Angular displacement is usuallf 2u-o8ubj,yv/)y b2 uo bue/xy express in units of

  Angular velocity is expreseq 7qp; .uajt8.hm x9wsed in units of

  Angular acceleration is expresdug+db2 .f qm8sed in units of

  A boy and a girl are riding owa-ah ,t54 wks2y d4cwn a merry-go-round which is turning at a constant rate. The boh -, sakda 4y5c42wwtwy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go9h2gp;)n vwx k3uw9d h-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the p932 d)xwg9k ;whhvnu center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round b*7wc m rr3.zswhich 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 3 wzrm7*rb.sc linear speed?

  A boy and a girl are :y:2f z)4ca6kp1a-shozpk n iriding a merry-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 greater centripetal accelera:a 6cs p p4z:hki 2fzna)oy-1ktion?

  A boy and a girl are riding a merry-go-round which is turning at a consdwyj8x9 h/z /i/aej 1htant rate. The boy is near the outer edge, while the girl8w91ya/zjhx dji/e/h is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotat2iu(; 67ow,yy s r3dmbir2mksing. Which of the following is an accurate statemeriwsm bok; 7326uisym (yd, r2nt?

  Rolling without slipping depends onvjergw+s1e rd+ 7lv/3

  Two equal forces are applied to a door. Therr) i7up 7i:u5r:hyhbve: d.k first force is applied at the midpoint of the door; the second force is applied at the door7ukr vbrph5ihe 7yu ::.: rid)knob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at us9 n5q6rf ojk1;g uf1bcs +o-the doorknob. The first force is applied perpendicular to the door; the second force is appcbsf ;g-1 sfurj1uqo569k on+lied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the dooyr 3uvuoxp zk5s/*;z sip12i-r. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the second -ir1iu 2xyk spu/3v 5;ps*ozzis

  What is the quantity used to c-ua70v m(fk0x8mt9 vcadr o2measure an object's resistance to changes in rotation?cv9m- 20r7a8 mot0caxu(f kv d

  Consider two uniform solid spheres where both have the same diameter,2ygz),1kko6v -aihq y but one has twice the ma2,kyyq-h z6a)k o1g ivss 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 7qxqo1nc. e/ nyemj 52the same mass, but one has twice the radius of the other. The ratio of mn21j cey5no ./ qxqe7the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass aa.m/0ur f ;cycnd twice the diam /f.u0c;myarceter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere 99tg-(wwu) 8p1hqzs/z2n oitkp p ;ga has mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of i tt(k/wgp 8pz1;ong w2 )pqi9-9ahzusnertia about a central axis?

  If a constant net torque is applied to an object, that object ij7qhk 7wa0w4will

  The moment of inertia of a solid cylindeu2pnv9au-6+ewe+fl1j oj9 v pr about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its 2no p jaefu96u+pwv1l9vj +e- rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 khc.l.hx9dau9 -uv u5 vmx js3u21ues-g, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic enehsua x31 u9jdu9xlhvu5eu 2.vms-.c -rgy of the wheels 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 without slipping dow opq./82iatra *o;,fq aka2srn an inclined plane startinatsrafiao o2 ;k8a* pq /qr,.2g from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of maw1pu(7 kz:7*,hj63ejpng ca -rv bdohss M and radius R rolls without slipping down an inclined plane starting from rest. The angular velogr-w 71(oah, * j:bvuh kp6npz37cdejcity of the sphere at the bottom of the incline depends on

  "The total angular momentum ereod0032c9,vx vl evof a system of particles changes when a net externald0e3 20 9vvecvo,rexl force acts on the system." This statement is

  In what circumstances can the angular velocity of system of particle27:x*t qiq5gn sjsu+e s change without any change in t q+x :qieu*5ns2g js7the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore anyy:y.5tay c3ydo hs4*m3 e i1ja friction which may be a1ymyc.j3h3 dsi eyy:*ot5 4 apresent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an kzr, y-u(1l+dv3 eckqelliptical orbit. As the Earth moves close to the Sun, then whicq1,evcdkr -luzk(+y 3h of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a piyra;9c6 2ysdf jm:)j+s(upq drouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotation?(dcs2)+rpm;fdjuq 9y 6: ajsy

  An ice skater performs a pirouette (a fast spin) by pulling in his outs393ek(aa mtxk 2:b8l- zpgzlktretched arms close to his body. What happens to his rotational kinetic energy about the axis of rota x9k8(3azzbpk 2: tekm g3lal-tion?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchedy ;roe9yw;tc0+ 52nx x c0y 3zqjq;mkg arms close to his body. What happensz3x;mj ;q9 y;k w gycn0r x+yect52qo0 to his moment of inertia about the axis of rotation?

State the law of conservation of .h.;x8*jbqfuzl;lt m2z 6yofangular momentum.

  What arc length does the Earth travel in a three month period in its nearly circ8jja-,fo/m j hft o:w2ular orbit about the Sun j :jwh8fafm2t j,/ -oowith a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length ofp.xn 0un( ble7 0.30 m. What distance does the tip of the second hand sw e07bun p(.nxleep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivd (z-*gzj3uj walent to?

  A bicycle wheel rotates unifor6 u o,eq(ppwih/:,uhm mly through 2.0 revolutions in 4.0 s. What is the frequ,( euquhio,/p :6mphw ency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequencyi.amar0h)1 hy8k+k gf of 0.40 kHz. The period of its rotatifm8+h)a.kkrh1 0 aigy on is

  A phonograph record rotates at 45 rpm. Through what v.3 dcsne)y jia6)2j sfft -o:angle does it turn in 0.20 i: ay-eonc)3st )fd6fs2. jvj s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the )qciwzs.3o u. 97ygqm outer rim move in .u9qow) c3 . 7qiyszmg2.1 s?

  A bicycle wheel rotates uniformly through 2ld,)t 48u*q2cnus mo1 isre4s.0 revolutions in 4.0 s. What is the averamou 8s tc24sn,i1 e4*sr dql)uge angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thg1j.k(rtsze / +5bkore linear speed of a point 0.10k 1b+ 5erg(s.kjz/tor m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable whijl/1u0z2pswpx(is9uf ;wx 6 dch moves the car is driven by a pulley w6 90u ws1xpuwsd p/xi2 ;l(zfjith 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 1.0cg :yjjl/: m0d m is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a pljd :m:jyg/c0oint on the wheel's rim?

  The cutting cord on a gasu. 02yxfb ;v+te u3g.olj4sjj-powered weed 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 of the 0tyjux4+o;.ues bv2 g.f 3ljjcord?

  A wheel of radius 1.0 m is rotating with a cons54oqp .c q)zr53hd wostant angular speed of 2.0 rad/s. Whatc.poz 3w sq5q)ohrd54 is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimetmx0o r a ,u6k8xx+l7fllmlp)4er of a bicycle wheel o0l8x7 lll xo,faxp4k)mm6 ru+f diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a 0p+ wwqxgwtap 7o89w5 circular, rotating space station (r = 1000 mw 9qp gx+5aww07p8wto) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of rad jp0.rw:ryn8v ius 50 m with a speed of 20 m/s. The maximum centryj 0v rn.p8w:ripetal 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 bynzt7n3 ;y71qrsr6k a speed of 20 m/s. The maximum centripetarb trzn7syykn; q713 6l 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 string, is whirled around in f3v*n0n)9h ppkv+ pf ja smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed c np3v +p9vnh jp)*kf0fan the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls withou ab1n)i*;(tesn4ikci t slipping 10 m down a lane at 4.3 m/s.i1k4as)e; ib (ticnn *
(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 accelx)kxj:r 5oitx1)jyi 5eration 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 accelerati5nxf+uyd. 7ydon 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 autvkvuob8pj wr ;ym-n9)/ )3nfpomobile tire rotate after starting from rest and accelerating a98v-n3k mr)njp;v/y op)fb wu t a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and nj5j *m9ky*nmpb38lkuf9 e 0phas an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating b;bfpho xoka ,m: ez 6;p2ivu;4d(-yt at 20 rad/s decelerates with a constant angular acceleration of;vaepy(;z -o4txfpo6 hd;2:k ,mib bu $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angut5dio* khd7x4lar speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the wheel?*d4hxod t ik75

  A wheel of diameter of 68.0 a4p+szzl:m4h 5choi,vy * ymvy gx-8+cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolu8vsp-yma i lymxzh*+v y4 4zog5, hc:+tions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 rs ca /e)*pdo+lu15i xm/s to rest over a distance of 115 m. What is the scrpe5 d*x a+) oui/l1angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest o4t9mzz o9za7over a distance of 115 m. How long does it take fo 7m99o4 ztozazr the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speedt agkhg(/seo s9oz4a2 (;q8mb of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before comi(bg /;qeo8tsh 4a gaso9m (2kzng 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 tightening to a torque o/+dof tuq nq6)f 90 Nm. If a 30 cm long wrench is used, what is the magnitude of+ntd6f uqo )q/ the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tir/-cp2. owr 2w axq3ug.h n.zxghtening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the forccx/xwrw.2hg 2ua-3.zr n .pqoe required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of i;z )4y- o)cjk ld,jbitnertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modele8zvty )j5 gc,ad as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at a,y5j8zv) c gtx = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is 8et bl* 8*qptypivoted 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 for 8y8ttbq*ep*l ce 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 frictionless axis thoughbum.u-9iy ym 9.mfp*yt the center O. A rope wrapped around the outer im ypf. yuyb-99 *mmu.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 hinged at one end. The rod is initially held in thqiokz7zk05no- 9uc1g2 n :jiv e horizontal position, and then released as the free end9ci zou1ji: qk-v57kn gzon20 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 1.5i;io5q4-q ;w . *;-wilkfhl dg/ejow m kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a spm/woili-;o ;; q-j*. 5wdqk4leihg wfrocket 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 frictionlesz, in.xvqk v a2d+g5yhaqqw0v+b +v36 s disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of t++vdxai0. , yvagvk+563w2qqqh zb n vhe pulley?

  A 1.53-kg mass hangs on d8ktxwk*-t;e9pi 7d vv+a +ie a rope wrapped around a frictionless disk pulley of mass 7.07 kg a9ved; wka tikxdvi 8 p*t++e7-nd radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store e.u .nfxzl8x c-nergy. 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 iner+;-u /leuvvp v9ur r0ptia 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 raddg w8kto*j (0y4jan t/+pxt 0xius 0.010 m starts from rest and rolls without slipping dodo4( tx0p x8g/n kawj+y0t tj*wn 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 0.010 m rolls with a speed or es,**5 ,oa;qikfk rgf 10 m/s. How high u,sa** k,5gri;kfro e qp an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released ov-iq3eh35 ml from rest and allowed to roll down an incvole-m i qh533lined 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 with ct0k/li9o u f83fx7gvout slipping down a 35e incline that is 7.0 m long. Assukucft8ol 9vf 3 /ig70xme 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 momenpf 7nkp-sfxzrn1r4:,f ohg8 veo:y;.tum 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 mx pewrr2 y 4dz ax3+(jmg6wh53oment 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.lqmu5cj f o- h2gj9wm1*g.,cvmij fl :;r2j2n 00 rad/s with arms extended has a moment of inertia ou91jmcjjl;*- rm.2mfo5w2 lcf g,hvjn2giq : f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?