Angular displacement is usually express in unitssvoej ou 7;7e.y) 0 8jivvhcr6 of

  Angular velocity is expressed in u-hl)zznpqvlvcx3:k38x2 hz 8 2p rpfiy+9,j units of

  Angular acceleration is expressed ie;(:u/ l c1mpu8 qapk x*wkv5pn units of

  A boy and a girl are riding on a merry-g x2oj,:hi/ uyn( llzw4d,hd,lo-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 displacemehj dl4liud,n /2x,:h(zo lyw ,nt?

  A boy and a girl are riding on a merry-go-round which is t cg31-qq km2 +dr1 7wfqavasdp-;yi3lurning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular sp3fq qp-l7d ma1;cr- 2avky1q+d3iw sgeed?

  A boy and a girl are riding on a merry-)oez;;6hoh,1kw l gqt asa7y2go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer toea w;sh h2,azykt1oolq76g; ) the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round whichw me de5mw258d is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. 2w8d5d 5 mweemWho has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constantz6nnwg(k (ie6 rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleratiok (enigw(6n 6zn?

  Consider a rigid body tsj yl,v3 :ydccv1yt ;,hat is rotating. Which of the following is an accurate styy jsv: y;1tvccld 3,,atement?

  Rolling without slipping depe ,dpyw;oyi:ear 0g29+ zo q(p)0wsollnds on

  Two equal forces are applied to a door. The first force is applied at the midpo)6 5s mnazxmj0int of the door; th 5x0z6) jmsamne 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 doorknob. The first fru*l sx6 i+d acd vf8o3)b fj,6p2vsv*orce is applied perpendicular to vi*r6ja3bu *v d fl2dp)f c68o,+ vxssthe 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 to the door.l(5f ee:kfd9e9bse;y mkh3x-pb4 p *h The first force is twice as large as the second force. The ratio of the torque of the first to the torque of:k emh;p9hd9f b p y*xfs-e(eel345 bk the second is

  What is the quantity used to measure an object's resistancz ao. -gu/)tex yod p c+oom3/-agao*;e to changes in rotation-ago xo-/czug ao3 /a+po)t.y;o*d me?

  Consider two uniform solid spheres where both have the same diamedn 9;zvzucw52,jcn6h ter, but one has tw;z z,wn96vjc2 u5 hdcnice the mass 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 the same mass, but one has twice thewslc1n (jv+q ;a9x* nh radius of the other. The ratio of the larger spheqs(nhv1w9n*;+c xlj are's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one ha y) ni8e34r8ejruaug z **nw8ds twice the mass and twice the diameter of the other. The 8*ne ugny d84)re3wriu 8*ja zratio 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 inzr,v o 5*yn ib)1rmlw)rat 7l)creased to 2M and 3R, what happens to the sphere's moment of ine,) z irya mbv57 ro)wtr*l1ln)rtia about a central axis?

  If a constant net torque is applied to an g1vr s:spl y4ur5)(p.fzwfk 4object, that object will

  The moment of inertia of a solid cylinder about its axi(d 4) bxkh;j uhbr8v:ds is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinev8u4h:;() hb dkx jdbrtic energy is

  Consider a motorcycle of mass 1j5,7.b;dqvlt ptxtu6 50 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 wheelqtxltv;5.t , ubj pd76s 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 witho ()tzob* u *gi/vrsu8ofud,y6g5wji:ut slipping down an inclined plane starting from rest. The linear velocity of the spheu5 s:8g z,*w6ri /doyvft)ug * uib(jore at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping downspive.c6(z q 1 an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depe esz6 icv(1.pqnds on

  "The total angular momentum or7l9fk/s-lbzz ( 1 ioyf a system of particles changes when a net external folb i lyfkrz1s9z7-o/(rce acts on the system." This statement is

  In what circumstances can the angular velocity of system of particles ch9,qddzl/ i2 wr x.hqhnl1/l8z ange without any 1 h lr w9dz8/i,2ndq.qh/ll zxchange in the system's angular momentum?

  The Earth orbits the Sun in an elliptical o8 ew yhqe nroa716/hie7e8)avrbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about th wyeor78h)ne76 1i/h8a qaeeve Sun?

  The Earth moves about thedm31m ws.:mkj Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of thed:jm .msw13 km Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretch+3oj (fpuah,0yq1k 5w8wu nq hed arms close to his body. What happens to his angul y3 8h0(q +wpn5w h,fuo1qajkuar momentum about the axis of rotation?

  An ice skater perfor i;d6,*ayyh;7jbamp ums a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of jhiy6by; a p,u;7adm* rotation?

  An ice skater performs a pirouette (a l em2b6ny la)dm+0eqsa 5ue71 fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of dml1beel an7eu q 5am6y)+s20inertia about the axis of rotation?

State the law of conserv.jv2x c g0lk:vation of angular momentum.

  What arc length does the Eartqsvl :5aflj33 lge51th travel in a three month period in its nearly circular orbit about the Sun witlt 1lla5:3e35 jq sgvfh a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of -qfwkrg 7c qln:1 :l*n0.30 m. What distance does the tip of the second hand -ql nlcg :1 nf*rq7wk:sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutio-0ksue5sip n:veg)9 ax10 wcens per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. W m --a6:qmxerrsmo g bx2)8y9hhat is thegrm 82r:o -ex-x9 h6by)mmasq frequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz.x nv+g e-+iyc0pcjc94l6y iuhk 8d (g9 The perih8vdg0 (cux 9e6 cg+ p-4likjycn+y9iod of its rotation is

  A phonograph record rotates at 45 rpm. Througkr5hlgo(798tju+ o wpv.m zkqb3n.l :h what angle does it turn in 0.20 s?h gjb(7wm. z3k5uol pqt:8o vknr+l9.

  A wheel of diameter 26 cm turns at 1j4,a.s xq1 wh ks)o-e(.xk- n qfcqrq6500 rpm. How far will a point on the outer rim move in 2,q k) aqofrq-q- nwj.exx 6s4k.1 c(hs.1 s?

  A bicycle wheel rotates uniformlz0ac*tzndtr av0 b4o3,8-kp n y through 2.0 revolutions in 4.0 s. What is the averag dvpato8 tnrc43kn0-abz, 0z *e angular speed of the wheel?

  A bicycle wheel rotates uniformly through w7v n8 0(kad3bs-tzbi2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from t(0bak-w 3dz7nt i8vs bhe center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cabe1ohbz0 yxk/f 0bn*v ;le 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 make the trip in 12 minutesyv*1k;/ x0efb0hoz b n?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 x6ilu*u c,ow0cb v gf+ 22 xwi*i4bug2,t )qzarad/s. What is the linear speed of a poinx)bw4co,*u 62uc+q,g zi*bl vf uawii t2x0 g2t on the wheel's rim?

  The cutting cord on a gas-powered r;ekz/ -lk5 wjm8yp (/gdgh1 uvyzn ,3weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end ofelwgz,3/d 5- rzknmv8pj1 gy/ ;uh(yk the cord?

  A wheel of radius 1.0 m is rotating with a cc-e)dtd dlkwfb -6m5:4 fig6s onstant angular speed of 2.0 rad/s. What is the cecdwegs46d--)d 5mifl 6kfb:tntripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycl;-3,s pm5 t 4c*mndbr/hwy .voz;xfdbe wheel of diameter 70.0 cm wh4pb5 snxot*;fyd3-mrd ,b/ ;v z. cmhwen the bike is moving 8.00 m/s?

  How many revolutions per minute (lslky.yhw;b m3hry4 : 2a6 dp;rpm) must a circular, rotating space station (r = 1000 m) rotate to producey y hmr34y2 hwadsbp.;l6k: ;l an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat cir.g 7skz( wfe 92qmxwm;cular curve of radius 50 m with a speed of 20 m/sgkwwefxq;2zs.9(m7m . 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 50 m with a speed on fsao o4ch+,lwuq7y3;l fow , ,f*e8fsa6/da f 20 m/s. The maximum ceaw7oll q f4 o8fdf ,sysf*;,a+,nu 3o/hcaew6ntripetal 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 end of pa .1p+ag,dr9m4lxrb : tu9ef 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 can the mass h u xpd+r fret91pm 94.agl:,baave if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cr) vqv )dfi11jm rolls without slipping 10 m down a lane at 4.3 m/s) fvd1i1 )jqrv.
(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 6831mdxh2bpzueste 7a constant 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 angular ac;x0j -hkv-vgi celeration 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 vm.s u1-by sd9a 0.300-m radius automobile tire rotate after starting from r mu9ysd.1vs-best and accelerating 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 anglm55p hq4 o,ycular 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 witn)gg svf-mm0u 4 uw,o(zn+i*p; ugw7m h a constant angular acceleration of ;fg+uz 0 s,- iogpvgnu )w7(w*u4 nmmm$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and 5:wpd:hpexca395 5 .z cmf)m1x8q) xgyli cmcreaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular accel85cxpl.yg c w hdem53mx mca5:q i: x9zcfp)1)eration of the wheel?

  A wheel of diameter of 68.0 cm slows dow oar9 xefh9)6ny-6kel+ tm5qln uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotl9n ko+txf)m9lr e5yhe 6a6q-ates in coming to rest?

  A wheel of diameter of 68.0 cm c0fuuge.t/0tslows down uniformly from 8.40 m/s to rest over a distan0cte/u tf 0ug.ce of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uni; )d h*tgvqkk:formly from 8.40 m/s to rest over a distance of 115 mvg )* ;hkkt:qd. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational s.2qifbdo b5 08yhsty1 peed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to rest.5t8 i1f boh.2sybyqd 0
(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. If a t i2 g+0mrjbi +8cez6zhl59ra 30 cm long wrench is used, what is the mab+ ri e8rzt05g ci2+6zh l9majgnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel reql0 zm in;m:m)q0f zwq2qnn6)guire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magn; m g)qlmq )0 wnz02miqzf:6nnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment k)k s: v)ddex plq-7c*of inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic moleculephi4ck: 6wh-fo h7xleq 2 - ;d;;otrjg is modeled as follows: mass m is at the origin, mass 2m is agkq -e o;;oilxtw;:rhhf7p- d64c 2jht x = a, and, mass 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 frictionlespr(gwdzs): cqgwxz:t57eh, k4 r28r bs 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 R2krb 5w2)8( wc:4 d:rrgse xzzp 7h,tqg = 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 frict/na z8azygu(pi0)xyhu )(m7e ionless 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 seconds, if it/m0p 8(gxyu)nzhz(eyi7aa)u starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially held in the horizo/lef s*2a/ mdn5vu1y bntal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is released? (The2ua1 vf *//ymsednlb5 moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mas-uu7 l5 axex5ws 1.5 kg. Neglect the mass of t55 x- xueau7wlhe 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 without slipping?

  A 1.53-kg mass hangs on a rope wrapp2j0bfpz;k4 bkal9o: med around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelerzm94fjk b ;k:abpl02oation of the pulley?

  A 1.53-kg mass hangs on a r(kvsj0ha ,pwg7 i;gh3ope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 6wi;j 7 h0v p(s,agkg3h6.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is ry9sid0 zh5m*i equired 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 oggoq h7)vu2 k:f $5.00 \; kgm^{2}$ 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 andugjxz*p9z e;qf0pm53 p5 a(bo rolls without slipping down a 1.0-m high inclined plane. What is theo5b zue9 3p j 5*0qpmzpa;xg(f speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1(x(9,w cp563trha(evk.st s yf/vddv.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb beftve d 3( dvfkv (ah(s5 w6cyx/.,sr9ptore coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest k vgfz; 696 j;uamnet/and allowed to roll down an inclg ; av6z/9fek;utn6j mined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass, qc9tsv3u.wex; )ub w 1.5 kg and radius 15 cm rolls without slipping down a 35e i.s,9w t xbeu;c3q) wuvncline that is 7.0 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 moaf;c3s2c vynht4 0j d*mentum 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 9c3)b4e -*hdhlxpox j 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 has a moment6 eaqw1zget ys+dj ((rye9z -( of inertia of s 9r-eez y+(y(61etzj (gawqd
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?