Angular displacement is 1dz 5s2nmov*+ vibo5-ep8r ag usually express in units of

  Angular velocity is expressed in uy) za1md t7 1au-0rc s7bkw7hfeyn8/onits of

  Angular acceleration is expressed in un--db a0kxo 7gnfc: y0tits of

  A boy and a girl are mwcb,y;cgpjw,s;+ , w 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. Who has the greater angular displacemen+ywpm, ,wws ;j c,b;cgt?

  A boy and a girl are riding on a merry-go-round which is turning at a cns-k 3ic-ls (i:eyzcbev 4 ,2zjn36yronstant rate. The boy is -,ec( k - iibjc3 nery:zvysl4 23zn6snear the outer 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 )ecln5iy57c f-o;on ya constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has 7c5-n )c5oyil ;ey nfothe greater linear speed?

  A boy and a girl are ridinnfxy 8ht14 4ffg a merry-go-round which is turning at a constant rate. The boy is near the outer edg tn8yff1h 4x4fe, 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 constant r;,usmw4kpns uj: a jy-/ g0kk(ate. The boy is near the outer edge, while the girl is closer to thu( sy4nku:-/j p0mjsw,a kg ;ke center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which oaef 7gqgni*q st)6i(8dn 2q5-iw ol6ef the following is an accurate staei s 2 lq7i(n6qng6 w)8fqa*o 5gd-itetement?

  Rolling without slipping depends on6 dhf+f6sjz7m

  Two equal forces are applied tooba5gang 53is(+/ 5ta8wvhawt28 iz v a 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 the d5sg+2awtw8 oiav5hva za(bit35gn/ 8oor. Which force exerts the greater torque?

  Two equal forces are a1acwe/va 6t u6ppn d9.pplied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force eau6v1a n6c pt.9p de/wxerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The firs mtlt +orp,r,/t force is twice as large as the second force. The ratio of the torque ofmrr, +t pt,/lo the first to the torque of the second is

  What is the quantity used tei6roq 3u/jbs(w )y0y o measure an object's resistance to changes in rotatio3q eswu)yr y 06/b(join?

  Consider two uniform solid spheres where both have the same diameter, but one 5qefs.ot:ngpmt sr:j,0; d5 xhas twice the mass of the other. The r55.xrtfd:jetngq : pos;0s, matio 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 af7 6/f ;smd e0*mhkh,fi4n-e7to xlntwice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smnlhtfnes6f kh-;f77iod, */ xme a04 maller sphere is

  Consider two uniform solidvukb-:r7i zeh5njjs(:/pt + nu( j jp5+q :drj spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smallen +:vr+zj5i jsrnd /7p5:kb(q(j: uph-jeu tjr moment of inertia is

  A uniform solid sphere has mass M and rd;y4n tut )if56r xpk1vq +u645tapkj adius R. If these are increased to 2M and 3R, what hatu pr+qktd na46jk5)4y 1p xi5vtf6;uppens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that objectu 7qc0 vlqd/kw;t m0n5 will

  The moment of inertia of a solid cylinder about its axis is giv;z3 xeun. b)32hwrw0 yuy qpm+en by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotationpu3.brw hyz; u0 23e+qxy)wmnal kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass ob8)*oi n bl,: dbcwx1df 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetnbc18 old,w:x i*b db)ic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of; id0ao638reoqw1:u szpb fs8 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 sfq8ew6r ou: d810oz ;3spa ibthe incline depends on

  Suppose a solid sphere of mass M akyj.0qf:7un p nd radius R rolls without slipping down an inclined planuqy7 :pjn0. kfe starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a sjvdnh*p , +g .t*tqna(d y00zqystem of particles changes when a net external force ad(n.0vy,ng*q+jz*a 0hp t dqtcts on the system." This statement is

  In what circumstances can the angular velocity of system of particlaqh72apz +bc,bz )xcy/5c 7zk es change without any change in the system's angu7 cy zzp/) +ca2k7ba5cz, xhqblar momentum?

  The Earth orbits the Sun in an elliptical orbit. Ig6tq 3grs:wb(h j5ufv 6nore any friction which may be present.sjg(f u6563 w:hvtrqb What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves cle*f-xx:zof0-ukzu7d ose to the Sun, then which of the following best describes the orbiting speed of the Ear--7 xzodf:z uexuf*0 kth about the Sun?

  An ice skater performs a piroukhb0x-+ridi;l c13)ykh,tiq ette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotation0b-rlx+i1t3dq;,ykh hi i c)k?

  An ice skater performs a pirouette (a fast spin) by pulling inu0 o)etm .ga48uczqt f ;u,zbw (mc2,p his outstretched arms cpou428,z .tbaumf0qc,;gwmctz ( eu) lose to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spih8t4p)tcydzp-0;x5s tt v pu3ph(7 nan) by pulling in his outstretched ay 7a3hpt( c)s-u8 xptvtt5z p;pnhd04rms close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conserva d1(me n39sfxftion of angular momentum.

  What arc length does the Earth travel /rs:r sjxw80 xodc,b; in a three month period in its nearly circular orbitxx;wd rroj0bc: ,/8ss about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a*nu ri+ ts*q fr67sutxxsw7)( clock has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 secf (w rx*uurstss+7x*q)n6ti 7onds?

  How many rad/s is 25 revolutionsn3vc l qf,.zj6 per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What isi3 l flc7zoeg5* )cpg 4r2vx.r the frequency of the wheel's rotatvlp 2c ori )74g crzx*.5g3lefion?

  A pulsar (a rotating neutron9mzze1 y,fr8 z star) emits pulses at a frequency of 0.40 kHz. The period ofr, eyzfz198z m its rotation is

  A phonograph record rotates at 45 rpm. Through what anglef7*j+ v1 p+zna1m gpyz does it turn in 0.20 s?a+gzf1 pynm1+p7* z vj

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the oog9:5da6i(r6xh o vv buter rim mov6i(6 bo9rdgv5x a: ohve in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutionsx z ujowy;05uvw2 p4 lvmsgchm3h.e/,/ j4lq8 in 4.0 s. What is the average ang/elcmj3s,hj .h845qv yuwu24m0oz w/l ;pg xvular speed of the wheel?

  A bicycle wheel rotates 8 6wyaxj-rgfi, 5(ek ek+dcmios4 4 6juniformly through 2.0 revolutions in 4.0 s. What is the linear feg- 5aw 4ciis8+o,6emr4k(dkyjx j6 speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carriesb(jo*w-obe : e7 lz6zmyrvx2- skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cable car to mazo2e6-vzbel*jm(:wb rxo y 7-ke the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 ry-wq16o j hp:had/s. Whah1p w-6yo:jqht is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m ise 7tcc+6zj0 l3v6g mfj4vl2dw*sqq ,n length. If the motor rotat qj4w q6lcfd0v2ls 7esvm3 +,6*gjzt ces at the rate of 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 constfr6 w wc dc. *yxq.lmc3krx7)3ant angular speed of 2.0 rad/s. What is the ceny l.)3xc w3 mfrw*x7k cd.qr6ctripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceley+b8m6 sgm k.//ug 7zz,9ar6 b san4ny+rwvq bration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bia+8bg yb6sk +azz yrn7,.s 9umw//4vmgn qr6bke is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, roz7-eg5y *a 4pbi nne/otating space station (r = 1000 m) rotate to pr e p5y47nzai*-neobg/ oduce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m/spdk *. ugs)0: y 9yxabya1fj/f. Thk.f a pgy a*:1sb)/x09yudyjfe 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 rz ac8 u/ehqdj trh1af-g2 yiu),*u+s) adius 50 m with a speed of 20 m/s. The maximum centripetal forcs r))ziqfh/2ca,g+1hj8 ud*e -tauyu e (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 /sjql y2 gt9unna/:a6of a 0.750-m string, is whirled around in a smoo/ nts qjy6n9ual/2 a:gth level table. If the maximum tension that the string can 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 radi,pa-k z;;mq ycus 9.0 cm rolls without slipping 10 m down a lane aa yq;m-kpz,c;t 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 acceler xs:3 zp( 3u3 obpiz)2zlkghy:ation 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 acceleration of2*t0e o x0g:og8 kwziq $4.5 rad/s^2$. 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 afk-go (vkh*r 0qter starting from rest and accelerating at a co-(koq vg hkr*0nstant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an an73b-g k1mhv.+yp ozl pgular 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 with a constant ang7k 6nz.r b:klaular acceleratibk .akn76:zr lon of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and rea2fisgc8awt e i7p f0vaat ;hz: k4u452ches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the avera ahiaf2;8:f5kiw sp72ug0ttc e4a vz4ge angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down unn- 7b .1xtmevuzbj8v1pwr5k3:wi q q0iformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotz-0pqmr 7vv.b1 5xknj8q1 b :t3uiwewates in coming to rest?

  A wheel of diameter of 68.0 cm slows down db;6 h e*3lpoz1mh,x buniformly from 8.40 m/s to rest over a distance hm 36ebp,ol;* zdbhx1of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slow6a4adio6v ctp - jg4j2s down uniformly from 8.40 m/s to rest over a distance of-2a 4jvdtc4a6opigj 6 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical lacnwzz 9w9nws :9us /l6boratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a cuw6w n:zwln 99 s9z/sconstant 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 anbtvco 9oj 5);vh)-em torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the fv o5-n;ecv)9 mhojb)t orce required when the force is perpendicular to the wrench?

  The bolts on a car wheel requiru1nc n(jr ik6o*wt 24qe tightening to a torque of 90 Nm. If a 30 cm long wrench is u j 6iot*(rkw1 4cnnqu2sed, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of 5zvc0nxl5ul* inertia $3.00 \; kgm^{2}$ 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 origin, massm r6zp y//ci(k0 opk*lpmj6:k 2m is at x = a, and, mass 3m is at x = 2a. What is the momen pclr6k0mi*/jom6/:kz(p kpyt of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axhy 4td69hf5 n8fh1y7fr. k zhxis thought the center O. A rope wrapped around the outer radius R1 = dhf h75y1tkf 69yx8z.hhfrn4 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 thoueo 2na(d6k+ 9q ebk7xwght 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 an67e(x2w nbq+dkk9eoa other 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 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initx pg1 :6s)iz:lmnqh6dl ko01 rially 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 moq1osi::pkh6)nmlz dx10gl 6rment 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 baez, u1r78puc(p .yr1.5 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, assuming it rolls with 1.p,yba(uupcr78z erout slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pul0*gk: b. pr le*ejars,ley of mass 7.07 kg and radius 66.0 cm. What isj,. e*kb spr0*al:ger the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a ro2h6ehlc w4r-jehd,the; i d 4,pe wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. ,jc6 le,4r2;hiwdhd 4-he eht What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is /gb6lm8:t hia 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 zy kh8oqtk 6,cy,q*2vof $5.00 \; kgm^{2}$ 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 radzpg f*t1qjh f13g (tbg6t7ot8 ius 0.010 m starts from rest and rolls without slipping down a 1.0-mj (hptfz1f318g 7 gt6gto *btq high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.er w7eck2/ux2a+ j:eh 0 kg and radius 0.010 m rolls with a speed of 10 m/s. How hier2jkw +ecea:2/7hu xgh 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 rest and allowed 753 ebb3ebkwcl*0dwk to roll down an inclined plane. How fast is it moving after dropping a ve*0 wc3dekeb b7wk3b5lrtical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rol5y) pwsphf 75w)j/ (3ko)cbb+ xlkcph ls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of i/f5h)lw)3y+ skb5 ko ( bp)7cxhpwcjpnertia 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 f5e/wr qhd4o5 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 z*c d kh;mfskmy,u7;qs-if1; moment 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 5 d:0w(kd;c( 5m) scwkudu.mch.00 rad/s with arms extended has a moment of inertia : 0k dhccscdkm.uud5;m (()wwof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?