Angular displacement is usuaxe ky;iaeee, qe 6a6p7/,8qvd lly express in units of

  Angular velocity is expressed 6nq/+ ptrp of4e: 7tbwin units of

  Angular acceleration is expres ;f0dx+uz 8owdsed in units of

  A boy and a girl are riding on a merry-go-round which is va hc -id.4i,aturning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who h-v hdi4 ai,.acas the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turnt y co9)b:m46n: ki83vg+wnyu xhx/ceing at a constant rate. The boy is near the outer edge, and the girl is closer to thew3gc4 ckx i869n+eu v bho):tmny/y:x center. Who has the greater angular speed?

  A boy and a girl are riding on a merrd,:54mfobt- z kwob.e j6nf2 jy-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to tjbz2t.5-bwnm eoff oj6,k:d4he center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning a8up w rphwtn6/b:j 2q5t a constant rate. The boy is near the outer edge, while the girl is closer to the centt pn/pwq bhj8u52 r6:wer. Who has the greater centripetal acceleration?

  A boy and a girl are riding wa24d)+fq+x mmd x76fo2h ics mkb,q+a merry-go-round which is turning at a constant rate. The boy is near ocfdm i 62w xqmbqas+x+ fd+7)h,4 mk2the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is jfz)+buuw, ( ct7rn6ean accurate statement? ec6n rzbu7uw+)f(,jt

  Rolling without slipping depem m2euclf0wdrs;y g 5*(x(vg.nds on

  Two equal forces are applied to a door. The first force bf-ivb1+,phqdntbda2p8 w. es(7k 9a n//xfvis applied at the midpoint of the door; the second force is applied at the doorknob. Both forcekb8p.nnv -1qdw9ba7 hbf +vtixsf2,//d(ep a s are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at theubux0/c fp8 i1 doorknob. The first force is applied perpendicular to the door; the second force is applied at 3fi 1 uucpxb08/0e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a dops rx :6i7e8tfi .vlc3e1f0ksorknob, perpendicular to the door. The first force is twice as large as the sefiv1l8sx: .67 ei3et frkp0 cscond force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measu0dahr;a 1(qagr5-im q1bx f6l re an object's resistance to changes in rotati-al;hg m a6qx0iq11f( rdb5raon?

  Consider two uniform solw xda efny7(c tt8 ;6qf2l(l;yid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smallelx8ydt(yf 67t( ;qnf2e ;l awcr moment of inertia is

  Two uniform solid spheres have the s59dfwgv8i tyydgznv- p/,k - /ame mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is yg ,df9igwvd-z85/y- kv tn/p

  Consider two uniform solid spheres where one has twice the mass :if(kfi:9ed m,my;.wxd* uqw and twice the diameter of the other. The ratio o;mik *qd:mxd w.,f(f9uei:ywf 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 wa6azq9 s tk92to 2M and 3R, what happazwka qs9296t ens to the sphere's moment of inertia about a central axis?

  If a constant net torque isd1q 989evn qagh,ie .p applied to an object, that object will

  The moment of inertia of a solid cylinder abou 6ls 4cd (k7.ezpwl5lvt its axis is given by $\frac{1}{2} MR^2$. If this cylinder rolls 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 which hj9 n zy /k/)clfsa6/wqas 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 bike? Assume the wheel)wsjk fcq/ zy9/nla/6s are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping down an i /.os7h9yyz f yue r-0ijk3od)nclined plane starting from resyk7y)oys hzrjdu.3 eo / if90-t. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rol*q ).jb .sxr/u+q cfools without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the botub os./q)+qr. xoj c*ftom of the incline depends on

  "The total angular momentum of a system of particlet*zk/pld -nm a9bs3 1is changes when a net external force acts on the system." d b nkt/ 1pzsiml3a*9-This statement is

  In what circumstances can the angular velocity of )wrf5rf y.,-jiys ) cqsystem of particles change without any change in ,5ry fsqi- frjw) y.)cthe system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which -z6qiy4 eaoz4( dp+my1 z2rmf may be present. What happens over time to the Earth's angular momentum abou1iq+-rz4 az4oy(6emfm2 d zyp t the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earc nvr6tzb8,g 3th moves close tbc 3ngvt68,z ro the Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs aff, s,nxas11 5zss:o;xe)w oj pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens ta w:1xs,oo s)j1sf esfz ,;5xno his angular momentum about the axis of rotation?

  An ice skater performs a piroue9j;r*evy b fb0tte (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about thef vjy;*b90erb axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstret* 7tlv ;yd.eb-:yk8zcp is3 jrched arms close to his body. What happens to his moment o y3t.rp7d- clskbz*:ei;j8 yvf inertia about the axis of rotation?

State the law of conservation of5cru9lienm :0sn vb,* angular momentum.

  What arc length does the Earth travel in a three month period in its nearly (wiz f,(q gzs9qv*t2y ioy;k2circular orbit about the Sun wisq2ki wq(tf; 9zy (ovgy i,z*2th a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the tittzy .0r/v/ss p of the second hand sweep through i.yztss //v0tr n 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per mfl+qr-mj-jnf r 18kk+inute equivalent to?

  A bicycle wheel rotates uniformly through 2h4 uwxz1u 4+wk *-gsrx.0 revolutions in 4.0 s. What is the frequency of the wheel's rotation?w4kgh *4s -r+z uxwx1u

  A pulsar (a rotating neutron star) emits pulses at a frequ :fr75tbqtx:wg7 h5 nfency of 0.40 kHz. The period of its rohn7t :wf 7bgfr55:txqtation is

  A phonograph record rotates at 45 rpm. Through ck3l1go* agk1anc55y- tb9pcwhat angle does it turn in 0.20 5bt11a5c9gplc3y*an kk g o- cs?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a poif1n( b)v fd0gfrr.4 49njugyc; /lwdi ;d5yu fnt on the outer rim movefn4 jfyw9;/ug buyi.r gd) r5(d14c;f0vnfl d in 2.1 s?

  A bicycle wheel rotatesg(6c hx sx9uy5 uniformly through 2.0 revolutions in 4.0 s. What is the average angular sp (56ux9gcx syheed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.08zahxd yz 0bag 4vg+-* s. What is the linear speed of a point 0. zyg bz8*vh-a4d+axg010 m from the center of the wheel?

  A cable car at a ski resort carries skiers a dgv -) bzi4ozwb(7;dqm istance 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 thei dvgzqo)4bmwb; 7z- ( pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating wi(ohlgynkc5 l;w55x*lth a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel's riml*;lwc k5loxy55n g (h?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If th4ekdh)4+vbg * s n8fdge motor rotates at the rate of 20 rev/s, what is the approximate lin48hk gb4fs*gd+ ) evndear speed of the end of the cord?

  A wheel of radius 1.0 m7n +4fh0 ctety is rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the whect7 4e y+0nfthel's rim?

  What is the centripetal acceleration of a point on the perimeter f /wnt2 b 8gg8plyer.5v9q(ibs/1e dqof a bicycle wheel of diameter 70.0 cm ww 8v/egypi5q2e 18t 9l/q rbgbdnf .(shen the bike is moving 8.00 m/s?

  How many revolutions lv:z (o g8 ,w)tybp wk-*td +xuca3or-per minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produtzpwoyxcalt )*b,:w -k vd-u(83g +r oce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m withq;ppxj;wlfc8.m r 88 x a speed of 20 m/s. The maximum centripetal force (provid8r8.l pqfm wpx;8xj c;ed 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 2gd +pp/ 0h55asc3abgpan3r 0h0 m/s. The maximum cen3+3c aag p pad55bgsnpr00h h/tripetal 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+g/ux9o m pmq/ end of a 0.750-m string, is whirled around in a smooth level to/q9m+/umxgp able. If 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 rolls without slipping 10 m d;xc,im/ ns5ul own n, ms5xc;uli /a 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 wv,u0w;kduj *80cj sik ith a constant 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 constant1s8- 4amdclhki5,mv b 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 y63(6m hlwb5zh 3ceu bradius automobile tire rotate after starting from rest and accelerating at a constant (mcb3buh6 z6lw3 y5ehangular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accel 2jtdun6i,pg 4hdu04v .xtaj+eration 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 constant angulu/gla :dg+i e:ar acceleration o :ulig:+ eag/df $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and rein5)ol -e aw,faches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular accinoe , )f-w5aleleration of the wheel?

  A wheel of diameter of 68.0 cm slows down unif tlsq7-9 l-srt9san0lormly from 8.40 m/s to rest over a distance of 115 m. What790tl-- l arsqns9s lt is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down u*v-qap / p/pwl7+fjf h 4asc6eniformly from 8.40 m/s to rest over a distance of 14 q67alvf + jpap*pws/e hf-c/15 m. What is the angular acceleration?

  A wheel of diameter of 6hh+- 0*sukrdeqq uu 9ae q/6b38.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for qqe- 3ud he/bau9s q0k*ru +6hthe wheel to come to the stop?

  A centrifuge in a medical laboratog-l w*wiqr)n/ sn;upl*7si*ery rotates at a rotational speed of 3600 rev/min. When switched off, it rota*rlws-q *lg)sn i;wi7/e* pnutes 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 require tightening toab 0 g7qgeq6x, a torque of 90 Nm. If a 30 cm long wrench is used, what i g6a0xqbeq ,7gs the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of i, -as1 wz0cjc90 Nm. If a 30 cm long wrench is used, what is the magnitude of th-iac 1scw,j0 ze force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of i9tik u eis7*x el8qv;)nertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mass m is at the origin, i+-b8;4,vzgx yzrzqn: w *fdcmass 2m is at x = a, and, mass 3m is at x = 2a. What is thefc-x+zw g,vzyz b* 4qr;ni:8d moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionle9p dnom4 hqzz 4b58jt 95h8 2kmq+luqass axis thought the center O. A rope wrapped arounplm9mu8z5n q+qk9 d2tz58bj4hhoq a4d the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a fr;vj8 8bd1azsxx y l*g6ictionless axis thought the center O. A rope wrapped around the outer rlvajxzysx;8b 6 1gd8*adius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 m+hju cw288efrod is initially held in the horizontal position, and then released as the free end is allowed to fall. 8hc2me w +juf8What 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 *ar 0eh- mf sg7mh9hu.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 speed does the wheel ea g*u7 hmmhfhrs- 0.9achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped t3ed p0ak r2 :ofzqdm2)+hi 5oaround a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the ang q) k0t+2a3h5dmzoepo2d:r ifular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped 2ljve 1,bbe (s gd ;ouu:9dnl*around a frictionless disk pulley of mass 7.b( 1,:oujdld b ;vnslg9* u2ee07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it i(.,j3zsdg 6oe t t*qzas 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 inertia o amndnp8g 1t3j4qo8m/f $5.00 \; kgm^{2}$ 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 fro(m : m p;0ikgs-bab 6p)hfdf qvdp4+d5m rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined pbfbgi+dd fm- p6) s;(a4m0q: dvhppk5lane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speedjo-t qs7;) 85gg*feicr- wx mo g/ze8k of 10 m/s. How high uew mg) gqc;7j5io/8 xers-k t8*-fozgp an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.2 7cu6izgje8hqa3n6- wms jbm 3if/)rb jp5..m0 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after droppin6nzaj8- 3fgwmmj ir./qe 6s57.iubcmpjh)b3 g a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radumw 0 w)whrxa6iil+ 16ius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of ineru6 wihl)x6r0+i wwa m1tia 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 changutt+f l 4u/jf 9.yz(hles 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 ofp0o p7. 0x7idrr gp)gq b:tpe( $5.0 \; kgm^{2}$ 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 a 9jchtg bv-u,9l0ip-bqs) 71kj ybp4b rms extended has a moment of inerti q,-bvptu4 17blg -ykb hj bj0ci9p9)sa 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?