Angular displacement is usuall .+(k zpoti(ol w-;bm*8o bcnly express in units of

  Angular velocity is expressed -gt donro itt;ik )6/ixd409gk8y f* lin units of

  Angular acceleration is ej+f(q0hcgs2hq u wjm(a 9+l0z xpressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constanzx(j.ya ir(7qqx(k(3nrikof x21 b qg h+(x2vt rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater anguk3vq (( x+in (b.fgxr2jq7 qhok 2zxa (y1(xrilar displacement?

  A boy and a girl are riding on a merry-go-round 2f l4-erbllp2zs8 ampt +o9( zwhich is turning at a constant rate. The boy is near the outer edge, and the girll+lms p 924ob(lez2af r8-pt z is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at zre o5(2su n1ea constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the es2zu n(e51ro greater linear speed?

  A boy and a girl are riding a merry-go-round which is turnvc*8/cbj /gz7 gom2kks7v44qcv t3hbing at a constant rate. The boy is near the outer edgekbh/47os3kv jggz q/cc42 c7tv 8b *mv, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a conse36vkr4ip.c pgk9mo w9 .lak+ tant rate. The boy is near the outer edge, while the girl is closer to the center. ivk3wkpprmk49 go.+9. la ec6 Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurat 45j i3ubftkx6e statemu 4f5tbi63jkxent?

  Rolling without slipping zeq iye.)ko4gh u02q:;ivjk8 depends on

  Two equal forces are applied to dapip* 9:ov-y6 ivgd i(f9cf:a door. The first force is applied at the midpoint of the door; the second force is applied at th *po:fy9:ia i96f vdg-cdivp(e 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. Tu k*9jsu)aw86l soz l2he first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force e2z aj*usw u98 ols)lk6xerts the greater torque?

  Two forces are appli; v;6q*wfmr:txib ;pfed to a doorknob, perpendicular to the door. The first force is twice as 6;ftm*rvp wq;fxi;b:large as 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 x)xuter t9 :;n kfrd7,to changes in rotation ,x7krtfxt)r;ud:e9n?

  Consider two uniform solid spheres where both have the same dg4 c.n pi7sen7iameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that opsni74e. c7gnf the smaller moment of inertia is

  Two uniform solid spheres have x bap*, zo6egw)be z;1the same mass, but one has twice the radius of the other. The ratio of the la ;z bwpe)1,z gxo*ea6brger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twicewg4 (d9:mx3qra 5h xvj the mass and twice the diameter of the other. :3jdw4xaq xg(rm5 h9 v The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased tttr*ig4*e 19vqhre 3k o 2M and 3R, what happens to the sphere's moment of inertia about a central39 te1*rk*qv hit 4egr axis?

  If a constant net torque is applied to y9*i f.x(nm7 tqwpgp6an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0nkn::lg+c;x i .5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kineti+g clxikn:;n: c energy is

  Consider a motorcycle ofz-todyflwj(u r:n 6g 0dr-(;o mass 150 kg, one wheel of which has a mass of 10 kg and 06gdoltr;ny- wz -u( o:f(drja radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere ofpq1q9.h()yd g3s8e0uut:(jsd qlau z mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of 8.ge)ju:h(9u psqzqqy( dalsdu03t 1the incline depends on

  Suppose a solid spher :urtj2r3pf9/jzc db.8;peire of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of 3r 9r;p fei8:/.ct jbp zrj2duthe sphere at the bottom of the incline depends on

  "The total angular momentum of s/bms cy;w52a -yg f.ma system of particles changes when a net external force acts on the system." This statement is2w;f5 sc-y msm/g. aby

  In what circumstances can the angular velocity of serew zy.4kq8t. y2qs :ystem of particles change without any change in the system's angularqe8ers q.y24.kyt w:z momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which n vm4(a8scmzdbtnq:rg89 6qly7 v ) v5may be present. What happens over time to the Earth's angular momentum about the Sun?vq lb58t yq8d6n 7mvs crga4( 9)vnmz:

  The Earth moves about the Sun in an3ox:fxu0zz * n elliptical orbit. As the Earth moves closezxuf*xoz: 0n3 to the Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling i n3aru7ov( 8htn his outstretched arms close to his body. What happens to his angular momentum about the axis o 3torv(nh8u a7f rotation?

  An ice skater performs a pirouette (a fast spin) by p5ozxf0 g 1ihn/ulling in his outstretched arms close to his body. What happens to his rotational kinetic energy hxzo 1/50fnigabout the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling imgnpjy4.d.obd we; xe)n4 3u*n his outstretched arms close to his body. What happens to his moment ofd.wu p*;ybx djem34.nn)e4 o g inertia about the axis of rotation?

State the law of conservation of anw7 u rv()ge: 51isgl+ eizxr)i q2u0ydgular momentum.

  What arc length does the Earth travel in a three month period in its nearly i5nlu tq2 2gf(. 7gdhu)8dy;n ofqy)acirculu 7ultdg ;gfa qin2 d8y. )h(y5q2)onfar orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. Wh0 oonxwkew) b/l/)hj(at distance does the tip of the second hand sweep through in 3 minutes /0o xlw eh/bk()on j)wand 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent to?+/po).amegg v : )7zmht klz7b;j5nbu

  A bicycle wheel rotates uniformly through 2.0 revolul x rl:+q*i8myp(hjj9tions in 4.0 s. What is the frequency of*qjhl8( 9+xr: ljiymp the wheel's rotation?

  A pulsar (a rotating neutrecubty,0ph 77aq0 )u t-exuw 9m ks0e:on star) emits pulses at a frequency of 0.40 kHz. The period of its rotation 9-m7x0qsy7c 0pbk :0huawee) ute,tuis

  A phonograph record rotates at 45 rpdb7v khad,+ ub. :do)tmj m.6im. Through what angle does it turn in 0.20 .hoau+d.6: mmd vi)dt,j7 kbbs?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a pob 8yyj/6hmr 4fint on the outer rim move ifmby8/6y4h rj n 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.m )d(wzj ii b/xx*2ca 9w;be 1zs)dx6d What is the average angu2 xz(cajb d;db6d w)m1x/*wi9zs)iexlar speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions ityc.r9hv9 * bvkgagc p+nr*+0 n 4.0 s. What is the linear speed of a point 0.10 m from the center ycg*p+avtr9rbkv*+ 9.cg 0h nof the wheel?

  A cable car at a ski resoyp8ex:s -y1c99dfdbp rt carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assumibxy-y8 fe c9dds19:ppng 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( rjl;e awcud3 7(gv,p is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed ;l(3(gwcra7 vp deu,jof a point on the wheel's rim?

  The cutting cord on a gas-powered weed cuttewk. eh d. 2ncdyp)a1a3r is 0.16 m in length. If the motor rotates at the rate of 20 rev/.d n3a.h 1ywed 2k)apcs, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.))n6wu br-ezy2v (qyvzke5 1a0 m is rotating with a constant angular speed of 2.0 rad/s. What is the centripetal accele)()v zweq5rayb12 ye k vu6-znration of a point on the wheel's rim?

  What is the centripeta fvct*8 p19+*wutxugpl acceleration of a point on the perimeter of a bicycle wheel of diamew9 *8p tvpgfuu1*xt+c ter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpumsia5:fw09d. t +4,s j+qzy usmry;rm) must a circular, rotating space station (r = 1000 m) rotate to produce an artifad 59+. msr0tmqu4yyij;s u: sf,+zwr icial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circulark+bupy o1z sa u +r;6f no47i1k:rs:yd curve of radius 50 m with a speed of 20 m/s. The maximum centripetal foa4 bp:rr1fzsdo n:y+iy7kk u61 u+so;rce (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radius 50 m with a si krmq4f4-w- ej :dsa;peed of 20 m/s. The maximum centripetal force (provided by stiwf-;r-ed4k 4 :ms qjaatic 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 z5v,;lt -fcdw.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mcl5d ,z -;tfwvass have if the string is not to break?

  A bowling ball of mass 7.5 kg as;cubfneer04l9u4f e c9.sw ks5+h /and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/sw+c9h e/lub 4asr sksc4ne.0u f9e5 f;.
(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 wito.:+7 h6csqqwyt: zk/e:z m hmh a constant 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 with a constant angular accel ofs+4jsn1 .p 7wcqcl8eration 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 0.3o)s j::mjk q;: )dzsec00-m radius automobile tire rotate after starting from rc:j:q;esoz dk:sjm))est and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and ho( n 7blw0y4aoas an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates w cd zomf2i29y j(.ops-ith a constant angular acceleration ofd (ozym .o29fcj-i ps2 $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0t+i e6(hm kdizxpu3 * y51.awv glao22 rad/s while turning through 2.0 revolutions. What is the average angular accelerag mtiz1e dh u6pk wy+alva 253.2oix*(tion of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to re;o::c y vj. 3alcf2vdqst over a distance of 115 m. What is:2q cf;3.vjc ly:d aov the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unif5a,v: 9 smcm,nl6caj zormly from 8.40 m/s to rest over a distance of 115 m. What is the angular acceleratm,na j:59zcv lc6sm,aion?

  A wheel of diameter of 68.0 cm slows down ;r.w+ ppj-gy;:vypy( slwh.my0j, uluniformly from 8.40 m/s to rest over a distance of 115 m. How long does ; .y:gpy(+hjlj;mw-.v,sruwp yly 0pit take for the wheel to come to the stop?

  A centrifuge in a meddy1jqo 84 qfarpdj+ g(q)l433kn 4 faiical laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angulaq8 rgad j1(f l4k)yi3pq fqanj4 d+o34r acceleration 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 to4iv8 d3,ivd-guan9r y a torque of 90 Nm. If a 30 cm long wrench i dvid3ng9uy-48,i arvs used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a oiuem;g 3h8:g 5;mr/bzx4/g2-mjmdf1s ueeb 30 cm long wrench is used, what is thef: g / 8452/r zu; -gbmsjb 3xmdhememogi1e;u magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ivxfh :zi(2jpjghb q*n7;t:.oji+* a onertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mass m is at the oonu )) 9n(j avi)gxqe*rigin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origio(nxvu) ija ng))q*9e n?

  A solid cylinder of mass 10 kg i7+rbisi41p/ k5 xq vd jmt96 yx**cqxjs pivoted about a frictionless axis thought the center O. A rope k v9 54 m*qjdxxtjbc/1qp7 6sriyix*+ 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.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pin1bl -bg52ktm r7pj9 dvoted 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 tg72l 9bndkpjr-b m51many radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially held in t )gh9syme r)3xhe horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is released? (The moment exyg ) r3)smh9of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to b )6k7utt fq7 fnpd5gx)f,ti w,e a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve nq5tf76)) pi,f7gtfu ,wk dtx, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a ro:hd5m3uz( hat j3ub.npe wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0b:3hu 5utzn3mhj a (.d cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of mhy56/hd*4j eo:ru n diass 7.07 kg and radius 66.0 cm. What 5o6ijhn:d/d e *h4 uyris the acceleration of the mass?

  A rotating flywheel can be used to store energy. If 4:w*tlkq.st t9 ;guoiit 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 inertia kyceig:o8dfp.1ww :) 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 mabl 2ucs jp 5pi)45p*uass 1.0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined pl5jp*lbu2sp 5 )u4paci ane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls w 7, lot:ml jo n3+5- p;hv,gkrmmmyc1pith a speed of 10 m/s. How high;: l1m ohgpok+ t7vc,mm5 ym-l pn3r,j 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 fiw sr5a7)(f2jswu*mm rom rest and allowed to roll down an inclin(sirw)j5*s7 2waum m fed plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.jp+ mq;f*ebc 65 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assup;f+je*mb 6qc me 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 chanm(c y rb)8sm/q9m *uotges by $20 \; kgm^{2}/s$ 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 of inertia dt .pii141cfgvwf 7*pof $5.0 \; kgm^{2}$ 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 arms wfs csdvfa1j( 6*(2d,wgp9 gvextended has a moment of inertia of gcv2,psdw (df6 ja9sv* w(g1f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?