Angular displacement is usually express in ble a 6rwcd945bp)y * vjvsus6wv(g-,units of

  Angular velocity is expressed in 1dv8wf4 5s- h ukakgv67ywn(s units of

  Angular acceleration is expressed in unit83to heq/s;bs( tbt( gs of

  A boy and a girl are riding on a merry-go-round which is turning at a constm62rol9op +f vd+:ggv3. yr3gn l(csaant rate. The boy is near the outer edge, and the girl is closer :g+so6a gvpd m+nvlf2g rl39orcy(3. 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 a constant ferameks*55t 3j46owrate. The boy is near the outer edge, and the girl is closerfm or*se 54k5ajw6e3t to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round wh nxqiyqr2. o,1alr 27c*dhvfrt 6i5,r ich is turning at a constant rate. The boy is near the outer edge, and the girl is c5 rr a.rt,i1n q6dfyiqrl7,h2 v *c2oxloser to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning atx++5+7on) dg 1xwnifa qqn 5un a constant rate. The boy is nea5nni5 +x qg wdfnx )un+7qao+1r 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-round which is turning at (m*8hv m5znbfh8klq) ahn 5c; ooo3,wa constant rate. The boy is neaoocn(35b)o hhmfv 8lw hz,q nmk5; *a8r the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. jauz03;n4nxen; x 1lm+ zz z.xv74iuwWhich of the following is an accurate stateme4+ni;wu 4xn 1z xuaz nzz730v; lxj.ment?

  Rolling without slipping depends oa c rs,8 ez1d*u8;di.1lp e0emxsw5rjn

  Two equal forces are applied to a door. Th3-cfu34wwx qh e first force is applied at the midpoint of the door; the second force is applied at the doh3c34wu wxqf -orknob. 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 force is a26n(couu1hm*mo+x,e )hwc cn pplied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exero 26xhccnue*hmo, w +(u1mn)cts the greater torque?

  Two forces are applied to a doorknob, .8xkox6igmcj-q a65 xperpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the secoj6 m-568iqx ogcakxx.nd is

  What is the quantity used to measure an object's resistance to cw/u e6.s2qcv zhanges in rotatiovsq/2w.ez cu6n?

  Consider two uniform solid spheres w6g+ibs 4cr1 pmhere both have the same diameter, but one has twice the mass of the other. Th1c6ib +4mg rspe ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, buq1jac, m7 hz y)xe zt-gfug2:0t one has twice the radius of the othe21aeyh7 x)z-fjuq t, 0m: gcgzr. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform so)m v+d* 9fa8ydeym:ho-oop3 eu4.r7d m rw*sj lid 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 sma y9.d) jo8 *pdfovme-+*:7oawdsr4 mmyhe 3urller moment of inertia is

  A uniform solid sphere has mass M and radius R. If. /zls2jt6)b uo*6rwpe bf2vywb2)vl these are increased to 2M and 3R, what/e2jyur)lzsf2 *b2 lw vbop.bwt)6 v6 happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wildzza e1.nd2 ci4f6wn6k) )7. dtr zohpl

  The moment of inertia of a solid cylinder about its axis is giv4 qt 2mu +pr h7we,ras,kkl7t.en by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational ltr7e .r,4,spkmw+qa k 27uhtkinetic energy is

  Consider a motorcycle of mass 150 kg, one whee ;g0)wio1rn qnl 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 wheels to the total translational kinetic energy of the ng0;1wn)iro q bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls withaf .z1tv)gz5/v /kk rjout slipping down an inclined plane starting from rest. z a.fzk/tv5/j)1 vkrg 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 down an infkqnts9 d,7 ke4 hd2d;y8 ql +xjxe+*tclined p92enyk7tt,e qls 8 j+hd fkdx;d+* 4xqlane starting from rest. 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 oxi7)9jl 8:ha:e-fip2oq kg tnet external force acts on the system." Thiso- 7k 2a)fteigpq8 x::il9hoj statement is

  In what circumstances can the angular velocity of s usiy8w2 gm+ .5ev,n1or/9a xcof8lhmystem of particles change without any chr9xo1w5ylf+ cn /g8vuio8s ham, e.2m ange in the system's angular momentum?

  The Earth orbits the Sun ingjbvs yq)*; ,lfu-g)v an elliptical orbit. Ignore any friction which may be present. What happens*g vqlg)f-jsy, u ;vb) over time to the Earth's angular momentum about the Sun?

  The Earth moves aboutrh9)t+ 8 dvrr:mczsm6 the Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed rmmd8 tr9svrh c:z)6 +of the Earth about the Sun?

  An ice skater performs a pibcmyf8 i3ju9 ymxa- rx u,wj) v8b31l*rouette (a fast spin) by pulling in his outstretched aw, ub3j8 3*yxyvj8xm)f1li -mcr9ubarms close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performszprd1 o1va:/c a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetrd oaz1/ pvc1:ic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outst72a m oi/6k4ib; ntestretched arms close to his body. What happens to his moment of inertia about the axis ;ns 42m 7aetbki/ 6oitof rotation?

State the law of conservation of angular momg6 duhl(h0w- hentum.

  What arc length does the Earth travel in a three month period infw;8gshihzs h+w.t sw66qy(3 its nearly circu;6 hz3wwfgwtss 6hq( y.is8h+ lar orbit about 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 d(9y/scirk*(c l; 2m x- 3vqvkpiui1vooes the tip of the second hand sweep through in 3 minutes and 45 sicv3 ilmyk2q(cspi v ov;1-/9xruk(*econds?

  How many rad/s is 25 revolutions per minute e4w 8- fvq 2clz19oiepmquivalent to?

  A bicycle wheel rotates uniformly tht 9u8+*hh ygirrough 2.0 revolutions in 4.0 s. What is the freyh*8thg 9ru+ iquency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0;9m2b -rnhyrkz7 dq /a.40 kHz. The period of its rotationrkn9 z 7bm/hr;- ady2q is

  A phonograph record rotat4jk)z- yd vh /rka4c)ees at 45 rpm. Through what angle does it turn in 0.20 s)4a4kc z/kde) v -jrhy?

  A wheel of diameter u0y;e8fg h5zwta -e5g26 cm turns at 1500 rpm. How far will a point on the outer rim move in 20 e-8gthyufaz;ewg5 5.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4dq )2jt0vtg;tkw4b3 e.0 s. What is the average angular speed of the whbg2vkdj ;qt 0)twte34eel?

  A bicycle wheel rotates uniformly tef0ln8 h0ss4kls8ac3hrough 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the ce 0kc3sshesa8l8l4f0n nter of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable h3wd q.r*4ocx which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must tq*wo 4d.r3xchhe pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotatingonax*2m gqs+/ with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on * +/omqg2 saxnthe wheel's rim?

  The cutting cord on a gas-powered weed cqpnkjvjq ( 6g xe4**sjv-a9p2utter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate liv jqp*sg9n p kj q-xeav2(j46*near speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a consu+9vjq vhk,stqgxj0, gq153 btant angular speed of 2.0 rad/s. What is the centripetal accelera qqsbkg5 v,,1v3 gjt+u0xj h9qtion of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the 41io nev:ii4fqu; 9yzperimeter of a bicycle wheel of diameter;iqy9ovii4ze :4f1un 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular ;quyrw 7:sb:qqj s 4m 6q10evomu/,nj, rotating space station (r = 1000 m) rotaq:, ob7rs:jy ;m /q q j16eqmuv0usn4wte to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m witso/9 anp+xlzinio; .+ h a speed of 20 m/s. The maximum centripetal force (provided by i pn;. nloo/a++9zs ixstatic 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,bl1qr9gmm 1 h.jc2sh of 20 m/s. The maximq.jhc 9b gsm1m,l 1h2rum 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, attat0zwvce - 7)6rblfyr1ched to the end of a 0.750-m string, is whirled around in a smooth level table. If 7fbr0elzr c1 y6wt)-v 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 r76ri0d/ksp jop q:k+ folls without slipping 10 m down a lp sj0/r67qi+: kodfk pane at 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 constantgcaxkf t g:z48r9.j )h .5rgqy 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 constan0.5-dq)qx dojs wd6kkt angular 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 tire rota -og; +cd bl)9mplh,8xt 9xnks,8m vfpte after starting fromp,h9vbkt lc;,ms)f 8xml+ o9pgn8 -x d rest 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 h + vjwu/ 1tspvwm(8eu4 sa(j1bll/mh7as an angular 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 conrax os hr3:3d,stant angular accelerati3xaor3h:d, sr on of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an)wdp0mu :pswe3ev nu2+p(a0g angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angularw(e3v a+ppeun:2 ms)gu w0 dp0 acceleration of the wheel?

  A wheel of diameter of 68.0 cm slowamprdfnw4- 8;jo1 sns h4vr1/s down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming w1ah/prdfn1o4s r 4vs;8n-mjto rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest o-d s4/m9yg+ r h flp4crqay2-sver a distance of 115 m. What is the angular acdshgp qm4a9lfyr+ /s-4 2-cryceleration?

  A wheel of diameter of 68.0 cm slows down 7 p:yj5vdd/ki) r 7esv.fimqbd;*x d 3uniformly from 8.40 m/s to rest over a distance of 11d)/bq edi d;v7.y xfvk35pd* imr:j7s5 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotatesf* p88g.;depbxb)dseo:qq4g f yb77 r at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a proq bsfxg;yd8)gp8b :f edbq4 7e.7*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 tighteningfs e.del 9cq-+ to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude o+ dsl.feecq9- f the force required when the force is perpendicular to the wrench?

  The bolts on a car whecv z n)q;jh..bel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required whenzb) hv. qnc;.j the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iners :2) i o(d/e4:6p(ljjwpcvmic4gm cjtia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as foq-ei pt9, 0zlillows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. Wh, 9iei zlqtp-0at is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a nuhvdy s-p14xl8q i2gj6, h9t frictionless axis thought the center O.iu8 p6n1-hd tl vy4qg 2hs,jx9 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 acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionl0w3eb ha;w5 asess axis thought the center O. A rope ww ase05bha;3wrapped 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 starts from rest?

  A 4.00-m long rod is hingetu ht bm7b;0/md at one end. 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? (T/ub h7 ;0mtmtbhe 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 1.5 kg. Neglelmpe09. z pj8uct the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radiuez pl9 u8j0mp.s 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 ropej/ln+ag l8) ha wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pulja+h)/ alng8lley?

  A 1.53-kg mass hangs on a rope wrapped arouu9e4ozbua c t537f hk) c0v5jqnd a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is thec 54 bf)q e97ko3zhu5tjuva0c acceleration of the mass?

  A rotating flywheel can5 sns3 sgmu;1m 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 inehw b+zi+xi78fwe p5wv9 ud 2f9rtia 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 anwtl4h.e 4n u(zd radius 0.010 m starts from rest and rolls without slipping down a 1.0-m hil(nwez .h4ut 4gh inclined plane. What is the speed 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 m/sg5kv,siuyl1 .3s xom59m,wej. How high up an inclined plane can it climb before comi553l1x9vu,.gmei mysswk , ojng to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released fro;cqqftgo/d cm6)f 1:wm rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3 6qcof;mw1qg)c: /dt f.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls withz6 jxa3fwd4n3 out slipping down a 35e incline that i4d33zfw jxan6 s 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 cabin ad10 x+6momentum 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 o1yr01qiubu q j9s-v t)f $5.0 \; kgm^{2}$ 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 mom mj(hqi4qmy zu*j)o337 2s+uvwgu9bx** vhd ment of inertiavsomi)hdm b m yqu9whx24 *g 3j(u7zv*+3*ujq 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?