Angular displacement is usually express in dy o f9-.xfrg.70x ipm0( t6sgwiy, beunits of

  Angular velocity is expyzx5l)3 ur6 atressed in units of

  Angular acceleration is expressed ithrgdz2no 4xz7k5x9 4n units of

  A boy and a girl are riding on a merry-go-round which is turning at a jnn1 z:7- hbc0 dgvsn*:o.zlsconstant rate.* nogvldh1.: -zcszjs:n n 7b0 The boy 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-go-roundy:q (u 9.knajk which is turning at a constant rate. The boy is near the outer edge, and the girl is close(y9jk .k:nqa ur to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round wt qad7l0 2rb / yyed,1bc.9q1ju1yzldhich is turning at a constant rate. The boy is near cl,dy0 bt/y .7zb29d11yql1 qe ruj adthe 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 4os6(,z; cwhhz3 k hzeis turning at a constant rate. The boy is near the outer edge, while the girl is closer to the cezce;h zo(4s,6hw z3khnter. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a conv3(l+xp)z(if wd iv:nstant rate. The boy is near the outer edge, while vnpz(iw (f+3l):vidx 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 an amod,qsoj,a9kjug z*)*,ccnr t-d * 1gccurate sta*sn, tocag*d,juqg)ro j,c*9 - m1kzdtement?

  Rolling without slipping depep0wh8vd8 h 6rcnds on

  Two equal forces are applied tor vn8 vhl n+1u/kj,e(y a door. The first force is applied at the midpoint of the door; the second f+ln(,r1un e8j vhky/v orce 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 forc-bt/pqi8*v rjk :;ro ye is applied perpendicular to the door; the yb8rtrjko:; i /v*p- qsecond force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, p7kaf/sk2 rmq8b22 tw jerpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the/ktmfq 28as7jw2 2brk first to the torque of the second is

  What is the quantity used to measure an object's resistance dc p )5xkeu3ox2s, s,nto changes in rotatio,,2spso cdnxu)53exk n?

  Consider two uniform solid s((1 ( biyplljepheres 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 smaller moment of inertip(e (1lil yj(ba is

  Two uniform solid spheres have the same mnzk.6x krq6s8ass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia t6kx6 8kq.r znso that of the smaller sphere is

  Consider two uniform solid spheres wheri4 vne5af7ju. e one has twice the mass and twice the diameter of the other. Thn.ui e 5a7jf4ve 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 m0z(xo;/ au2 r7 pbama2M and 3R, what happens to the sphere's moment of inertia about a central axis(oaa 0p7 rzm u;/m2abx?

  If a constant net torque is applied to an object, that object wildx47bs +*c oo 3k3ooxnl

  The moment of inertia of a so0 l pr f/;(yi; *lhpk.m,lqmymlid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the r (yhml,l/f;rylqk mm*i.pp0; atio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle ow;qjo z*) u::gg (csjcf mass 150 kg, one 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 wheels to the total translational kinetic energy of the bike? sogwq;:ugc )j :(zjc* Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping d*q16ahqtlo 2gg:t.guv 5 4qcuown an inclined plane startinga5hog 1tuq.l2:*u q46qg tgv c 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 slipping do 4z1.k+ ybvsi 10wkt ra4d)kqown an inclined plane starting from resi4t.ko zs1 0 d+b)w1qkykrv4at. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system ofm9m76e t4o dmb particles changes when a net external force acts on the system." This statement6b9 7 oedmmm4t is

  In what circumstances can the angular velst9t-) elo 6g 27e*p1fz wlyjlocity of system of particles change without any change in the system's angular mjt9llpg-6fse)z l2 w7t1yo *eomentum?

  The Earth orbits the Sun in an elli:xu mx hr33.: al1kqenptical orbit. Ignore any friction which may be present. What happens over time to the Eaq.n ex 1:k:r3hu3lxm arth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orrvlov)0uj 4ch8xur 6 *,1h yzbbit. As the Earth moves close to the Sun, then which of the folb1l6 40 ,hu j*cu)8vrhxyrzvolowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) bydxm+e-ukq7p z965byf pulling in his outstretched arms close to his body. What happens to his angu7p k5y -m ebuq69x+fzdlar momentum about the axis of rotation?

  An ice skater performs a pirouett i ejbd8d1f:mx+9kx:in9(yi pe (a fast spin) by pulling in his outstretched arms close to his body. What hap 1j(f:ed :xb+ xydi9pii nm9k8pens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fasti6q)ftb(0ntz spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of ro b0z)q (ft6itntation?

State the law of conservation of anguxw j;ux:y f:x8yi3kq20 dopi)lar momentum.

  What arc length does the Earth travel in a three month pequuxe8 x+m .7yu gs05l8 txps;riod in its nearly circular orbit about the Sun withs0spu+7lxt5qe8 .x m u8;xugy a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of xlzysa: cdw4 r.o0)1o0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 4zx) rcws d:yo40 1.alo5 seconds?

  How many rad/s is 25 revolutions per minute equivr0cdx*qbd* .* oty26iw cdgk2alent to?

  A bicycle wheel rotates uniformly through 2.0 revza;w 2z itpp6q0q1js)olutions in 4.0 s. What is the frequency of the wheel's j12p awstzpzi)qq06; rotation?

  A pulsar (a rotating neutron star) emits pulses at hj4k2vwdlg(qr-qj o qvo) c0o23/w g-a frequency of 0.40 kHz. The period of its rotation-- qk/ 2wqvj)rjg3d4(qgo0h2ov ocwl is

  A phonograph record rotates at 45 rpm. Th5o oxmu -cxm2k0 - ujx;)+fhhgrough what angle does it turn in 0.20 s?k0 ) mhu -mxfo;cxh -g+2oxu5j

  A wheel of diameter 26 cm turad f: :iuf8s9gns at 1500 rpm. How far will a point on the outer rim move in fugi89saf:d: 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revby cl8ms4prd9k;6hz i6uh:8g olutions in 4.0 s. What is the average angula 8;ybrpu49dm i hzsclg:6 68hkr speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wh 6 b7zz/ywd+k or si0vm-0bvi2at is the linbyimisdz7-o 2vvr/ + 60bwz0kear speed of 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 cable whicm)wqbpje*gb4 d2rvt-4f 8 i (sh moves the car is driven 2v8b)g* qsj pi(-wtredfmb44 by a pulley 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 with a constant angular speed of 2.0 ra /cdxhl()oack6e b;e0d/s. What is the linear speed of a point on the wheel'k0;(cee)x 6b o d/lahcs rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in leh+d gy1gr +ob8ngth. If the motor rotates at the rate of 20 rev/s, what is the approximate 8 oybrdg h+g1+linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 ra:pe(p*o* mri8nf uh5ld/s. What is the centripetal accelerat:o m rlp(ue5h*n*f8piion of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle+wa,z2.j6,jubo0nq(i5p tqpssmpg 2boj , 0l whe62+ gmwo n qp,,0 jbj(5.0psoluqzi batps ,2jel of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) musgp(j9;x;y ah,i yfmec6 2( fdst a circular, rotating space station (r = 1000 m) rotate (sacxfypi,y ;j;9fm ghd62e(to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 501)njdd3zywd61 fo l 5x m with a speed of 20 m/s. The max6d)wyx3 1dj nzdf 1l5oimum centripetal 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 radius7gm-gnx-jgwaq*q j . / 50 m with a speed of 20 m/s. The maximum centrng*/-mjx a-gq7gwjq. ipetal 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-:x/w z x-fxe 3jc-vc*gtap 6: mmj4m1l -e1cilm string, is whirled around in a smooth level table. If the maximum a-c/li:-x-14*e g mf x wx3mm6:cjet zpl 1vcjtension 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 dpcemnw0,*nu unih1gp651b d1 own a lane b5 cg e1 ,*mpnud0innp whu611at 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 angularzs1 e,- ,ek3)ss gqonw 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 constant angular accelerationp ose.k5 1)9jromuy y0 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 stavtwm).b781;cwn m s+l a8rjeurting from re;u)r.+vmb t1w8jm8n ecl 7wsast and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and6yphi x:m*8 yx)7 zdpr has an angular acceleration 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 angular utx .u;l4ffz 6acceleration of6.uu ;l fzt4xf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest -qhhj hkr8qsi. ),c. 5-4bgttubvkq9and reaches an angular speed of 6.0 rad/s while turning through 2k,v.i r45t-)qkjh- bcqqt .hb 9 8hgus.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slop -ai ej0:-asi6,pvzg ws down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to re0 izi :,gaa-ps jpev-6st?

  A wheel of diameter of 6 pzwc swfa583)8.0 cm slows down uniformly from 8.40 m/s to rest over a distance owp83zw)sf 5 acf 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40mdag+ g/30ucgxp/g ,opx -/ tnq )x1qm m/s to rest over a distance of 115 m. How long does it take for the wheel -gxpqng//mu0 oag/xp , +)q3 xgmd1tcto come to the stop?

  A centrifuge in a medical laboratob ffv,/ sx *fx(q m8jw .8wmfvozu43u+ry rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0szm48mqux3 x /, bvwfjfw.o*v( f8fu+ 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 es1n/ gq3e zlo)*v5tbrequire tightening to a torque of 90 Nm. If a 30 cm long wreb)n3 ev/5esqo *ltg1z nch is used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a tojk: 9wpd1.yvkk0 c1kkrque of 90 Nm. If a 30 cm long wc vykkk k1p dw0.19k:jrench is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment oftr;ydxo (u l29)uq, yk inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is mgo4l, 48chbmrya8g3 godeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is,gcgh38ym8ro bg la44 the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis v:s0+(c 6vooen plz:e 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 seconde :voencvlso+06 zp (: 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 10 kg is pivoted about a frictionless axis thoul,.( ogdzzqw(f a:c8 nght 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. dnlgw, qoz (ac:(.fz8How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod isj 27qrqf g)qd (qq*0jg hinged at one end. The rod is 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 moment of inertia of a rod about one endqq( *gr 2qd )j0fq7jqg is ML2/3.)

  Consider a bicycle wheel to be a ring oc-a bz/24zym k :uu4qmf radius 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 ra2uq/:m yuzm-k 4bc 4azdius 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 frictionless disk pullev;6c) pn3zz cd y+8) pzcjps3xy of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of vcjyx3;nzcz )p 8cdzpp+ )3s6the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a d+9hl(w3tqvh rawj5 *frictionless disk pulley of mass 7.07 kg3hqw9v5 lthd ra +(wj* and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to store 0s k,qmbk/ dv/.ys,iu1p rh8 *fkez.b $1.00 \times 10^{6} \; J$ of energy when rotating at 400 rad/s, what is the moment of inertial of the wheel in $kgm^{2}$?

  A wheel of moment of6o2e b,jg ps7qb:kl e8 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 radius 0.010 m starts from rerj+)teueyuik;b-u8c5 9 .p j fst and rolls without slipping down a 1.0-m high ;bi.cft r+u uyj 5kp8-) j9eueinclined 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 spee c-f0))v )mocogaise c;3l2eyd of 10 m/s. How high up an inclined p03c)es)m; v a 2cfy -)iolcegolane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released f0wu)f 0usk- q-fi egz0rom rest and allowed to roll down an 00u0f w--igsekuz f)qinclined 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 without slipping down a 35ebe/d ik e/ p+c8iii8/dkf .xf, incdie 8c e.xf+/ibpd/ k/,k fii8line that is 7.0 m long. Assume 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 mome;l98o* qykh 8 tm j)hapcqsh6v)8y8d entum 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 morc:45h05d )ljy kc enqment 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 rabu/g6c .ori3rcv :0 aed/s with arms extended has a moment of inertia o6:r3v a 0ibcgcr e.uo/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?