Angular displacement is usually ex4fz3ti19jr(93kg mzsr t rl/ qpress in units of

  Angular velocity is expresseddv ,mo*zz6s7amy k h89 in units of

  Angular acceleration is expresse:d wyw;+j*pd0n ja5u pd in units of

  A boy and a girl are riding on a merry-gkk2(l pw,n(jzxle)5 xo-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 angulalx w5,lpe2 (zj)(n kkxr displacement?

  A boy and a girl are riding on a merry-go-round whfxfde*mi1. wx6(c v8eich is turning at a constant rate. The .wee*8d mx f6(vifcx1 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-go-round cm7soa . p.7gxwhich is turning at a constant rate. The boy is near the outer edge, and the girl is closer mp s7cxoa 7..gto the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is 9)*1mydxblpy ndb 7y5turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater cen*1b y5) myyd9dbn7px ltripetal acceleration?

  A boy and a girl are riding a merry-go-rouf zy2f+ vqr 6j. g:p7rf18pjecnd which is turning at a constant rate.pq+zj f:v82 76je.1ry cf fpgr The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that m bk+ow5me8y 4is rotating. Which of the following is an accurate statemeye45mkwo+ b 8mnt?

  Rolling without slippik,/0du:n e ;xv/ rilthng depends on

  Two equal forces are applied to a door. The first force is applied at the4;e*i5+ o uaer3mqcdswn 5 vfiu4;+da midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exertqo35 fni;iev +54wua s m*eu +d;4acrds the greater torque?

  Two equal forces are applied to a door at the doorknob. 3rvd j8)a3 jzkThe first force is applied perpendicular to the door; thez3 j jva8kd)r3 second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied 8gc:nn m;b9mito a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ra8nicgm: b9nm ;tio of the torque of the first to the torque of the second is

  What is the quantity used to mey:da+ 0zlvd 1lb4hrw8 asure an object's resistance to changes in rotation?al:b h1wz+r0vy8 dl4d

  Consider two uniform solid spheres where both ha/if 1tyv upiyyd0*q3- -0ttcn ve the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the c*tnid3uy tf1 qy-0/py0iv - tsmaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius l+1jz75wy p6noc+7b p h k8kd5per j7oof the other. The ratio of the larger sphere's moment of iner7z5pywo7ojj7+h8 ler61kbkn5 dpp+c tia to that of the smaller sphere is

  Consider two uniform solid sphertc4yd;+ lb91e hxcjt, es where one has twice the mass and twice the diameter of the t,9+lcj4;hd1b cxeyt 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 incrim3 ky0pnk(.l o pvn)6sz4 qj 1h:scq5eased to 2M and 3R, what happens to the sphere's m4:ni(cspk1)k ql5j vy sqpmzo.n6h03oment of inertia about a central axis?

  If a constant net torque is applied to an object, thadgjqv5v kyfe2*cz-k/.23,zw* wv mfbt object will

  The moment of inertia;o 044 ahzywuv of a solid cylinder about its axis is given by 0.5 MR2. If this cylinder rozw av 0uo;y4h4lls 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 why3 uc:;ue0bk. v,ze /azajjz6ich 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 energy of the bikzv.jee ,3bkzaz0:6jau uc ;/y e? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M an6- o-pt:vwaws d radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the ioas--wp6vw: t ncline depends on

  Suppose a solid sphere of xtdn:56z ,df;;gow,a75t 8dbe ypcalmass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of thed;zt8d;afyw,bd :5 75tg o6lcpx,na e incline depends on

  "The total angular mome(g/ouqcd x6 -*;nqp xdntum of a system of particles changes when a net external force acts on the syoqu x(pnd;xgc/-d6q *stem." This statement is

  In what circumstances can th8.n2wendnb:ac 62o qae angular velocity of system of particles change withouta8aenc6:bo .nqnw2 2d any change in the system's angular momentum?

  The Earth orbits the Sun in an ellipt6i5 kf ,so ywjtbq ,+ogcg;d)*ical orbit. Ignore any friction which may be present. What happens over timek,bis)*j +w5og ,cd ; fg6tyoq to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical m:xx*f 4 s0mitorbit. As the Earth moves close to the Sun, thetmf*xx4ms0i : n which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) x3 v7*po.oaxc76x dwpby pulling in his outstretched arms close to his body. What happens to his angular momentum 3 x.6cd 7w7o*p oxxvapabout the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by ie/yw* l e*2 3oy5j(fev rc1ezpulling in his outstretched arms close to his body. What happens eil(f5 e v*yze312yre */owcjto his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretche evj 9p2 bqrjf:;7.6oivzp:g)axm:;5mxph ied arms close to his body. What happens to his moment of inertia pm6h a;mxj;g9ez vq7ixev bfpo:25:i pj.: )r about the axis of rotation?

State the law of conservation of angular ms;-wrs lp 1 kpgad5e2)omentum.

  What arc length does oxc02nt(c9fgh+ 4 tdjthe Earth travel in a three month period in its nearly circular orbit about the Sun with a radiusofc0xd n2jg4ct +th9( of $1.5 \times 10^{11} \; m$?

  The second hand of a clockqwe))ev 9/-j mvtbpaaej(g3 3 has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 seco/3a (q wbv- jepg3 ))t9eaevjmnds?

  How many rad/s is 25 revolutions per minuteb lf;b yod+5/00kfxue equivalent to?

  A bicycle wheel rotates uniformly through 2.0 r4 nhjj7i3 ljuwi;ak d bn t68i5d34n3uevolutions in 4.0 s. What is the frequency of the wheel's rotationnjb8d; nji4 3w3utk il3576 nu a4hdji?

  A pulsar (a rotating neutron star) emits pulses (wu;ffa 9z/k8e ; awtaat a frequency of 0.40 kHz. The period oa;w a (afwz9ft /euk8;f its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.8gstiny.p 4) 2 dtnxo,20 s?xsn i,8gt4n dyot.)p2

  A wheel of diameter 26 cm turns at 1500 rpm. Hobpn +z 34mxo8huu it88w far will a point on the outer rim mi4x8uho8mu+3p t8bzn ove in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.8vhly(g damfg.n8d1zi )5vo-(a 8peu0 s. What is the average a8 ohd8.(a meiagg1- )(vpn8dv fzuy5l ngular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 repd); radd 9.ifvqlv 7o26(zvuvolutions in 4.0 s. What is the linear speed of a point 0.10 m from the c vrfpddzu2l7 dv a( .i6)v;9oqenter of the wheel?

  A cable car at a ski resort carries skiers a dis,f8e- l/zigf ktance 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 gl8-fi,zk /efcable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotatinglcnc/74knr .zdc ufjh* ) -v-g with a constant angular speed of 2.0 rad/s. What is the linear speed on/l guj)c4c 7.hvnc k z-r-*dff a point on the wheel's rim?

  The cutting cord on a ga:((cgsj t) ix qv7y+ass-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, wj t:(sgxs+yaci7(q v)hat is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2srj vvyz;,a)i25g jb(.0 rad/s. What is the centripetal acceleration of a point on the wheel's rim?j(g,vy );i5b sva j2zr

  What is the centripetal acceleration of a2*8(u wnerv2eofhj ma n4* hl6ivf ew(8g*5hn point on the perimeter of a bicycle whe5(vm8*4n6nrh2 uwfl * 2ghveaj* n eh(ife8owel of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minuya7svke1n(6 *itjz(x/cw 5o jsjbh*qq 4.v q4 te (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an art(1zin4 .*6ts s wy4(jvxvq*k5q cq/bojahej7ificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 505ci0kep, l5 ty gcezh 4pfr 5*(s26arb m with a speed of 20 m/s. The maximum centripetal force (provided by static frra *0cze sik y6h55(2fbe p,l4prc5tgiction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radiuu o : d1ykh19sj3nn*jks 50 m with a speed of 20 m/s. j:k1yok 3*jnu n 91hdsThe maximum 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 end of a 0.750-m st+ey 8 exl/ w*wc)xd8pxring, is whirled around in a smooth level table. If the maximum tension that the string canwl8x*ywee/xd+ )xc8p 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 slipping 10 m jbv1fgl hg7y0o q)e )79 jcki.down a lane at 4.3 c9vj kqef0717l )yg g.h)obijm/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 angulaj mak,k5hm5 9y +veteo o:l;y5r 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 acceleration ojwy so7 xh.p*gyy0 7;th6xfn -f $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angular velocity at t = 2.0 s?

  How many radians does av( j7fj/lli30 zuci3t 0.300-m radius automobile tire rotate after starting from rest and accelerating at a constant angular ac ufjjzv(i33lt7 /il0c celeration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleratioqzu5:4 q10r 8 dfbksktn of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates wit3jqh9v3kr i:r;8 m dshub7ps3h a constant angular acceleration jhsks vqur:3h397 bm8;3ri pdof $-5.0 \; rad/s^2$. 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 whilm0vg3t1o+v6cfx i r,qe turning through 2i vr otcf1+ x36mgv0,q.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly 3 +3q;heav pmy:rto1ifrom 8.40 m/s to rest over a distance of 115 m. What is eohrtp ;i: v3mq3a+y 1the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly frg7m zm slvi;(x6zq,* lom 8.40 m/s to rest over a distance of 115 m. What is the angular accelerationqlmz sxi*vg 7(m6z ;,l?

  A wheel of diameter of 68.0 cm slows down uniformly frkdytu 10 bt;3com 8.40 m/s to rest over a distance of 115 m. Howk; 0ybtdt u13c long does it take for the wheel to come to the stop?

  A centrifuge in a medicao5l fqio(am*+xfi pp-m8e p 8.l laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a consof5il mqo-p+8ae *( x.p mpf8itant 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 /ksf- iwnoyotd i :07i3/3ndktightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude ofwik /okd/7nndtif o:30i-3 ys 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 t.j9hfm35js3 koe, br qckl*p zs;,c130 cm long wrench is used, what is the magnitude of the force required when the fhf3c ,lj cj5ks3pb1t *9k.;omezsrq ,orce applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerti;m.n5szz l/ h0g mqi2wwo;t5sa $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows:vbe,i)jgc0w/6wh - zo 9 my*cb mass m is at the origin, mass 2m is at x = a, and0m wcw*6cv,9b/ -)y zi begohj, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is0;;+fjayn ;zc32v mkkv*quku pivoted 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 th; ujn2 cmuvk+f;;kvz 3 ay*q0ke 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 istw )yxq3y7uv +uy95v a pivoted 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 aroundax 5)+vyty 39uyqv7uw 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 is initi a +a4ehlgd4d(ee yewk5+c7 d-ally held in the horizontal position, and then released as the free end is allowed to fall. What i-d+y hal 4ege4e5ka(+d7 cwdes the angular 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 radius 30 cm and mass 1.58,1vd: ort wgq kg. Neglect the mass ofowdt 18:g,rqv 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 without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk p6b a. k/dafu 88a)t egml5k,ykulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleratiob6ekdlat/5ky uamfg k88 a ).,n of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a -ot/,nw5t tvhsb(x k8 frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the maoxwh/n , 8v(tb-ts5k tss?

  A rotating flywheel can be used to store energy. If n5fp yw:nk a*1it 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 inert0jqq+0-o,q,km/tc y9yqhe j jia 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 rolls wit(xe-h5 jd .mvk8btr3 ahout slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined pl 5xv (b.hm8redkj-at3 ane?

  A solid sphere of mass 1.0 kg and radius 0.010 m r0)h* e qb)kton:uw px2olls with a speed of 10 m/s. How high up an inclined plane can ik nh0owx)*t 2eq:pbu )t climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is rel42e6e;9ec 9qp3 j jhocd:b bhjeased from rest and allowed to roll down an incli qhede9c:j9b3 co ;4j ej6hb2pned 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 :ep to+b . gq ij(lb/(u*6pw)d*fnpnu slipping down a 35e ind(+ :). f*pnj nuqe*pig bubpt6(wl/ocline 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 momentum cha nt*ml:4 nb. w2,hfbmenges 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 ofjm6o)*dm cru6c st. :i 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 wi s-pq;24 ic1 (k54rkgzqft/ ep)cqzoith arms extended has a moment of inertiati1skkz5ope)q(4-irqq2; 4c g pcf/z of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?