Angular displacement is usua jq( 6216h2d:uxy fxtizlv yt9lly express in units of

  Angular velocity is expressli06vx ewrqq,p f8g.)s arq6 4ed in units of

  Angular acceleration is expressed in unitsc4u+5ms1 yi5lf- zkll of

  A boy and a girl are riding on a merry-go-round which is turnlg,rx0 xju :q4ing at a constant rate. The boy is near tx0l gu, jxq4r:he outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are)i k yygz3twr+m9lp m;3e5ds/ 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 center. w/ msy+zyki ;elm)5tdrp33 9g Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a cons5u2qi .z)uaty2wiw0cv (h7 dpa9 qzx*tant rate. The boy is near the outer edge, and the giz.wa zqcp 0 xi( t27hy9qa* wdv)u2u5irl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a v15gk9;enguy merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleyek9v nu 15gg;ration?

  A boy and a girl are riding a merry-go-round which is turningv zos7m+k6;et v4ou3n at a constant rate. The ;3+ v6uekns4 ot7mvz oboy 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 the following is an accurate wv7 (0temffr+ k x,op19myqw( statemen 0+7mqwfxytk mp9v(,fe1( rw ot?

  Rolling without slipping dep sjz+ s,hyro v5tid2.m-+ca*aends on

  Two equal forces are applcp/n+ 6wdi7j4 u9infeied to a door. The first force is applied at the midpoint of the door; theci nwfd /9 e4nuj+7i6p second force is 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 doorkn7vc fab4d p4py6u/+ykob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerc+upf6 v4yka7d/p4 ybts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. 0 0edt- j+7 )put5r;hrjofdmnThe first force is twice as large as the second force. The ratio of the torque of the firsotd fuj)p-enj +75;0tr0rdm h t to the torque of the second is

  What is the quantity used to measure an object's resistance to changes inm 4hy.jk70-lx,zyb:) *qesnemz9 f l m rotatiq:7. 4bsxfz j9m,z0) h*lylkenemym-on?

  Consider two uniform solid spheres where both have t//ul*jfin yssc,*e+ma ong x0)(u 8flhe same diameter, but one has twice the mass of the other. The ratio of the larger mu/*aync)flumo8 x+ *sfi0,e/ ns g(jloment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twic+ 89vyqw,wg3 zms )mdgdm-qi:e the radius of the other. The ratio of the larger sphere's moment of inertia to )g- swdzv9 q w:mm,ydg38q+ mithat of the smaller sphere is

  Consider two uniform solid spheres where one has twij*0k+bj;b,.cey1 ki)x sphiji( hrz(ce the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller momej *b c(x+z k)y is( hr0.ijpi,1bjk;ehnt of inertia is

  A uniform solid sphere ha/4a rtds tk1n5s mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment onk1 r5t4a/sdt f inertia about a central axis?

  If a constant net torque is appliedaedv/yq0xeu r:q)wb:9- w cso.l q19l to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2a)ka gk7vn)+j. If this cylinder rolls without svk 7nkj+)ga)a lipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 1f1a4; 1a:; zfg,w j7xykfor fj50 kg, one wheel of which has a mass 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 energw: ,k ff1j1r yfoa ;4axj;gf7zy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M a,o/e lynj87to vd 4c9wnd radius R rolls without slipping down an inclined plane starting from restoevw4tc/ , 89nojyld7. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls wj9rte..0 aa ihithout slipping down an inclined plane starting from rest. The a 0tj..eha ar9ingular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system os k3 440/bmk 66 zonmaqvzcvs3f particles changes when a net external force acts onzo0 v3bksm6kvqns a6cm4 z34/ the system." This statement is

  In what circumstances can the angular velocity of system of particles changpcfo /l,8nzbx )db+q3 h/ j7elq32 lipe without any change in the system's anx3q e,jz+3lnbf7lo/lch / )d p 8bipq2gular momentum?

  The Earth orbits the Sun in an elliptjkr6n1ph( jwu p)lq,q l(49mi ical orbit. Ignore any friction which may be piq6w,4lnr1lk (q9p j( hp)um jresent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun i zypzz/ 04g+vtsg7 x9pn an elliptical orbit. As the Earth moves close to the Sun, then which of the f4zg7xs z+yp t0vpz g9/ollowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouetz63e j x +fc(+dmcq;h ijhpq22te (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotam+2;( ejcp6hh3xijfdcq 2zq+ tion?

  An ice skater performs a (ta+/ bmsg1jbz ilu 8k: /wf6spirouette (a fast spin) by pulling in his outstretched arms close to hablf6 m/1 i(z/sutkgbj : s+w8is body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his oxgqd;kiwf +*(rci: m.niy1gg6e k9 i3utstretched arms close to his body. What happens to his moment of inertia about the im 3w.6;qe+1dcyx (ki igrg 9n*gi:k faxis of rotation?

State the law of conseaah*3gho 3ieytr*4(aw0 k5t1z c4pip rvation of angular momentum.

  What arc length does the Earth travel in a three mon54 qgrrmof))jn 3ydm/th period in its nearly circular orbit abou rr3nfyogjm5m)/ 4)dqt the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a ldrmch35 24mlx c;yfz0 ength of 0.30 m. What distance does the tip of the seconh05 x zf2mycdlc; rm34d hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolu1r ni 9,h(v.l*rhx/ l+tevdjutions per minute equivalent to?

  A bicycle wheel rotatesj0ibw,kg2y1w ad8. kh4- b tus uniformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel'sk14, bhw-wbug0aj dty. 8ik2s rotation?

  A pulsar (a rotating neutron star) emits pulses at nacfb*9tj j 9f1zwq++ a frequency of 0.40 kHz. The period of +9faf+j 1*jbn 9q tzwcits rotation is

  A phonograph record rotates at 45 rpm. Through what angle does6nae f:.ha9scovma 7 ic2hv+: it turn in 0.20 s?79::cva.fo c+eihvh6m2 naa s

  A wheel of diameter 26 cm tu f8w epa4yw a26r6+ht v3l, 1htv/vmdxrns at 1500 rpm. How far will a point on the outer rim move in 2. 8wew+ t /m,lar3 1yv6hd64t2fx pavvh1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is t5p1fqsf*k*y,r ywwtcvsm )ux(/2 x 8whe average angular sf/ yvsxwtp5qcwr1 8)k mf(y2 *,wx *supeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is uf7s q*or. ,-nx/ abmothe linear speed of a point 0.10 m from the c/ rn .*oo,xbas7-mfqu enter of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 kk ce-tuat 2n00m. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pullek act2u0n-t e0y 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 speed of 2.0 raz,/h/rjl1dzd d/s. What is the linear speed of a point o/jh/ lz,rdz1 dn the wheel's rim?

  The cutting cord on a uccw6/ p: dsp(gas-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/sc w/: u6pcp(sd, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a f*2hp qsv()d gconstant angular speed of 2.0 rad/s. What is the centripetal acceleration of2s d hf)*(gvpq a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimet.6agh c7 myr l55qo/p;ncuyi9 er of a bicycle wheel of diameter 70.0 c5rq.n9ouic;/ca y 6mhp 7lgy5m when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) musthpx 0up *0xabx3 cd*e/fpcs)0 a circular, rotating space station (r = 1000 m) rotate to produce an artificiaspeah*/f* 0p3upcbcd00) xxxl gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius eg7.a /kbashd) u55nu50 m with a speed of 20 m/s. The maximum centripetal force (pu5ed ns5 .ub/h ag)a7krovided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circul+n l1dc 0fas6lar curve of radius 50 m with a speed of 20 m/s. The maximum centripetal fa 0n6l1clf ds+orce (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-m string, )r.rm2 bj/;pzkg5b6kby v2b o is whirled around in a smooth level table. If the maximum tension that the string b bz/5; j2gvbp2rk6 mr oy.k)bcan 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 rolls witho ao2 b5 tfaw1gk*,5wogut slipping 10 m down a lanew5fg o t*ao 1k5,gb2aw 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 angul6zviv*tu )93nlb aw 7har 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 acceleravye 28xc; b0qtq1dkq 1tion 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 radiu qpfg)g .)vdzg72 tmar,p/u yi1 ts/,fs automobile tire rotate after starting from rest and ugf. mr2pav/zt/fg7i) t )qyp, 1g,sdaccelerating 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 ofl g.dntsz3 /xc2fjv1x c ao:lm:. e/;u $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at ,7b0ncdb ub(j 20 rad/s decelerates with a constant angular accelerat c7b,(jb d0bunion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and rxqf j0q1glpb99 i 7r+eeaches an angular speed of 6.0 rad/s while turning through 2.0 rev0jb q1eq9+x f7rgp il9olutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slj/u yx;cm-fwu5 8+ ziiows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in cominx5ij;-+uci/ 8zwuf ym g to rest?

  A wheel of diameter of 68.0 cm vut2 )tth2mif: /fk,6k .rj)7qfqlvu slows down uniformly from 8.40 m/s to rest over a distance otuhq7ku2 jv)ffr6 q.k/tm 2: )vf,l itf 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8:+rlbq1mu hm( 7*1 nvnnht/:sdyh-os.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come *dusso+n1q/v ly:b-rt 1nmm h7hhn: (to the stop?

  A centrifuge in a medical labormrcj*w5;h. ybdz u7d8atory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular 57.8 wuj*ddhz m crby;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. z:0k+r ktum+ l /e;dqa If a 30 cm long wrench is used, what +: / tk0+qldzmkue;a ris 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 ) oj95j cdf*wc30 cm longo9f5c wdj *cj) wrench is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertiaj*2pyy;3b0xq: g k tha9j 0yxi $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeledy d9qdj,1i w+c as follows: mass m is at the origin, mass 2m is at x = a, and, md1q+dw ycj9,iass 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 though5r)8f x odpn)3. y)edhbj. tbwt the center O. A rope wrapped around the outetbf)w eyrh.)p.j )xd od5 bn38r 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 pivoted about a frictionless axis n/m0ih) d*ba) ,fe. dlzi bm(qthought 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 rod.ifn mz ,ha/0dib()e b* ml)qtate 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 :tfw+6raczi08om 5ks the horizontal position, and then released as the free end is allowed to fall. What is the angulaw+i 5mcr s:t0a 6f8ozkr acceleration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to, zeu1t mq4(fx be 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 tangentially4,e1u f q(ztmx 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 wrapped around a frictionlexsc0kvu( 7 ky;iw7n8 ass disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the akk uic7;s7 y(0xwv8n pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionlessgi.e(dh d t;yyq61dl) disk pulley of mass 7.07 kg and radiustqeh i1l.dy;) (dg6yd 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to stov+* xsb 1ww,ucix5 c2pre $1.00 \times 10^{6} \; J$ 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 fse yl+s.kms. bl.80yof $5.00 \; kgm^{2}$ 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 starts from rest and ro fy)i 1bsjqxhapf)fh3ei8+ 71lls without slipping down a 1.0-m high inclined plane. Wha e ) +31fjqsy7ifhhx) bf8pai1t is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a553sz c c2qakv speed of 10 m/s. How high uas2cz5 qvkc53p 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 d(s0bjw.5vno:ahm,a b :u u7 creleased from rest and allowed to roll down an bv:ad0 75:nhmujo ,(.aucbswinclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slippid y* 5wfx(uz(-e+uj* jboj5 jtn*u(x nng down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere ib *u d x*uwxo(y( jj5nt+nz(ej5 *juf-s 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 bd6jikw 5 p39+qapn; swy $20 \; kgm^{2}/s$ 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 ofu* d, ++9bo0g6wppd ladcm8hr $5.0 \; kgm^{2}$ 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 rotatinxi72vzyj +beoum:7k ,z7g,dins 1 d l7+jk4qtg at 5.00 rad/s with arms extended has a moment of inertia ofg1:t,v 7lodxbk7 zez+ imk77q+ nydu, 4jsji 2
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?