Angular displacement is usually express6k3 hwn bl rn0q+v26 /gx 0ax3h1qtjce in units of

  Angular velocity is express 4tbi n4men917g0rxat y:e4s ned in units of

  Angular acceleration is expressedfd foufg4-2bcc o n(./b0ai 2b in units of

  A boy and a girl are riding on a merry-go-rousoa3,x83vva/nd 9 +xwg xup 8und 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 disp8vxx9au 8 vupg,sw/oa3 n3+d xlacement?

  A boy and a girl are ridingeqpn ( +p,o8 lbcw8ood*dr, 4e on a merry-go-round which is turning at a constant rate. The boy 8qn* rod lpoceo(4,,d p+8bweis 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-r/xaltpxs:ec 1) ptxjk;z,8;t ound which is turning at a constant rate. 1 ,tx t/8p;pac;:k jxetzs)lx The boy is near the outer 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 turn nkl r(8 ads/zgn;b2i5ing at a constant rate. The boy is near the ou bg5 8d;(/zri n2naslkter 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-rouiyr + uax yjz1;;3*wy v0(76yh.lkcspw-bl lgnd which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who * rx 37yiyh06wlzly(vbw; j+cay-ul g1psk;. has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the zf r1 8 ,ue:vrjfj(ok:following is an accurate stateme8,ojrku:zf fj(1:v e rnt?

  Rolling without slippingjslx3 a+g4+ro depends on

  Two equal forces are applied to a door. The f1t)z/tvolnv 1 wvo3n/irst force is applied at the midpoint of the1 ntwv3/vl otv)z1 /no door; the 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 force is mj,6g:6 wxzfl applied perpendicular to the door; the second force is :lg j,x6mfw6z applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicc 5tm(tgq58 uejrtf s u0s.9)mular 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 s5t8tqsmj s0(5femtr) u.9g ucecond is

  What is the quantity used to measure an qguph; q 574if3tdw8 fobject's resistance to changes in rotation?pd7i fhq gu3fqw;5t84

  Consider two uniform solid spheres where both have the same diameter,h/.drd9zf-ev+5y xz n dblh84 but one has twice the mass of thrxz8 zh v4y5nb.f- d9dleh+/d e 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 twice7vie,zbfx1k92k y m6k the radius of the other. The ratio of the larger sphere's moment of z,ixe 12k y76vk9m bkfinertia to that of the smaller sphere is

  Consider two uniform solid spheres wher4r u:3a3 bpwldncs,a+bnfc( 8e one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertiarn nuca:d34w ,p+ sf8 (lcba3b to that of the smaller moment of inertia is

  A uniform solid sphere has mass M u0hi58jhdxrw2d y9gm anm 7ea7359ex and radius R. If these are increased to 2M and 3R, what happens to the s2umagih57a 3j m85ee9 nxdwyxhdr 970phere's moment of inertia about a central axis?

  If a constant net torque is applied to an oad;5mldhc, n4bject, that object will

  The moment of inertia of a solid cylinder about b+ ,.i ()xurphqqmk*h5 t,grl its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to rl),( imkpb ,thu* rxqh+q.5 gits translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 10 kg avh - uylah6t*-nd a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels th u-yh*l t6v-ao 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 sliz(v6/ gsghq6spping down an inclined plane stg v6(/gqhzss 6arting 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 sli9 dcaby +w6 b acfukvrhl3;75-pping down an inclined plane starting from rest. T6k95hbav;-dbw 3ca fucr7 y l+he angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of nrtu::q ob0 i269g bxvgl1(fr particles changes when a net external force acts on the system." This statement b (6 it uqgr:r0bvgn2f:ox9l1is

  In what circumstances can the angular velocity of system of particles c 98kl;ttt( 6b zknlft0hange without any change in the system's angk8 l z9kb;t6nl0tf t(tular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any jg;f4gg wuz(my ( 7di.y/)r; h -xclavs5d ty,friction which may be present. What happens over time to the Eartgr(yit-sjv 4 gu w5clh (;z,7.m/yfddx;)agy h's angular momentum about the Sun?

  The Earth moves about the Su c1j b+qx4a.* plnk )u1vhak:wn in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes tn:j )u. hxlpvq114k* cwaka+b he orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hi,awngr2s c fy,g-m+5 js outstretched arms close to his body. What happens to his angular momentum about cam jr fsng,g+25 w,-ythe axis of rotation?

  An ice skater performs a pirouette (a fast spin) by ytfi(e.yc:3r0o w6yopulling in his outstretched arms close to his b( f.yyr30 icoy: eto6wody. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchex,v r4wtyrq.7 d arms close to his body. What happens to his moment of inertia about the axis of rotxt.r7w , yr4qvation?

State the law of conservation of angk *1. vl)gqoelular momentum.

  What arc length doesczd0x9m *m1mw1uoi s/ the Earth travel in a three month period in its nearly circular orbit about the Sun with a radiuc z m91mmsuxow/d01*is of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance b-c sz)w*owd; 3, cnpidoes the tip of the second hand sweep throu*wc ;znd, bi s3pwo-)cgh in 3 minutes and 45 seconds?

  How many rad/s is 25 rev e3hq1f) vy tz*kwzvsvui0421olutions per minute equivalent to?

  A bicycle wheel rotates uniformly throb(:2tpt3:o:y3 yh 5 fpwo kchkugh 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotation?thp :f2okty (wb :k:c5 h3o3py

  A pulsar (a rotating neutron sta hb f34.ki+ runizn n+m-gtf6mcx x)7:r) emits pulses at a frequency of 0.40 kHz. The period of it+m7bc ff zixnn:u+m x-3n.)gkr h6t i4s rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it t;nsxywax z;c6;k y;0zib1 ka7hb hc/ 1urn in 0.20 s?zi7as0h an; kxz;kyyx; 6w1h/b 1c b;c

  A wheel of diameter 26 cm turns at 15 f(wd,(ep j1v 9uu/asi00 rpm. How far will a point on the outer rim( epdvju is1aw9uf/( , move in 2.1 s?

  A bicycle wheel rotates ar -bwtbrpq.btaxe;b--2o : 9uniformly through 2.0 revolutions in 4.0 s. What is the aver:9q2aet xr t.; b-rwaobbp-b-age angular speed of the wheel?

  A bicycle wheel rotates uniform81h(ch yrdm 5ij0py s-ly through 2.0 revolutions in 4.0 s. What is the linear speed of js1dry50 p-y8mh( cih a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The c13r5ar s+ srudc. 6yqjable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the yd r.s 3sqj+rua516crpulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angulard,-ff z:s0r5 )xxopxii9gx: t speed of 2.0 rad/s. What is the linear speed o9t-5pfi g:osx:i x ,0r)xzfxd f a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the motofa46lkrc p7jp9m ( 4xy2--* lqeiqamjr rotates at the rate of 20 rev/s, -l*4ayef6pqj-92qmj ma kxc47lr(pi what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant +nq/zics * el3angular speed of 2.0 rad/s. What is the centripetal acceleratnecl3zs*q+i /ion of a point on the wheel's rim?

  What is the centripetal acceleri*0 e iptbpkt.9f0/l cation of a point on the perimeter of a bicycle wheel of diameter 70.0 c.bk i9 lie 0tpf0p/*ctm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotatin/)f74*l5rbbkt bw (as1i fz ,a ere5fpg space station (r = 1000 mr lb /b157f,fb(*5a4zsawe ) etp ifkr) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius xzu8 6o vv1nb950 m with a speed of 20 m/s. The maximum centripetal force (pr98uo n1x6bvzv ovided 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 wi9: gdawy /sm- 0,lcfzfth a speed of 20 m/s. The maximum centripetal force (provided by static frictiond9s/ cfz ym:0wlaf -g,) 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 whi0uhhb0 8f4rl8 yyd z:irled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, 0ry dh:i z4uhbf8yl80then 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 d)v)rbs f8kmlb 1vc5.yu o-+ k, hq4jxbown a lh kxlvq ,-o kbv8m )5cy)r+bf1b.4usjane 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 constantd0(fhoeo4:z (j bs(p8kekcy ju,7 )f z 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 withu* uy33s)jzbqnkd5 b, a constant 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 rotate after stfpi 8a++nst /earting from rest and accelerating at a constant angular accelerasf8i+enatp+ /tion of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleri3m 4. 4eucpesation of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating ce plgnz6(3a )at 20 rad/s decelerates with a constant angular acceleration of ) nl3 pc6(zage$-5.0 \; rad/s^2$. 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 while tur)duarx ud:).l ning through 2.0 revo) l)d:.rdu auxlutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows;-gkhb5oa.wh - r7fsmh ty(c rq k8./q down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rot .rbfmh h5ow;/k-c78.ar-sqt(hy q kgates in coming to rest?

  A wheel of diameter of 68.0 cm slows dowwg4/h3(bmk.8 qwko4u 7nfw whl (zh sipv:t-4n uniformly from 8.40 m/s to rest over a distance of 115 m. What is the a4 7bwg8fhiw.nzp k :-sqwu k4hmo/34 vh (w(tlngular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest overaamouka;h we29zqio . iw *058 a distance of 115 m. How long does it take for the wheel to come to 8mw.aow azua2q09*ki5 i eh;othe stop?

  A centrifuge in a medical laboratoryv u ga +vog2u5r/*ql5y rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration beforevr2gyoag +u*5 5vuql / 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 tightenuw8s6 e0a; vjning to a torque of 90 Nm. If a 30 cm long wrench i68v 0u ;swjenas used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel requirs 0 +/;wzd m b/2kbxv,zwjqnm4e tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of t n/j+qzzd2 wx;v/m0 s4mbbw,khe force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ine,g3 u9t zzkxmzyob433 rtia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: 4.khz7pb*e 1rc 8ri ojmass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What ei4 z.j*r hkbpo817rcis the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about7jm/dy7i68t ,mw uclz 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 ayd8 jz ,7m tm6/7culwingular acceleration of the cylinder?

  A solid cylinder of mass 10 kg i4peflm8(rym7 s pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius Rr8e7m( mlyp4f 1 = 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 hinged at one end. The rod is initially hel: t6+ x*ioiwf 3/sjpydd in the horizontal positiosyd+ j/f *iw pto:6i3xn, and then released as the free end is allowed to fall. What is 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 1.5n:if:6z1jp o(6va aq+6t zoch kg. Neglect the mass of 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 t:1+z6cqznv: p6 j f6aoaioh(without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulle (8hl 4+gmwr 5ch6mpday of mass 7.07 kg and radius 66.0 cm. Wpw 4g+cmhar5h d(6l m8hat is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped aroui xumbf8 +-:do8ohfb)os2c7rnd a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleratioo)b8fb2 xhom-oc7 d8r+fi: usn of the mass?

  A rotating flywheel can be used to storqk rsy uw(6q-x0yl(o:e 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 of3hh x 4qaqg2/-vw5m9y .ld yfz inertia 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 radiuwvla4 z5el5 o:s 0.010 m starts from rest and rolls without slipping dowlaow5e: 4v 5zln a 1.0-m high 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 0.01iegzc58 x,r 5j2w/hsi0 m rolls with a speed of 10 m/s. How high up an inclinhis/5e82g ,w5rcxjiz ed plane can it climb before coming to rest?

  A hoop of radius 0.50 m ldrt 6r.+g alw/3ya8j and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it mow3y6/ja.r8g d+ alrltving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm ro 94rbn+e (x8h *mrmof,ju uxq6lls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere 9+ub (huo x6n* 48efmrjqx,r mis 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 chaiv7a 1*oqse l76v-tqfjoc23 fnges 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 m0m 8b3-o 2mjc6d moesl*(i fxa 7dbi,foment 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 har x6u1joh t11ss a moment of inertia outxj1 r16 sho1f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?