Angular displacement is usually express in units u*i/t 2nl)y +ui6ek2;j ysey pof

  Angular velocity is ex9 iviu*v7k34 afgpj n.pressed in units of

  Angular acceleration *4vb52ff flptis expressed in units of

  A boy and a girl are riding on a merry-go-round whi+xkjwi j4ll7 9/rp j,mch is turning at a constant rate. The boy is near the outer edge, and the girl is closer to t+r4l l /i pwj,x7k9mjjhe center. Who has the greater angular displacement?

  A boy and a girl are riding on auwzbvkjwxq:i8 j ,20 * merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girlu,q8j: bkjw* 2wvxzi0 is closer to the center. Who has the greater angular speed?

  A boy and a girl are ridin,40awmqr :ll+bpsh- dg on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girlma-q:b+l ,hrwl 40 sdp is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-roulmf+(vw/wbu5jhf )w1+*vmclnd which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who habvvwl (1 +u+jh)fwf/ml c*5wms the greater centripetal acceleration?

  A boy and a girl are riding aj,s9hne 2v ibv3*pbw, merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the centerp 3,bv v*2jiwnb, h9es. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following 2jov1ym s dnno(2z4i0is an accurate statnimo41( 2d s on2y0jzvement?

  Rolling without slipping2ro zb 9f 9)z,65p kmzo)cvdamfav q2( depends on

  Two equal forces are applied to a door. The first force is applied at thip1.y8 1.tgw;soyj zie midpoint of the door; the second force is apisyj;o .8 zi1y.1twp gplied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are appli g(xlv(5j ace3 go vlw-2*y8lred to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. W a3gxvg 825rye( (*-lclvwoljhich force exerts the greater torque?

  Two forces are appli(g4j ia5 f*dr6pv;t qned to a doorknob, perpendicular to the door. The first force is twice as large as the second force. Thjnqra;t 4 p (vf*gd5i6e ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistac;a8*6 a iedupnce to changes in rotatio8uceap *6d;ian?

  Consider two uniform solid sphn 6j n-)zum-wheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of iner) nju-hz-6mwn tia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same massg xmu63l 7-mug gfmouh+f --)o, but one has twice the radius of the other. The ratio of the larger sphere's moment of inl-xmu)o+mgugu7 fo6g h- -f3mertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and t7ol .lb4j1fi awice the dib4a.llijf 1o7ameter 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 to 2M uh 5g(n:- a6 g*owli(vmudl.y and 3R, w.va(-* g:l6wm inguy lhu(do5 hat happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is apvqrn: h.(;y;vvkoi8mcu -uy.y/5jrsplied to an object, that object will

  The moment of inertia o8r,ehb gg9 i pse c5d-+9.enkfpvfl8+f a solid cylinder about its axis is given by $\frac{1}{2}M{R}^2$. 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 has a mass of 10 kg ab bi8. +i)lc uz.,dcpnr9*calnd a radius of 30 cm. What is the ratior)clp9cn 8.i.bcz,+ib d lau* of the rotational kinetic energy 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 down an hju bq i34*k4nm0ftc s2 -mh9dinclined plane starting from rest. The linear velocity of the sphere at the bottom ofh4sjnfm -9k23 cm0 4dbhuqti* the incline depends on

  Suppose a solid sphere e-q4wxbj.,y jc uqevqq4 )3r,of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity o4q -vrwb.qx,cj jyq3ue4, e)qf the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles cha d98nom-2s*adx;e- sns soz+-vm8qz.w lh c4jnges when a net external s9lv-d+cjz-s8- mh8 msnwa4se o *o.xn 2 ;dzqforce acts on the system." This statement is

  In what circumstances can the angular velocity of system of particles chmu2kwa+ i816lx h b(scange without1 wksh8ubix+l 6ac2m( any change in the system's angular momentum?

  The Earth orbits the5u:p( ot- 7d5xopnzsw Sun in an elliptical orbit. Ignore any friction which may be present. What ha5uno-potd (x psz7:w5ppens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Ea f3hqr. onhko1x3(oo: rth moves close to the Sun, then which of the oo 133xoh nqhkrf :(o.following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in :, i/ztnnjv)x his outstretched arms close to his body. What happe ixv),jz/t nn:ns to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette e4535ck 5:mkpzzv cdn(a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotationapezkc 5 dvmk:cn4z553l kinetic energy about the axis of rotation?

  An ice skater performs a pirouettetnyu3oag f)mu51(m 2 ;uxklx3 (a fast spin) by pulling in his outstretched arms close to his body. Wh(3 mtx2x5g nu o; mkfuua13y)lat happens to his moment of inertia about the axis of rotation?

State the law of conservac4kfhgo i1.fqtg +38 jtion of angular momentum.

  What arc length does the Earth travel in a three mont (atqz4kvcq+:b z;nnc ,rl)k/ h period in its nearly circular orbit about the Sun with a radius of vcq ;(+/annzkc)zt:rkb ,l4q$1.5\times {10}^{11}m$?

  The second hand of a clock has a length of gcpg,z k /,3352qhs ti4yq6iblqy(x e 0.30 m. What distance does the tip of the second hand sweep through in 3 m i z h 4gtqq2bxyqg,6,/c3kp( 5y3isleinutes and 45 seconds?

  How many rad/s is 25 retqv,/a, b; vnxy7 au8hvolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutionskxd6+ihd8n lzefp 9 4. in 4.0 s. What is the frequency of the wheel's rotationkznpdd.l 6ei8+f9h4x ?

  A pulsar (a rotating neutron star-efdr xeu.o0*i3 vmg5) emits pulses at a frequency of 0.40 kHz. The period of its r *.-ridfugxem0e v3o5otation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn 7r 6097+kcppya9ztfzrv v+y rin 0.20 sr70kr+ 9vz 7 pazft+yr ypcv96?

  A wheel of diameter 26 cm turnt +y7 h 1rhfm*h.l:wsx4zpy:qs at 1500 rpm. How far will a point on the outer rim move in 2.1 s?1mhyf+4y:hhtw*px l sq z. 7r:

  A bicycle wheel rotates uniformly through 2.0 revoluo7hv: s51yumgtions in 4.0 s. What is the average angular spy 5gv7o uh:1smeed of the wheel?

  A bicycle wheel rotates uniformly through 2wq. ce rf7m-,v.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 mfm7,-qvwc.r e from the center of the wheel?

  A cable car at a ski resort carries skiers a distance ofw 19 vy5:k:tyss);-n/sw( piz w7lfut emgy/a 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, ym sa(t :/ sw1svuwzf-ylw )gypn7;9ekt/:i 5how 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 with a constant an t-0)kkxzc1 g 3qgjb(jgular speed of 2.0 rad/s. What is thjk(k -g0g3q jzb1cx) te linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cut*obxatu/3 lm9(rf nuj (dkwf(ab 0p*.ter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the( k(dtj/ o3nbfawu*(lf9b r*ma0x.pu approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m iq ir: u+d(qpc+s rotating with a constant angular speed of 2.0 rad/s. What is the :r+qqcuid p+ (centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the pexiqo)r8gm 27hm2cer5 rimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 m/ mr2 e)r57 ioqxgm2h8cs?

  How many revolutions per minute (rpm) must a circular, rotatilyfo13 x + pchi1t2p(xng space station (r = 1000 m) rotate to produce an (2yhifc 1t1lp3 opx+x artificial gravity of $9.80m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 glz7 b8fi 2pg3m/s. The maximum centripetal force (provided by static frictio3zg 27lbfpgi8n) 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 ff:r1 y6o)brh 20 m/s. The maximum h :1fo yr6fr)bcentripetal 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 0b9ywf0jb60/u 0o5 +lrmagvzn .750-m string, is whirled around in a smooth level table. If t0 l5wvr9bbyoum/ 6ja 0nz0 f+ghe 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 with,fuj 7z0*jaww out slipping 10 m down a lane at 4.3 m/su7 z,w aw*f0jj.
(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 acceleration ofqpdrq/p*c8)th w 86;aoqd. 9 cdhd9bf $4.5rad/s^2$. 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 win j8 yi3ny9q7cth a constant angular acceleration of $4.5rad/s^2$. 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 aftete4)4q- pr /6twh6mde5ygcqm1hpm o 4r starting from1) eehq4goq6mmc/dp hy w44p56mrt- t rest and accelerating at a constant angular acceleration of $2.00rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an aapk5sr x)z+pz 2+vi:bngular acceleration of $4rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at lix u5j +jgh,9mm19oe+ksia2 20 rad/s decelerates with a constant angular accelerax+h lo,k9g 2i 1ij+euj5 mas9mtion of $-5.0rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from re,;qpjn m6:v gvst and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acc;:nmq pvg v6,jeleration of the wheel?

  A wheel of diameter of 68.0ojut n -eid-vr5cgx69 :,x(es cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of re 5s:v dxjuc9( ,-i6tr -xegenovolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unt 08aiq 72 4uzcc .f(pf4atefbiformly from 8.40 m/s to rest over a distance of 115 m. What is the anbu4piccf af qf0 et8 a24(t.7zgular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformlyk:lzr,jglnvp (jxc s9+(xz-d93k2 l k from 8.40 m/s to rest over a distance of 115 m. Ho9jgl(lzzs3v+ rcxdk2 k:njk lp(x,9- w long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/mjotb.b8- //xj gyvtm/y(qq)c in. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to res/y/q8)b.tj y(gmo-c jtb /xvqt.
(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 od je :7xii-n/kf 90 Nm. If a 30 cm long wrench is used, what is the m:xn kiijd-e7/ agnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 301k hdm vw s6xs- h0y4t-2bpexcr9p7o0 cm long wr -x t7s-hbp260ok 0wvy19 dpshxe4mcrench is used, what is the magnitude of the force required when the force applied at ${53}^{\circ }$ to the wrench?

  A wheel with moment of . e/yldjvny6 j z5b znd.uk138yr.5/tcl 8cqsinertia $3.00kg{m}^2$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled /wg 62acxzwk, as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is tw/kca2w g,x z6he moment of inertia about the origin?

  A solid cylinder of mass br l2 1orua-*i10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outelar1- ubiro2* r 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 aboutf s.c. oung/u/ a frictionless axis thought the center O. A ro/sgn ..ocufu /pe wrapped around 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) 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 isa 8wah xeq ngyy;7:7i( 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 release:ah7ey;n w aiyg7 q(8xd? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wh:,3s pbvhr1i5dorr9 beel to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mas:p5s r3bih,9ro v1drb s 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 without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionleg u,o 7-0spmzqss disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleratioz7o- qmpu 0,gsn of the pulley?

  A 1.53-kg mass hangs on a rope c.eu)symn -3(s 1cm)w lqbo:wwrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the accelcn us wym1e).:l- o3mwb)s q(ceration of the mass?

  A rotating flywheel can be used to store energy. If it is required to store uztsb4l/i6a( $1.00\times {10}^{6}J$ of energy when rotating at 400 rad/s, what is the moment of inertial of the wheel in $kg{m}^2$?

  A wheel of moment of r3v3 +qcmbv06le;qy hinertia of $5.00kg{m}^2$ 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 staala bco 3/r9ckd( 0tk9rts from rest and rolls without slipping down a 1.0-m high inclined plane. Whaa3/lk0b rac d (co9tk9t 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 rdc. yry50.g zgolls with a speed of 10 m/s. How high up an inclined..0zgg cyryd5 plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and all,a7 -oyg+iv 5k npkj2lowed to roll down an inclined plaaljn, ykp7 -i+v k52gone. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg an,c*8 q oi5imxwd radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere ic 5woi8mq,*xi s given by $I=(2/5)M{R}^2$.
(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 c7tij 4l1)u, *hhr1p wfe5m vplixw,4p hanges by $20kg{m}^2/s$ 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 iihy9vwc9 / b.dsu99a ezd4w3qnertia of $5.0kg{m}^2$ 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 $2.0kg{m}^2$, how fast will she be spinning?

  A figure skater rotating at 5.00 rad/s with. * y)m.0nwvwbhnpn;b arms extended has a moment of inertia o bnwpvhnm 0 n.yb.)w*;f
$2.25kg{m}^2$. If the arms are pulled in so the moment of inertia decreases to $1.80kg{m}^2$, what is the final angular speed?