Angular displacement is usually express in units of(qwja wyx1tk8r/ 66p b

  Angular velocity is expresse ; px5kceq(zap(r+z4tuq)-tz d in units of

  Angular acceleration is expressed y7j q :1:c+42n)rima qgo9vv4d httszin units of

  A boy and a girl are riding on a merry/q miu+h f,fvt(0i5vg -go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is clostfvfm05huqii ,v/(+ger 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 conah hvv()y;ch:6s jdj3a7goizbi6 ; +gstant rate. The boy is near the ou a3(hyhb va+h j;i 67jdi:govsg );6zcter edge, and the girl 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 a .wgeao gjtp; +4,zze 6constant rate. The boy is near the outer edge, and the girl is closer to thew+a,ep; 4ejg 6tozzg. center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turningvekm623tc1i*b 6qjn8erhw) m6c tf v4 at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the grebve6w 231qi 4*mh8vfme) nctc6kr6j t ater centripetal acceleration?

  A boy and a girl are riding a /6dxpwy nimz: sg+)*u merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to th6ds/gzx*:w)+ip numy e center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of tv93 -jrqq e5qnhe following is an accurate statem -rev35q9 jqnqent?

  Rolling without slipping depen;emynt n od9xycsl c8f7 (s*3,ds on

  Two equal forces are applied to +mfyn)ipbb3hb7q a/sj:x6dy r)7 e s 4a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the7y6x r ibd:) as e/j4qpn 7+b)bshm3yf door. Which force exerts the greater torque?

  Two equal forces are applied to a d3rp /vvbuz s.)oor at the doorknob. The first force is applied p).v zbv3su/ prerpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular/y-s.z ettc0 o 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 second t.yoc0ze -/st is

  What is the quantity used ( e5 p8zqe8o:zt*h .nn/fvmvn to measure an object's resistance to changes in rotatih mvnf/ etop885 *(n:nvzqez.on?

  Consider two uniform solid spheres where both have the same diameter, but opl m:t9ll 8r .tkkf8r+ne has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of i89k+llr8 krl t:t.pfm nertia is

  Two uniform solid spheres h5j3:: ifbxa;- kifvykdpu +0nave the same mass, but one has twice the radius of the other. The ratio of t f: 5;bnxi dp:0j 3fuiv-+kykahe larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass an5cfd opyz -;75d8 6p(agka sayd twice the diameter of the other. The ratio of the larger moment of inery gp z-;7oy(6paasf58cdak d5 tia to that of the smaller moment of inertia is

  A uniform solid sphere has mass Mj(z7xp,:o*)stwnvj m zfhv;/ and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia ajsj v()*x ,;/nz:twpzhvf 7mobout a central axis?

  If a constant net torque is applied to an g gk5f3,nx bt.object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2 6of4t4j: gh3t2xqlss. If this cylinder rolls withgsx4 l:qh4s3ojf6 2tt out slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 i)*ob u4a 2loxkg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kineti*o)b24 ux olaic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radiuslt -7befsjr gz73fl 07 R rolls without slipping down an inclined plane starting from rest. The linear velocity of the spherb-7 sgfl0jft3 r7lz7e e at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R,rgudr )(e +sej 3wyt; rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of t ;erys+u r,ed)3wtj(g he incline depends on

  "The total angular momentum of a system of pa)(bt,a6przx , q +dxpirticles changes when a net external force acts on the system." Tt,p dbprizq)(,6xax +his statement is

  In what circumstances can the angular velocity of system of particlap 4 gi8uu7ro 19qwh(res change without any change in the system's angulia17h 9 w g8oru(uqrp4ar momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction w-c9 efg4jssx1hich may be present. What happens over time to the 1s9c-g4js fex Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Eartp ejdd3 yeu*cz a76j;.h moves close to the Sun, then whic;3jc *7e. j d6epyuzadh of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirydz*kh bqo*yaxdvis* tcq:v,3 k4t 3 178hsa1ouette (a fast spin) by pulling in his outstretched arms clit doaa4vh 1*vsqb*73 8yt d:kkqxh3,1yz* scose to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstya65+o4 xrl ox8jds3(ywq un/ xc)wq7 retched arms close to his body. What 3lnrwso87q)ac x y5x qj4/wud+xy6o( happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirou-q3godr p yk9:ette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the 3rqg d9o:yp-kaxis of rotation?

State the law of conservation of angular momentuu7 u 34(ne17 myssjhlim.

  What arc length does the Earth (szlwpxf+wwq)9 g 1z40i v bv:travel in a three month period in its nearly circular orbit about the Sun wii)0x4+ glwvpwz(b1 wfq9 v:zsth a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distan0 wa q7-f (nrom/vp.yvl4es8vce does the tip of the second hand sweep through in 3 minutes 7qvr/.mva8w04vf oplsn(e - y and 45 seconds?

  How many rad/s is 25 revolutions per minlwa5i:gs8mm*2i; zy gm.r5*kqr jzt4 c*6pt yute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.kmum q+g. 3pwcg6+bl- 0 s. What is the frequency of the wheel's rotatio+wu3gk6- bm. c mq+plgn?

  A pulsar (a rotating neuu; 8z fpqst3g*hscw ,/tron star) emits pulses at a frequency of 0.40 kHz. The period of its rotatig*s3/,hq8 c;szt fup won is

  A phonograph record rotates at 45 rpm. Through what angle does it turn pjzoe(xo5n;jyu/1. t 3 1 el-e+i bovhin 0.20 iujoy; pe1x/3h je(z-vo+ 5onte . 1bls?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a pointl/xoxr 1w32irm( d 7fu on the outer rim move in dxl2wr/r7 o1i (mufx 32.1 s?

  A bicycle wheel rotates uniformly throughb5kv09m; izb+xoq,lp 2.0 revolutions in 4.0 s. What is the average angular speed ,b +oxv;9l0mbiqp zk5of the wheel?

  A bicycle wheel rotates-ds 86v 3m*bmun .hxjx uniformly through 2.0 revolutions in 4.0 s. What is the linea hxmn*v-.sum 8dj63xbr speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. 3jv7oiuz* wo-g1w2vm The cable which moves the car is driven by a pulley with diametv o2wwim7-zju 31*gvoer 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 rotatin8590sb3-okkzwi t bqkg with a constant angular speed of 2.0 rad/s. What is the linear speed of a pointbk bk9sk0qo w5iz -83t on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.n2xc2ui; w xq516 m in length. If the motor rotates at the rate 2n2cqxwu ;ix 5of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speep2pk 3x96 3ruit;jtc8 + xfhp+bnw +pd;cvv6 zd of 2.0 rad/s. What xb8 u;jt3+r62vi ;xk9ft+p+cwp3v hznpd 6 pcis the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a poin b-t1. l-5sir+u 0hzvbc j5psq le6y7wt on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is mo.esqtwv j-565 70hzirlbup+bl-yc1sving 8.00 m/s?

  How many revolutions per minute (rpoxi6)hx8 wir +c-r9d w+dbef/m) must a circular, rotating space station (r = f+x8cw-erhi9)xd b+/ 6wrio d 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a fle qg s1 bhd5hh95nd1d-at circular curve of radius 50 m with a speed of 20 m/s. hn 5 egqbhhdds-d9115 The maximum centripetal force (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 npnb4u1,aj i7f14vlw 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) isf an4vwj plb7ui141n, $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attachv89ck0ih: pw/ifo u5/d*/huj n ycwr/ed 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 linear speed cap9h*w0i / /kcu/58vnu djcw:/y io fhrn the mass have if the string is not to break?

  A bowling ball of mass 7 5p 2zbpv.:vk0y0cy*/ vxpu la.5 kg and radius 9.0 cm rolls without slipping 10 m down a l:0y.zb5 yaup2l pp/vvv c k0*xane 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 constant angular accelerai4sis5 +u uda0g 6(3b*mgvz/dr (dgcxtion 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 constak;m m 3ykrf40r(cthe5 nt 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 automobile tire rotate after starting )-h0l ffw ;al x9aq(olfrom rest and accelerating at a conhx)a ;(lowq0ffla l 9-stant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an tri*x :y1l4+v/ aatt qangular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating dzxgr1bj *qc (y/ )3abat 20 rad/s decelerates with a constant angular accelerabaz /rjbq(g cyx31*d )tion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest m4. /oxdsx60 a3+rf 3)zblpmqe1(q n6vuh ebdand reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angulaz4)f1xu vambo60n x33(.qhd mspq+/6de e lbrr acceleration of the wheel?

  A wheel of diameter of 68.0 cdk-s( or:ne/t ukl2 h0m slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total /el ksdh:(uokn -2t 0rnumber of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unifor s3h5jvk44qqomly from 8.40 m/s to rest over a distance of 115 m. What i4 4h5kq svj3oqs the angular acceleration?

  A wheel of diameter of 68.m+:nec h;h1 sr5rxnmik:-r)e 0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. Hkh;emrh n5c-m :r) nr:xe +1isow long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotat5zaf,rd 1p a,kes at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration rd1a,k5f,p z abefore 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*u ouzy4 d.xegk5(yh + Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when th gouhu (xy4zykd+* 5.ee force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a tgcw1tnr f8od ;7f e/s1 wn8g mc3-cr-borque of 90 Nm. If a 30 cm long wrench is used, wha;sgecnb cfcwrt8r- - f1mw n73o1dg 8/t is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ife4 ,hv (- izsqgtjs92nertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modelb ukxr1e,:lh2,f f3u ked as follows: mass m is at the origin, mass 2m is at x = a, and, masxe,fl,fr k2kbh1 u3u:s 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought fjl9un r q69s4 m3+cod1swc ki(ynt73the center O. A rope wrapped around the outer radius 1o 3+c9 j9mqi3ss7kn (rfy4un wdc6tlR1 = 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 pivoted about a frictioe)his8 ly1 u krrd-au4s+z5 8jnless 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 through in the first 5.0 k yr-hdu i ej58sls81a4urz)+seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. xzq(:fmg1 / golwug8r.p; )gm The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular accelf8gzl/1q;gmg . px( wmgo):ur eration as it is released? (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 andl;sq m0cqg.m; 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 achi0mc q ;mq;.lsgeve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrappedwgvm)qy 95dhq/j: a-tl/gs u6 around a frictionless disk pulley of mass 7.07 kgs6y:gm 5u twhg a/j-lq)dv/q9 and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped aroun4viiul y:bds ;+ai 6*yd a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the 4+*bids;6lvy uyaii: mass?

  A rotating flywheel can be used wi t9tfimft )-0 ;sf(yto store energy. 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 inertia/u83pch5e o.3vy ni9nunf,yu8ol lhha5 -g z) 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 u2,bx;zu l 5svstarts from rest and rolls without slipping down a 1.0-m high inclined plane. What is theu vz2;bs, 5uxl speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg 14fl 4ktd(y xe l;o8kyand radius 0.010 m rolls with a speed of 10 m/s. How high u 4(yxyte8l fok4ld k1;p 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 rudbv ,o.a3 63wq+speueleased from rest and allowed to roll down an inclined plane. How fue, puq+w obd3av3.s6ast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm roikg(41 x2 xtaills without slipping down a 35e incline that is 7.0i agx(k14ixt2 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 b2oghv4 fd),e,k3.twqo wl/ wb)) lpoxy $20 \; kgm^{2}/s$ 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 vypdj;(z. 6bjmoment 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 rotating at ak /i7k/4h6t em ckiu8 fps3*f5.00 rad/s with arms extended has a moment of inertia7es kck4h/*/86im ka 3f fuipt 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?