Angular displacement is usually expres ovs (z)qa1i6tsbp 5g9ev1 .ups in units of

  Angular velocity is expressed in units l:i+ q ;: j:ae;rpy,2ogmxpszof

  Angular acceleration is expressed i7 fzwpa 0zh0vwxqcuxv) k5 )0bq.m7ph2x7r1an units of

  A boy and a girl are riding on a megzrlyv 3xxz.q63 k9f0rry-go-round which is turning at a constant rate. Tg6lxfzr3q3 .9zkx 0 vyhe 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 tuvlqn8,gh(xa 8zv cy/)rning at a constant ra ,x8qnv l)g8azvcy/(hte. The boy is near 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-g)qb 9lf7 mumjk*u e0b+:msgk5 o-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 linkj uum)q m97b lfk+eg0*sm: b5ear speed?

  A boy and a girl are riding a merry-go-round which is tb:)49g wnp4 g7y hcnyrurning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who h4ph)y9:n7c wyb ng4rgas the greater centripetal acceleration?

  A boy and a girl are riding a mezesiv ()xq p-+rry-go-round which is turning at a constant rate. The boy is near the outer edge, weq )ip(- vsxz+hile the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the followi5+mmd k vyie0:ng is an accurate st 5ekmv 0+:dmyiatement?

  Rolling without slipping depenw g3rj;7r2hnw ds on

  Two equal forces are applied to 9s)n-we:u;pof gudzhp0*t f6 a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Bowg9 dp0 *ftu:-u6)hso nze ;pfth forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. T4-g .r*xu; zk +dpxtmp p3,kqshe first force is applied perpendicular to the doormxru+.gp qtz;p*3k4p kds,x -; 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, :ijvvfr x htcfe*6qm (r97q *2perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque 6( ** fv7vtrcqr xjeihq29fm:of the first to the torque of the second is

  What is the quantity used to measure an object's resoe(r8z 3wfp/a(6l:rvxiz c js)d+ c2 3tb- isaistance to changes in rotation?vt6p8/z) doea3rfb+x- wls :3rjsica( i (2 cz

  Consider two uniform solid ,uo)ne(4vjym spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertiuv4 ,m yno(je)a is

  Two uniform solid spheres have the same mass, but one nk ga4 j4 oy2kv:xiu(;has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of g :o( 4yuvja; 4k2knixthe smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the d j5d ecbrn5d93 rye03piameter ofc5 jdd53b y3 ee0prr9n the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increasevk; iy(-8fsbdd to 2M and 3R, what happens to th8(fbkds- yi v;e sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, thatb,4g bl* 75fghi1hkno 1ouk:o object will

  The moment of inertia of a solid cylinder about its axis is given by 0.nthi3m 278got * *h *)wu urux*tom-vq5 MR2. Ifmx*r -t n*m7g qt2u3uvw*8uhhio*) ot 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 hn7dw i*5dd xgc ,uf..,nxmq, kas a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to th wdu,n d mgn.x xi5fcdqk.7,*,e total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls witfla byy)j,h.2sf hz0,4ve9q qhout slipping down an inclined plane starting fsqh) .y09hq4zbyel2,vj, fa from rest. 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 without slipping dow8ho4xg)f h3-nfjtkcr*t 9)wm,. gg (jmnd po.n an inclined plane starting from rest.m,c 9dn8x omrj(3)kgfnght4-. w. go*phj)f t 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+. r0p a;i3 zuuhgky/y external force acts on the sy0g/uupha3.r i + z;ykystem." This statement is

  In what circumstances can the angular velocityb vwh h/.k)n8j of system of particles change without any change inhh.bwjk) 8n /v the system's angular momentum?

  The Earth orbits the Sun in an elliptical or*8lxgsoq*m hk v4:)e(l 8hoo bbit. Ignore any friction which may be present. What happens over time to the Eqoe(8o:lhom4 ghl8 bx*)v*k s arth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth movectfso) p*hkzo +4r(+ty.d +nplm k1j9s close to 4drspt1z .+m)oph+* klc+ yjot9 (kfnthe Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin)sk6lxq bzph7 mq8b)idywz h( vi3m;k,4) g92c by pulling in his outstretched arms close to94lzqghkm(pdb )s6iq;cw,xybzki m) 7v2h38 his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) bor:k,1tqv iehot m:*1 y pulling in his outstretched arms cli*rk ::1t1o etmv qo,hose to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouett52 -l;krrz a+ie k3ngde (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about-rkn;a2 +rle 5dkgi3 z the axis of rotation?

State the law of conservation of angular moos8o66z7 c.4fsizxy6 .wkx fvmentum.

  What arc length does the Earth travel in a three month period indu,p6r/f-u ;n(bko: i evyp7f its nearly circular orbit af on7p :b;y(e d-6u,r i/kvpufbout the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the 8j61w4:g/ j6cq hpc ,/ej5wlxdjjv jttip of the second hand sweep through in 3 minuj8pjj d:6/j4jjlvq,e g1 x6tw chw c5/tes and 45 seconds?

  How many rad/s is 25 revolutions per minute equival 8fxw/4+/uy frgzf(9yct.tw cent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What 5cg5h6g qr*xo is the frequency of the wheel's rotatixr5*hc 6g5goq on?

  A pulsar (a rotating neutron star) emits pulse 7:i-uxbsqoe+p)rul 0 s at a frequency of 0.40 kHz. The period of :xo-+0p sulueq7)i rbits rotation is

  A phonograph record rotates at 45 rpm. Through whayvf9k *p s56dk1qq. rpt angle does it turn in 0.20 s?fvqq.kd5p*s 16kyr p9

  A wheel of diameter f3k8ze jvg8xi i2t03/3xdbpm26 cm turns at 1500 rpm. How far will a point on the outer rim movt3 8/ p3ixekb3m02f vzg8jxdie in 2.1 s?

  A bicycle wheel rotates unifd egumu2z.-otn7sq *8i 2:lgwp1 ok6s ormly through 2.0 revolutions in 4.0 s. What is thed.-zws2u :onps7*it omgk qu 8126gel average angular speed of the wheel?

  A bicycle wheel rotates uniformly throughvshc1 )2xt) la1u; /y/rwxyph 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m frou ylhyxa w1)s) h1;/v2x/cpt rm the center of the wheel?

  A cable car at a ski resort carries skiers a distance o57au gde p41qb 8kku(df 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 pul8ddeg1a p ku u7k5bq(4ley 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 rad* y6gjj7ri*xi z r:j,c/s. Whazrgjx67* :*jry ,icij t is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0is/tpf +gxr,ymxfg xi: 43h39.16 m in length. If the motor rotates at the rate of,ys x4xmf 3hp+g93i tr :g/ifx 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 hx9aud8zg (8i speed of 2.0 rad/s. What is the centripetal acceleratiu 9x8z(d 8ighaon of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the p4dgjg ky.q +du8, mqe(erimeter of a bicycle wheel of diameter eq 4dj,y +kqmgg.du8(70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions pe n;z11xtvjny 2vm1 1obr minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce anm1vvnyt zj1bx12o 1; n artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 melngm,a6:71 ki1 qp d8l)wur(q*gm su:6 ixvz with a speed of 20 m/s. The maximum centripetal force (provided by staticv*:i ,1guiz6pgw7l k ) e8rxn(msm16:aqq du l friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat)ohtbh4s+ :d+usw j0rq-y rv6 circular curve of radius 50 m with a speed of 20 m/s. The maywhj 0o)hr trs:6u++-s b d4qvximum centripetal force (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 enzn4/13dufj 5mrlj,yw d of a 0.750-m string, is whirled around in a smooth level ta,r1 wn4u yjz f/3mlj5dble. 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 radius 9.0 cm rolls without sjjqe ; :416curtz*4d ya5 u;hdybzev+e ,uo3plipping 10 m down a lane at 4.3zuua j4r*y5;6edcq eh; ed14z3u jv: y,o+pbt 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 accelerap8,jzl vodmf)/ v b/s3tion 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 accelerationb9dk;d z2kad8 3.dq6mi ff-ah 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 automobil;8q:. utmclnu e tire rotate after starting from rest and acceler;u .unmqlc t8:ating 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 on*y-3* gue)gyc1vw nyf $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a ucgaea5u9p u )ekk1lr4 1yk9)qmr x,(constant angular accelerati )rau54p) ag991, rqxk(uy mueckke 1lon 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 wm/ )l1x vn6gqyhile turning through 2.0 revolutions. What is them1/vlg )qnyx6 average angular acceleration of the wheel?

  A wheel of diameter of 68.0 csw 3 gxd-*vpuwuj:-7ym slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total pwu: jsxug dy7wv* --3number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 c af.jno o;tm nbhe*bl916e(+ts-m :m nm slows down uniformly from 8.40 m/s to rest over a dis9. enlbno1 h;6ts o*(etan bm j:-+mfmtance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniform j3 hswxfauup-w:b1;-u)((e jcubva ) ly from 8.40 m/s to rest over a distance of 115 m. How lo) u jbpuhsw(vxfwac (b--e:)u au;3j1ng does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/m 1wt,)i,(icn lore)-9hjqxy sin. When switched off, it rotates 50.0 times at a constant angular acceleration beforei )w)nqhe(xi 9,j t,1sor- lyc 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*lcvahj93 gj;a e2 w0g tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is *a 9l v;0hjj age2gwc3perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. 3o kd 1gw5t0mj+2 0tvd7)ojh civp(tt If a 30 cm long wrench is vtojd3t)5wt120ikj07tg h dp+ ( mvoc used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment o3asa1ys;dm9 pny74i b6h fkoi2 :k5if f 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 origid: rxp)x1yd( 1le +whin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia h1) lp dy:eix(wd+ xr1about the origin?

  A solid cylinder of mass 10 kg is pivo a cm7og57udlnid2fc fz80x+8ted 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 downward. (See Fig. 8-1.) What is the angular acceluf08m 2xg785if 7zcod+ dacnl eration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frih npt.rn0a;y)ctionless 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 wrat. np y)rh;0napped 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 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod i2-zfd(pw /uz ;qwzzm 9s initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angulw qzz9 2/wz;zfu- pdm(ar acceleration 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 rad:ie f -j5m f/bvde;scoe +m/8aius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N-v+eodj em/:efm/f acs8;i5b 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 robit:dghcmoflb5,a*2 j;j /8b pe wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelerat,*8b c: ;fjlm ago2tjih db/5bion of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frica0*zd dv s(4pli)k*sk tionless disk pulley of mass 7.07 kg and radius 66.0 cm. di( l sd 0s)*4apk*kzv What is the acceleration of the mass?

  A rotating flywheel j j0tyo1m (tn-can be used to 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 ineu*;) bfxqo* 8ufh n:usrtia 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 ros,r pe12y rvt.lls without slipping down a 1.0-m high inclined plane. What is the speed 1 tsyrv2epr.,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 a speed of 10 p-7bli (0t2kxdk1yjde,cx :d m/s. How high up an inc0 ed1,kjytbx :d2 (pdlx-7kcilined 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 b6k(7lfcf9bpm0 vyy7 rest and allowed to roll down an inclined pl mcfvyl by9b767f(p0kane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radhm 0l*k( ;cy vlg9fae5ius 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 il5 khf09ey(m* v ac;lgs 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 chant;cny 1u6 e /;nc5-dsyl(of nnges 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 momv 1ev p:q* cruf7zej*/ent 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 5.00 rad/s with arms extended ha-0u0z9v- lv b7 pf2spqw z:bmds a moment of inertia ub zv -b-0:2 7z0d pqmvflwp9sof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?