Angular displacement is usually express in u/pe+3uwxhh e9w ez/l( nits of

  Angular velocity is expresse:-rwho 1b u5z+)dfco fd in units of

  Angular accelerationey-7fqh e 66ih xbv86k is expressed in units of

  A boy and a girl are riding on a merry-go-round whi-96(8lh) 4 ru)y8u*ccz ao/wjw :pqnopzgcii ch is turning at a constant rate. The boy is near the outer edge, and the gigripi(4ol8z6o / 8)u-znqccya:h uwp)9jc*w rl 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 turning r+is r*w1)h,t r/uvjo.xy, pkat a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater a h1/+wk)py roxvuir, *s .rt,jngular speed?

  A boy and a girl are riding on a merry-go-rosa ko r(xu omg.2e//7pund which is turning at a constant rate. Thero. //uk7mse2ao x(p g 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-rf)iwze xfba9+*eyp (qvq8hk 98z -/rmound which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleratx8r/h mp ikf)b9qy9*qf -awze+z e(8v ion?

  A boy and a girl are riding a m 9rrgq,6bhr2uerry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the gub ,rgr9qrh26reater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurateea5q g8o52m .1yrxc4 ( bsmxye steqa5 xrmx8by(oc4.y5 gm21esatement?

  Rolling without slipping depenbmjhr2z/b7(lnp e )+i d81rfcds on

  Two equal forces are applied to a door. The first3yz xl9+;ttp m force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater ptl x+z9tym; 3torque?

  Two equal forces are applied to a door azd elv .w4.zj7t the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of 4d.v.e7z jl wzthe door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. Tw,m qe5pe2 6;d c/mg6 gwumgn6eil( :fhe first force is twice as large as the second force. The ratio of the torque of t;(66g ummdwg:q ,2w cg liepe n5f/6emhe first to the torque of the second is

  What is the quantity used 5ezrd/q4 vcv (to measure an object's resistance to changes in rotation? e(d q5/cvzrv4

  Consider two uniform solid spheres where both have the sam/ h7l1usp.jf+. nkv. h+ev yaegxu g41e diameter, but one has twice the mass of the other. The ratio of the largervvu 1sx. e ekygp+l+/4.un j. h1f7agh moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twidwad/e n,36a 4ab2 55gjs 2osysu4 zmxce the radius of the other. The w3dm2bnosu5 ds5a, 6 4gzx2a/4syj earatio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice ii 9yawtk4e. 1the mass and twice the diey 9w.ik4t a1iameter of 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 increased tj/ qe99bdt07vw-vhf ho 2M and 3R, what happens to the spherfhwq-tv hv/7jeb09d 9e's moment of inertia about a central axis?

  If a constant net torque is applied to an object, tteu6 h,rajq2fw +tk( 3hat object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2fb xrim6( ir17. If this cylinder rolrrim1(xbf 7 6ils without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, oc6+fdd p y/gjycx;h09 ne 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 c+ yj0dyc pgfx6/hd;9wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M anmn wk4u ly/1l5gy)n c;0vs- ood radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depeou0v-y1wc /y)4;lsl n mno5gknds on

  Suppose a solid sphere of mass M and radius Rpp+0r90 v oux01ahvk-efu+ o itn(c.f rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline d (+x0 -ovc v rp+ pak9h0.ut0eufon1fiepends on

  "The total angular momentum of a system of pa)qmqrf2 cs -**it vkx s.z-7rqzsy ;j3rticles changes when a net external forstj2 m kfzsq)-c rix;y-.*s v37qr*zqce acts on the system." This statement is

  In what circumstances can the angular velocity o1 gd:a 3dqyl m0 ooh29l2hj+je,+ xpecf system of particles change without 3+od hqme1c0d+9 poxh:yelg2 a2jj l, any change in the system's angular momentum?

  The Earth orbits the Sun in an ells4.x ph)nmbum3 :v s11sftz4biptical orbit. Ignore any friction which may be present. What su:hnvp)fb.34z1 xb1mtms4 shappens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. Aslxs82i;tp 7 s+n/elzf the Earth moves close to the Sun, then which z;p +8xef/ltsinl2 s7of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrfx4lsh)x 6 f*metched arms close to his body. What happens to his angular momentum about the axisl* )4 msxhf6fx of rotation?

  An ice skater performs a pirouette (a fast spin) by qh 9f4jp 4.xsvv)-nhyfi .fg3pulling in his outstretched arms close to his body. Whqfhnjffvy3vi. h.- xp)4sg49 at happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette5n ur60kq kk3b (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the ar50quk6n bk k3xis of rotation?

State the law of conser1xjmbel7 kd-ry(o.8mgx, od; vation of angular momentum.

  What arc length does the Earth travel in a three month period in, q 4eihhuy,. :wuo/ bie8o8pn its nearly circular orbit about theuyo:8,4bhnpi u, i8eqwo/e .h Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lrgh ao2 plik(--c*joqyv1s k9i u)l;3ength of 0.30 m. What distance does the tip of the second hand sweep throughipc;lkgr(ou1- -*a)v 2i ok3ql9jh ys in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute/0z4nzq wyhqpql 3+w; equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is -6nc:ko *gxi8i;rk a ethe frequency of the wheel's rota *8n;:kocr -xk6eiiga tion?

  A pulsar (a rotating neutron star) emits pulses at a frequeaonp- 1 2 cgyh 9d.u8ue al4f/ttcxy6+ncy of 0.40 kHz. The period of its rof/4dg 61hpyatc exu8cl n.9 -t2youa+tation is

  A phonograph record rotates at 45 rpm. Through what angle do;i; bpmbv. :j-rv-is0c sdg.yes it turn in 0.20 0vdbp ;yrg- -ms;.cij.sbvi: s?

  A wheel of diameter 26 cm turns at 1500 ro 9guq6l ,m64o(osyahpm. How far will a point on the outer rlqo,h6 sga4umoy(o9 6 im move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. 2x3q0:v qg by;jz+oqwm:p5f1elrg 2w What is the average angular spel 3me: qfg0:;2+jbrgwq 52 1yzv pqowxed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 sf dnh 4 9nc3+pxw8v 7rpdgx:g:. What is the linear speed of a point 0.10 m from the center of tgp w x4n: dh+n vf8r9gd3p:7xche wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cablevcnl5 zgpkwir w7 0ig29c2, 6o which moves the car is driven by a pulleyi, 5zv7p9wn2 6r klog0wccig2 with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating-cfbn78, hln4go) naquiy8 yf:qt;-g with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on tu8-qnn :gf7 ync- g ht,b4 i8lo)fay;qhe wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If thw9jm wa-c5+l ke motor rotates at the rata+wjw -5m9lk ce of 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.wwn rz6j3ux; angular speed of 2.0 rad/s. wrujz36 . nxw; What is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a1:nhv cnezti18.kj jq g-6d4j bicycle wheel of diameter 70.0 cmh41vi kjng qzjctj8-d.n6 1:e when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space station (4v8fyq;uu v,r 9hmx 6z4de)oa r = 1000 m) rotate to prx4uaf; q98vurz ) e,od4mhyv6oduce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circuzro f7z)n-sw4o3coxzg 0hck(x sd2mhi* ;0 j.lar curve of radius 50 m with a speed of 20 m/s. The maximum centripeta70( f*i.kgwsz2 orzs o3) -xh jd0 hcxz;c4onml 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 of jsuc mdz0i 9ith5/ o8alh20o. 20 m/s. The maximum centripetal force (providjio8h icu. mdzoa/05l 9h20s ted 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 string, is3ac skp9.au,lq wq65vh0 :bx9xwx:ja whirled around in a smooth level table. If the maximum tension that the st9cw.6 k:l:vapwua9 5s3xq hx 0 ,xqajbring 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 ( alyg:w2v5au.he4fh 7.5 kg and radius 9.0 cm rolls without slipping 10 m down e fw: (ay2h gu.hv54laa lane 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 constant angular 29+gi 6t38umrfg7sm 7n orjlntyk5 :yacceleration 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 accnassyxl( k4 ;ly9 h2;zeleration 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 av+rjd jw8/ yox2/m.bofter starting from rest and accelerati objv.x d/wor2m/+8 jyng 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 s5 ;l4o7anikec0/xb y of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates wi9uxoh 8s1qdul2xw4 c5b )6thfth a constant angular acceleration of lho1uqts fxub)458 d 2cxw9h 6$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an ak) o; 7+zfyxwyngular speed of 6.0 rad/s while turning through 2.0 revolutions.kx)ywy 7 +fzo; What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest overe: d(4wvc6:6 ,2dhgq qo muaou a distance of 115 m. What is theq 6d6u4(a qdogwvem: uhco:2, total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly fax*6 0drf.tz erom 8.40 m/s to rest over a distance of 115 m. What is the angue 6z*xt.dfr0a lar acceleration?

  A wheel of diameter of 68.0 cm slyrrm: -m33.xz :sn lllows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it .sly-3zrmxnlm:r :l 3take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates akx4m)n+0 pxz3*7v a6pd ofs lczqn5 l2ag /lq6t a rotational speed of 3600 rev/min. Whg 0n*xsovknx 4zp7l5) /qapal6c3fql6 2+zm den switched off, it rotates 50.0 times at a 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 reqd a 3,*mdk c:4vm/i xd,yte0tnuire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of thd, t,t iy ne3akx4/m:v*0cmdd e force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90wgyz1n 6hro )i,u:zx)jhlsz 1eg 9r(6 Nm. If a 30 cm long wrench is used, what is the magnitude of tz r zlx19 e,ihynj)z6wu6(or)g1 sg:hhe force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of i+zih/)vbic: dnertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: m(n.z nus0ngk9xw x58 vass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What iszu09xgn(nk.v8s nw5 x the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless amx2h:um24:2zxmeixu,ag p;ced(y 0oxis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the rigmxi x2e0xyum 4 ;g2p::(zm,2 uehodcaht. 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 .gd9kh9az; cul 7l8lb 10 kg is 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 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 frog.kbl9cdl9 alhzu7 8 ;m rest?

  A 4.00-m long rod is hinged at one end. The rod ityaub;wqku o6ny(.o6* 8q 8fq s 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? (The moma bo wut8 *6 fou(q;qk.y86yqnent of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radiulnq8z o/8u0 mo2jm (xkb.zto7s 30 cm and mass 1.5 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 spezj0b2xkt zqo m8.u /lom(n8 o7ed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a fricc ifa/6s+7df btionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of thb7c6 i+/ afdfse pulley?

  A 1.53-kg mass hangs on a rope wrapp49 k jth-fjvck3xi/u.ed around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration 4it3-fkukxjhv/ jc9. of the mass?

  A rotating flywheel can be used to store 0n pg5m )v p.24yltixeenergy. 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 in)kr if*zhj .slzc8*o,ertia 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.pso ah*-o;- mx0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the hx -s o;p-m*aobottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10 fbcod1vljz7 ) .8vs3km/s. How high up an inclined plane can it climb before szc73kobl1f.8vj )vdcoming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is relea+yxto l/a-4 mtsb w( rj8p75ca6aj1 sised from rest and allowed to roll down an inclined plane. How fast is it moving17 +4aai-8o(w p sjtb/6a5xsltcrjym after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and rahwm( e7c3h9b6rff yz l r/ai4(dius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The momen b4(i/eyl 7a(rchf9mfrzhw 63t 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 changes 5(g zu: gmh7, fycqx0k7:vdanby $20 \; kgm^{2}/s$ 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 5* j 2eeues( bw1tf0sumoment 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 has a moment of .k pcp5,. i wz0xt jjggp(i1.vinertia(g..i t5wvj,pzc 0g1. ikp xjp 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?