outstretched arms close to his body. What hapogqsw f g1p;k 1-pc;7ete*5i ppens to his moment of inertia about the axis of rotation?

State the law of conser;- i3tqhux xr5mvra..vation of angular momentum.

  What arc length does the Earth travel in a threv jmcw*g52 a gli3u- o(a)1wsie month period in its nearly circular orbit about the Sugm*cv3sow-1) g l awii2u(j5a n with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. z+iv)4 p e7go,70hbqv x 6egpu What distance does the tip of the second he+bv ) p 0uevg,z7xio6hp 47qgand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions p/*ceg0h7 o*k; ti fib;tphd+xer minute equivalent to?

  A bicycle wheel rotates uniformly through 2jq 2wsvu u:2 *jo00+8hh: h9gfevcgw m.0 revolutions in 4.0 s. What is the s+f02 ge9vjmcu8 w*o2h:jq 0u wh:vhg frequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0b *v,-( .m0eaq /e qj jcg9issv0vwtw0.40 kHz. The period of its rotationgc 90tsbqwe*( j,j me0w /s- v.0qvvai is

  A phonograph record rotates at 45 rpm. Through what angle does it vvl b51 5knwh2 *pyun*turn in 0.20 sv*n ynhkl 2u*w 15bpv5?

  A wheel of diameter 26vld2,; *ys2n uao *ryl cm turns at 1500 rpm. How far will a point on the outer rim move in 2.1 u;y,s2v r *ally*n2ods?

  A bicycle wheel rotates uniformly thr7t :4iqt -gcnjough 2.0 revolutions in 4.0 s. What is the average angj i: 47gn-tqctular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 r06g gx 4pzb 07wf7ah7eflg2vrevolutions in 4.0 s. What is the linear spegg7g7l02brff p6h7ze xvw4a 0ed of a point 0.10 m from the center of the wheel?

  A cable car at a ski f9 lko+ k2br*hnoz2cst * 2uh-resort carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pullko*n cr9*z f -khl2uo 2b2st+hey with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular s,y1c ahi6d2um 9z(m cje)jwl9peed of 2.0 rad/s. What is the linear speed of a point on the wheel's rile d)jw,9uy m 6ja 12ic9hzmc(m?

  The cutting cord on a g f7 iv vas.0(.kzv,czk+xi+dlas-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate li.k,vvkcsa +divi+ z7 (zl0x.fnear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant2jgbzm)eo1 xf0 vm 35 k1i qmiyxc,77w angular speed of 2.0 rad/s. What is the centripetal,z)mimb03 f 57qg xciem7o ky x1vw21j acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicyclcq.4xe8l/c:yo u y 2ppe wheel of diameter 70.0 c p/2uqylc.8:pcyox 4em when the bike is moving 8.00 m/s?

  How many revolutions -3qbd*7zen.i j h4g iqper minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gra-4bngie 7hzj.diq* q3 vity of $9.80 \; m/s^2$?

  A car is negotiating a flat cikwd-3+cpqr+u-2m*nqzu i9b yi: p 9pg rcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (prov9 r3-c -qiuk:*+bgpqw+u 9mi 2ydn pzpided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circa,+zp n- xg,0+te5zyfs(bpevy7mc a: ular curve of radius 50 m with a speed of 20 m/s. The maximum ce +by(+:z5cpts0g p 7m-f,, eneyxaazvntripetal force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.750- 4/i (/vmh. /jjldxo.9gdhlwl(o w8dim string, is whirled around in a smooth level table. If the maximum tension that the string mlw8.di.l 4/ h(xjo/( 9ligd dj/howvcan withstand is 250 N, then what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm roll:ai /n 6;iaslceq2) a r/yod7ms without slipping 10 m down a) diq:r;al/nmoi7 a 2 6scey/a lane at 4.3 m/s.
(a) Calculate the angular displacement of the bowling ball.   rad ( fill in numbers only)
(b) Calculate the angular velocity of the bowling ball   rad/s ( fill in numbers only)
(c) Calculate the radial acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)
(d) Calculate the tangential acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)

  A wheel accelerates with a 53rw an 5sde a k6o9 6l(pmjg*xji1z5fconstant angular acceleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angle the wheel rotates through in 2.0 s?

  A wheel accelerates p- 4 p7m k(m)+doof.5i1jly gelf1cyowith a constant angular acceleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angular velocity at t = 2.0 s?

  How many radians does a 0.300-m radius auto,cb.e j+ hx lawg26-wkmobile tire rotate after starting from rest and ac wjgkwlabx+c2. he 6-,celerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration orh / 3,mjpuioe1b:kf(f $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a constant angular*jnw n,n/-duu accelerajnudnnw /*u, -tion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rak 2; ki2+ugh mk.hope,d/s while turning through 2.0 revolutions. What is the avhkg2 2i,kpho+ uk .e;merage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over-s cnx0u ,;s -6 7riw5ttojsnh a distance of 115 5 js;7x ochsu s-i 6nrtt,0n-wm. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows j6.a6t yt 5cgedown uniformly from 8.40 m/s to rest over a distance of 115 m.5ty a6t 6cj.ge What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 mi0 liy(46dbj aivx:.zo +iq0g/s to rest over a distance of 115 m. How long does it take for a.qgd0oi l +yizjb( 0ix:64v ithe wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 369i wjx+zh,9;yi j 0r2+d lybmh00 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleratb9;9h0i l yxri y ,jdjhzm+2+wion before coming to rest.
(a) Determine the initial angular speed of the centrifuge.    $rad/s$
(b) Determine the angle (in radians) through which the centrifuge rotates before coming to rest.    $rad$
(c) Calculate the constant angular acceleration of the centrifuge.    $rad/s^2$
(d) Calculate the time necessary for the centrifuge to come to rest.    $s$

  The bolts on a car wheel require tightening to a torque of 90 Nm. Ir1y 3m sjzyl .r:5zpl0f a 30 cm long wrench is used, what is the magnituder0.ys l:m5lz 3zpy1rj of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tighten hkc+ijo gb72* 3yc1kso 2x9iuing to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force ukioo jhyscbik 1+9*g2x73c2applied at $53^{\circ}$ to the wrench?

  A wheel with moment of 6agn-(if 0cbl 4,p ashinertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as foll6h8m4;2 sh juhshk5fgows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia abou2jgsf ukhhh;68 hsm45t the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis th cye5cow qdwg8 n0 7y:uve+25tought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) 0dvgeuey 5wy8o q+ cw5n7 t2c:What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivotedwc*,23o7cii hf3l i lg about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. How many radians does the cylinder rotate throiwcili, *7332olgf chugh in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at onz r:u:sh0 ehh/e end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is released? (The moment of inertia of a rod about on heu/z :s:r0hhe end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and )b0c ,kzcqv-xmass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangen-cc0 q,zk) vbxtially to a sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrappe,mc)t b5w rkbarf3 3+ld around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pull crb3m53wbl,t kfr+a)ey?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pullex ry0 :zx;d ctf3n7ij7y of mass 7.07 kg and radius 66.0 c ic0z t;7rj7f d3:xxnym. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy lmei-98 njyr+. If it is required to store $1.00 \times 10^{6} \; J$ of energy when rotating at 400 rad/s, what is the moment of inertial of the wheel in $kgm^{2}$?

  A wheel of moment of inerti;ibvp:riqcqkbub-o w + ;o:, 4or8;cra of $5.00 \; kgm^{2}$ starts from rest and accelerates under a constant torque of 3.00 Nm for 8.00 s. What is the wheel's rotational kinetic energy at the end of 8.00 s?

  A solid sphere of mass 1.0 kg and radius 0.010 m startss 2 :v,/q(xc ndaj5dxz from rest and rolls without slipping down a 1.0-m high inclined plane. What djnxx (q,zc5svd:/ a2 is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and r34hu ug2nvc.po5z u+i)w0m yj adius 0.010 m rolls with a speed of 10 m/s. Hoz+cjiwvop342n h 5) u yu.ug0mw high up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from (**ooqha9 go*f;b6ms e8 cbeu6dr.kn rest and allowed to roll down an inclined pland*;ro oon*fe6a8*k(q ebsh. m 6guc9 be. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5nd3l3e4 sob: tg4pua7zxff 2 p6e8q .g kg and radius 15 cm rolls without slipping down a 35e inc tp:dxfluf2.e paenb 46qs3gz8 o 7g34line that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is given by $I = (2/5)MR^2$.
(a) Calculate the linear speed of the sphere when it reaches the bottom of the incline.
(b) Determine the angular speed of the sphere at the bottom of the incline.
(c) Does the linear speed depend on the radius or mass of the sphere? Does the angular speed depend on the radius or mass of the sphere?

  An object's angular momentum changes bk( wz xos5c78ky $20 \; kgm^{2}/s$ in 4.0 s. What magnitude average torque acted on this object?

  A proton of mass $1.67 \times 10^{-27} \; kg$ rotates with an angular speed of 2 x 106 rad/s in a circle of radius 0.80 m in a cyclotron. What is the orbital angular momentum of the proton?

  An ice skater has a moment oft2:rz avtjj4; inertia of $5.0 \; kgm^{2}$ when her arms are outstretched. At this time she is spinning at 3.0 revolutions per second (rps). If she pulls in her arms and decreases her moment of inertia to $2.0 \; kgm^{2}$, how fast will she be spinning?

  A figure skater rotating at 5.00 rad/s with arnxkum +3j yl0/ms extended has a moment of inertia on j/m 0xy3ulk+f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?