Angular displacement is u);0 vh moq8wmv0vff/qsually express in units of

  Angular velocity is ex1f )7c (ayro*r0hpst u(fmpk. pressed in units of

  Angular acceleration is expressed in7w5i s xn0r+hd units of

  A boy and a girl are riding on a merry-go-r rco,2n6h1t6f(d) av8qsg fipound which is turning at a constant rate. The boy is near the outer edge, and the girl fihpt,g6o cf6sd (8r 1v2nqa) is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-goq:f(0.pccd qn -round which is turning at a constant rate. The boy is near the outer edge, and the q cnfd(cp :.0qgirl is closer to the center. Who has the greater angular speed?

  A boy and a girl are -l.w5xgywxyu/n) p r;riding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the cenr.xp-un ; )w/gxl5y wyter. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning a dkm(wk;qn03m k;jc0zt a constant rate. The boy is near the outer edge, while the girl is closer to the center. Whn3m0kcz(dk;kj q0m ; wo has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-rounz 7pe6.j/f2lg khckxo1b(y q6 d which is turning at a constant rate. The boy is near thez.lc7f(p g bkyo qh/6kex6j 12 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 the celd r3t6u)))y/c5 lhusst2,.m o ttq following is an accurate statement2l3 , /)h6c)el)tscm ur q .s5uydttot?

  Rolling without slipping,mk vkco3rtnye0x1/ 2 depends on

  Two equal forces are applie-h71s**we wyxqh t8sld to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. By-xhw e*q*71wt8 lsshoth forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknocn),fj -jc ok*n4bnt y0fo x95b. The first force is applied perpendicular to the door; the second force is applied at 30e ton4f- bn5otxjco,*k )c fyj0n9 the plane of the door. Which force exerts the greater torque?

  Two forces are applied t*,ym4*ij i o/q5lvobgo a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the sec4 *yijqvo5/gbo*, mli ond is

  What is the quantity used to measure an object's resistance tou1;fl+o hc r*tso2ch + changes in rotatic2s+hol r +f;uh1*t coon?

  Consider two uniform solid spheres where both have the s7k/.-mm0 x .gmin3 lg awfjzb*ame diameter, but one has twice the ml0mkn3g/ f i *mj7x-m.zg b.waass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the 4u m4oqvzg*f8q860kydy d (u iradius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphu8(qfk m 8oyzuv0ygd*64d iq4ere is

  Consider two uniform soligf+(vkcibx m bj 1yr.x3zr eqa.,29 f:d spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia j +e:r3xzyx1b9q r.f ,ikacv .f2m( bgto that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increaseb xl9)*kxfmh qx2k1 h:d to 2M and 3R, what happens to the sphere's moment of i )xxq1kx fbh9h 2*:kmlnertia about a central axis?

  If a constant net torque is applied to an object, that objectge*i(0ihz jh1 will

  The moment of inertia of a solid cylinder about its axis is gi dbcd52 al(y,v5 yxbm)ven by 0.5 MR2. If this cylinder rolls without slipping, the ratio of bl55)yycxm(vd,b2 a dits rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a massu2zluh ,h:- )hk3to cg of 10 kg and a 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? co,hkhzhg )3ut2ul: - Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls withoujfz9 ,/rygn oursy7i5j; 9gu/t slipping down an inclynrig9u/ 57 y ozr9/;jj ,gfusined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of massds e(2am74khl w51k3t :vnjbb M and radius R rolls without slipping down an inclined plane starting from k3jb7kevt5w (a24mnd:1blsh rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net tr0v3x)fz rn /external force acts on the r0 v/rxf )zn3tsystem." This statement is

  In what circumstances can the angular velocity of systemz0zwq phw:2ymep4*(t;myv c2u9 / m+dphs* tg of particles change without any change in the system's angue9p*mpv(yw;u:y0h t+2zsh*p4/gt m 2d zc wqmlar momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which may l7-jvc flwp ,+be present. cll-wv7j f,p+ What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an el z8qov1awem lthq(9 5*liptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Eartmh89 1wovzet*q(aq5 lh about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchedxt:37sfm; p*+2, sx gd c)bptkxdo8bp arms close to his body. Wd,) mfgbt7ct *b k;2sxsx 8pppo x:3d+hat happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullin-o seuh7x +sa vkr,g.;g in his outstretched arms close to his body. What happens to his rotational kinetic -x+vae ,7.kg; osrush energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by p jet9+llz9 aq9ulling in his outstretched arms close to his body. 9z lelatq9j+9 What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular moment0wlix4yg d(5/t 5p phsum.

  What arc length does the Earth travel in a q;a/fs 2gzs7vp3xpb: three month period in its nearly circul :/3qvzfap7xs2 gbps; ar orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a cls6p2w8jws 5ao ie)vb3 ock has a length of 0.30 m. What distance does the tip of the second hand sweep throughvs6s3 2 )w ob8a5epjiw in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions ad b/d)n8cpg1mn-f lr-x9h7z per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revop8-k25xgvn x qlutions in 4.0 s. What is the frequency of the wheel's rotationpn x-kv x8gq25?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0ezyd3lg-xt4j. is-cdolhjj (cg-l .nx)m ; ;).40 kHz. The period of its rotation i 3xl.g( --es;xj ) )h;cygl.4cndzlmid o-jj ts

  A phonograph record rotates at 45 rpm. Through what angle does it turn in :agqipmz*z jvl5( aed-txc5hw 8a0m3 f))x1s0.20 s?)m5 c 8-tx p ia(qzlw :3je*0gxvhafsaz5 m)1d

  A wheel of diameter 26 cm turns at 1500q t4kl ;afr8(ff(zd4r rpm. How far will a point on the outer rim move in 2.1dk(rt razf(q44l8f; f s?

  A bicycle wheel rotates uniformly through 2.0 revolutions imqkk+ o39b*tgdul 4c- n 4.0 s. What is the au ctbodg+4qk*-l39kmverage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolut.6iah 6kb ezh0ions in 4.0 s. What is the linear speed of a point 0.10 m fh z66.khb0 iaerom the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6bb2h14(j r *wdp ,a9wfvr:mg7p t/fpr.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slipa 41pgdf hr9/tf r*2p 7,wvm:rjp(bwbpage, 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 i)8bf m7iyy wzl 9n vior..u.3speed of 2.0 rad/s. b w38.zi nm7ir.filyuo v9y.)What is the linear speed of a point on the wheel's rim?

  The cutting cord on a jnk.4 bq.3/ ,yh u,jgvd ((swk qc.chnn8lj(lgas-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate libu(j jncd4qkgy8k3.lh c .qwlsnv, (.nh( /,jnear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with anf u5,z;)bxsi constant angular speed of 2.0 rad/s. What is the centripetal accelerats 5)x; zfni,ubion of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicy mxns6s +f9zcbco:voe,/y4e: m6o*p acle wheel of diameter 70.0 cm when the bi fyv49 :+6:*b6mm oczp a,esoocsen/xke is moving 8.00 m/s?

  How many revolutions per minute (rpm)s+pr*)cujj* bk :erpr98 r v/d must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravity of rrj:cd*kv pe j)b* +/rup9r8s$9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m w gy abffxm8zp32(r/ v.8 sx4emith a speed of 20 m/s. The maximum centripetal force (provideg 3 mfy8xp4x2b8 f(/zr.asmv ed 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 wit) 1s7skp08upek9 b)sqcdzg o.h a speed of 20 m/s. The maximum centripetal force (provided by static fpk s1p s.g)9b8)u7qcdk0 osze riction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, att4uv olyu91 mn:a1b+yfached to the end of a 0.750-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 li 1umnu+boy1lyf4:av 9near 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 rolls without slipping 10 m doykut rzbew w 29u1/p61uo(md1 wn a lane at 4b 1wd1 we2(uz mpou/1 9ukry6t.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 yez:gj * s cz3frk6n:6a 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 constanx o7bt04- rbtzo:d m6/;ygtf ft 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 automobico g i):/eye4ebfwtc.e ud 7:,y0wr 5rle tire rotate after starting from rest and accelerating at a constant angular accelery0ucwdeee:4c7, )e: w/ro f5.r tbigyation of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angki e4tvlk;cq )p87dt6 (e .jn0judya 2ular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rarmw)9h j2jh(kd/s decelerates with a constant angular accelerat(hkj9mw j )hr2ion 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 rad/s wn47exuq *5pqmq02 l(jzacm( thile turning throzpmqjtq4* m (q(cul70xe2 a5 nugh 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slofyzw29p lu (3fbp e+p;ws down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotatwppe+y(;9 2pbf fluz3es in coming to rest?

  A wheel of diameter of 68.0 cm slows down un/1 1iclbwn +ujiformly from 8.40 m/s to rest over a distance of 115 m. Wu wlcnib/1+ j1hat is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniex mf)s8sp -q5formly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel tox8smef s)q5p- come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/sk r7..9mv. 8zjjlmj gmin. Whengmsr. l9.jmzjj. kv87 switched off, it rotates 50.0 times at a constant angular 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 to a torque of 90 Nm. 5l, c h,lyieuj17kr, :/xqpf n If a 30 cm long wrench is used,1q l,5pyc,kr nu iex/,lhj:f7 what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening uptd5/ 6 th z-ioig-dw4i ju/2to a torque of 90 Nm. If a 30 cm long wrench is us4ugoz5 dt 6/idh juwpit-/-2ied, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner/6 4-doyob e* h o*(e,eonzipmtia $3.00 \; kgm^{2}$ 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 tj wsy750eo sm5he origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What iym5e50s w7j oss the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axisl,5 gun*q hjx ;pqt:-x thought the center O. A rope wrapped around the outer r5gxx:jlqq tp, ;-nh u*adius 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 k2g ;7 9ewm hzzo4feu5 okev :2mw,hitd;1qsa5g is pivoted 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 dowd7uww;1t 25;e g4h,hevfm9z2sm:aekzoqi o5nward. How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod isjwdq9t7 7 *ttf hinged at one 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 releadf*79qtjtw t7sed? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 k t7gc ssb0q*nbjn4+3pu. 2ybig. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radius 4usisyp0bq+b n23*t n 7bjgc4..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 wrapped around a frictionless disk pu. w7mga05 .kk4:kzntqm vqw,glley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the p z ..70qnwmk4,q:5mkagvwkt gulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of mass)8pyuu+hqoyomfbvd707 y z-7 7.07 kg and radius 66.0 cm. What 7-yhob 0) q+umfvo udp7z8y7y is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is+pjdedpc ; y4h6-a14hxmz(x w 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 o(mka6mexuphe (wq +6/f $5.00 \; kgm^{2}$ 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 3 c. g7*x6ieh rwnlshz t21)y16zli qnstarts from rest and rolls without slipping down a 1.0-m high inclined plane1le7 n)cz1izs*n6ti r w.y3h2hlgq x6 . What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and+7ea jwc1qiqx0evl 2 5 radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming toc ie+51qx wla702jq ve rest?

  A hoop of radius 0.50 m and a mass of 0.pz7rj:t6sx khh ,d;k;2vw w-yuhde2;20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical d y ;x,jv 2s6krp;dh;zkh2d7 ewhtu -:wistance of 3.0 m?

A solid sphere of mass 1.5 kg and radl)pgc1 a1l sq1ius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is 1p a1q 1gs)cllgiven 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 mome4o.y )c2ilp zfntum changes 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 mo)ncm .qz+ jz2mment of 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 rotati+ kt 24-)cwex2te;6l dczocding at 5.00 rad/s with arms extended has a moment of inerti; zt+c -4 e2d6wt)kceod2xci la of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?