Angular displacement is usually express in: a3zv+wn7ac wj2*ohr-w vg1o units of

  Angular velocity is exjx lz8 c- 2qb2 0blnb:0fmx:bzpressed in units of

  Angular acceleration ihnmsvzgi7 1f: p2e /i9s expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constant rcmn7,auz pa 4o.j y31wate. 3cnwmj . z1pu,7y4oaa The boy is near the outer edge, and the girl is closer 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 axl r.i7uc(4 xa constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the gauc l (xirx.47reater angular speed?

  A boy and a girl are ridingmvs:hud vb:. xxrr4*h9a ;8 kv on a merry-go-round which is turning at a constant rate. The boy is near the ou v:8xdrxm.h 9abv*h;:us4krv ter edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant r(l4f.4xb+xu 5i ikon oate. The boy ib 4+x5oii u4nlk(f o.xs near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-roundxgo.h5vz5l m9 which is turning at a constant rate. The boy is near the outer edge, .mzov 5xhg l59while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is ro3v6w8k bap0gzyseqj/4l3z -ytating. Which of the following is an accurate statementwp svbk4j g3-3aq zy6/el80zy ?

  Rolling without slipping del9-ycz de l -/o0 jza3slszij rt:q))5pends on

  Two equal forces are applied to a door. The first force is applied at the midpk6 v3 ets1: mt8/zx lhbr)r .pmeu-m1moint of the door; the second force is applied at tm mr6 8 -ltrtkv:m1epzx1)3 u.e hmsb/he 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. The firke2 ( hjb767yvk6 ola4jqhn/5wgwu o:st force is applied perpendicular to the ona jvjlkg7ewq/ 7(54h2kwb o: h66yudoor; 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,-sqsg/; cj,jw wq+bs : perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the :cs ;qwq/b w,js+-jgsfirst to the torque of the second is

  What is the quantity7+jrrbm6b 7twn np x2h9;yk 0v used to measure an object's resistance to changes in rotationy ;9v6px0km2w nbj7b7 hrtrn+?

  Consider two uniform solid 2 zj 1/ 6.4yrvf9avhcjr *uakmspheres where both have the same diameter, but one has twice the m .uvc1649mrh /z2avafy kjjr*ass 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 trt wg3ppxg)gv dw0/7 -he same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertiax7p3gw-)r/d0 gg p tvw to that of the smaller sphere is

  Consider two uniform solid spheres whecq67quet s 1;s9j(5d zao*jnd re one has twice the mass and twice the diameter of the other. The ratio of th5d;1stj*7 9sqouq j d(6nz caee larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid spherew5-.ygp1phg y has mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of in p. h5p-1ggyywertia about a central axis?

  If a constant net torque is applied to an object, that object wilq+ +8hm *9d e(if8hkb+ zjnpdfl

  The moment of inertia of a solid cylinde)kr wo zd92zf/r about its axis is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which h1wlg-:,eeid up:qy1 nas a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of thdu:ge lywq p:ie n-,11e wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping down ankbh (,v4rhfk2ucyd4( inclined plane starting from rest. The linear velocity c kvd42y4,(ub r(hkhf of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls withoggs tb7wa 46i7ut slipping down an inclined plane starting from rest. The angular velocity b67 ita4sg7g wof the sphere at the bottom of the incline depends on

  "The total angular momentum q5 qi ksc5 /8drz*lkfn.u/q- wof a system of particles changes when a net external force acts on the. uqf/ -zikqcqd5kl*s 8w/rn 5 system." This statement is

  In what circumstances can the angular velocity of(a u9b5+e yhxf system of particles change without any change in the x( ye5ufba+h9 system's angular momentum?

  The Earth orbits the Sun in an egg9+ -al p:e*4vqwpfz lliptical orbit. Ignore any friction which may be pr-vf+ e 4gwz*p:aqp lg9esent. 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 E hopzmt avguu*8q1gc1l;h( n, r/2/learth moves close to the Sun, th a(1ugv r/ e*t,p/mg 8lqnc1;hzou2 lhen which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pia:s2)gr nuv95- zo:nawg puqg7 /q2ovrouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his an rg7q uvg2qwn5o)apaz: :9/vn 2os-gugular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outgogb:-thx)byj2mo*97t ee 8wstretched arms close to his body. What happens to his r9b g7)wt : yeht2moj*eox-8bgotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrjc0/ wnacuk.7aq .uoxz2,/ ojetched arms close to his bo ano o0x/2 z,.au7w.uc/qjjckdy. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momenys,a. b d;s4* tslrt2ttum.

  What arc length does the Earth travel in a three month peri8w dhitp1v;v:2w r/f ulff5ire5z6-god in its nearly circular orbit about the Sun wi6 8ehu1:ff twrvi-vg z 2r55i/fp l;dwth a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance3vd l/; vu4a ut2a anro3-hvp5 does the tip of the u ;35vhlu-a4ovvpa r3t/ n2adsecond hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivib./ yigyvn-nn8z4 h*46- fig.otmu walent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thcpg .7sy:zn nd1lx)p. i52u rd+c.rl oe frequpc.du2nl.7xigpc1.dr +) lsz:r y5 noency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequeno ecb6t9sk2)qcy of 0.40 kHz. The period of its rotation is2os6q e)cb9k t

  A phonograph record rotates at 45 rpm. Through what angl73a9k yb ,qu 7ntexn2y ym(v,xe does it turn in 0.20 s ay79vy,n xn3ktb7em(uy qx,2 ?

  A wheel of diameter 26igt7*bj7em t3q 9g3 gg cm turns at 1500 rpm. How far will a point on the outer rim movgbgg9et7mj3q g*ti 73 e in 2.1 s?

  A bicycle wheel rota 4yqosi39(.i x ( /o( g2lqntrnw+mtvptes uniformly through 2.0 revolutions in 4.0 s. What is the at /n(p4t r gxyo+q.(sn(9qmw3 lov2iiverage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revol(hqx;fb;j0t(kolsp 5utions in 4.0 s. What is the linear speed ts;o bj ;k50plhf(xq( of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skie8ye 2f fxvsf64)vf,bt,lmi4s rs a distance of 6.8 km. The cable which moves)4tbv, 2ff6s efxy v,fml8i4 s 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 make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant ai05+gh *lkk el fn,3ssngular speed of 2.0 rad/s. What is the linear sph figl0 *ksnk ,s35el+eed of a point on the wheel's rim?

  The cutting cord on a (ja0 b:i)s cs+ e6thbegas-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 r(c +:saije0b tshe)6 bev/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 angi5pd6 o0 7se4j f.9+odaxnzxo ular speed of 2.0 rad/s. What isdzd jx9oof6x5.s47 p+neao0i the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicyclerb,i7 iw(fz* c wheel of diameter 70.0 cm when the bike is movin( bi ,7cwi*zfrg 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating zwt+6twijjy+v .*1alq/ 1daq (el9cispace station (r = 1000 m) rotate to produce an ar9.qtya+* l+/i w(diclwj61t vjqaz1 e tificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular -jos qix;ywa(d/6j(in 2prq/ curve of radius 50 m with a speed of 20 m/s. The ;( -apw//ijio q6rdsq yjnx2 (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 5fzgo 61+a:jh t:2zdfbh;km56idf6v d 0 m with a speed of 20 m/s. The maximum centripetal force (provided by static fri j:1f6df; h6dbv:+mda6 ogz2zfhtk5iction) 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, is whi6jw+3odsvol6 rled 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 mass h6+ doj3 6oslvwave if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls wit;-8xur9vqk m gol(b(s /gep5ihout slipping 10 m down a lane at 4x rk(/ gomqe-gu8p;ivb(9s l5.3 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 c-l g 37j4hbicsonstant 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 aa)n2v/v*qwu hk/v /b 3zc(tsyngular 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 ph4p,ea;6 jfetire rotate after starting from rest and accelerating at a constant angular ac46, p jp;ehfeaceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angulp ooqm9pk nn 8yl q :6vce5l 5de.1(w+ned5;nwar acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s deceleratmz1z aq(+c q c0c*c(zyes with a constant angular acceleration q+ c(cymzc z*(c0 a1qzof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches a pk v. j,7)wkk7 gu0qf)-oflecn angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average fo)l.ukgj0 kv f7 7ep kq-w,c)angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slo3;nxt yt:;p tekcn , .rbiz2n:kwz)p5ws down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number ocrbzp5:kx3;zt; ie. nt) kw,p2t:y n nf revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest n3ixt i-/3hqlcr h9:f over a distance of 115 m. What is the angular acceleration?/9hxq3thiic:r lf 3-n

  A wheel of diameter of 68.0 cm slow(;aons +.d t ola;c2xjs down uniformly from 8.40 m/s to rest over a distance oj a(xo tco;;d2s.nla+f 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotate l9smx.:f.5c ubm-,lw4vhc,6p fg abds at a rotational speed of 3600 rev/min. When switched off, it rotates 50 pc-4uhvmf.bmgw5d ,,xclf 6 ab. :9ls.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 tighteniss ah0o ;p8dkfm pz(.d;m *du3ng to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude 0kp3p dd ;s8 mf*.s( ;zmodauhof 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 3vrs g9is;kk 6;6.rse iqw ,xu:0 cm long wrench is used, what is the magnitude 6 ;;rqs 6gi vwis.sx,:kuker9 of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of in9 j/p : uvoak4wpibh/p 56ci7uertia $3.00 \; kgm^{2}$ 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 )oae92yq: o.e2hcq uuis at the origin, mass 2m is at x = a, and, mass 3m is at x = c2o.2quh:o)quy9 e ae2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted ab0iw gldsw d, rbyie9po-e427 9out a frictionless axis thought the center de,dbw47g9s- p riy0 l29o ewiO. A rope wrapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought q(c 8jtvz*n/3 (lvsluthe center O* l3(8tql u(vj/zns cv. A rope wrapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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. uccb gyj1+-d o:ya,a- 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 released? (The momebc+ auj-,cyo-1 yda: gnt 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 kgf+)+l cu /nxk mamu84g. Neglect the mass of the axle and sprocket. au m)cxm /4g +ulk8nf+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 without slipping?

  A 1.53-kg mass hangs on a rope wrapped aro fpb ug21uvd)zhqb-(, und a frictionless disk pulley of mass 7.07 kg and radius 66.)pf( hv u-2db1,u qbzg0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulwy1rls p4n:* aley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of tsrlp1 4n :wy*ahe mass?

  A rotating flywheel can be used tox pkt f9eb+-0q 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 ine e el grz*tv0;g4q3+aa zrf0.xs n2m1brtia 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 starts from rest and rom9 dk;kg+ ,/ezac 5qxnlls without slipping down a 1.0-m high inclined plane. What is the speed of the spzmgn9;c/k + qd,k5exa here when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.amunx4s /gsr3su. *plyy. o *.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane.4 yn 3oax.p *.yu /rgmsusls* can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0zf ;za vhv7fx (y(nx)6*h8z aq.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical zvyf xa(8n a h;7fq(z zxv)h6*distance of 3.0 m?

A solid sphere of mass 1.5 ypx,6s )qg h0v;g9e ow:wnsj 1kg and radius 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 given by yp9 0w),vq6seh w1 s;:oj gxng$I = (2/5)MR^2$.
(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 momentv2uqpbt;gblc4y n6.5f,; b d ium 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 moment of inertia ofzt va0tosh*0t;)ir atk 0wj 28 $5.0 \; kgm^{2}$ 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/swigv19fn a7 v* with arms extended has a moment of inertia a7w i*ngfv 1v9of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?