Angular displacement is usually z(nbp:z4*07isdud fd express in units of

  Angular velocity is expressed in(dt;hfrk-j;8b* 5 qfr5d swzv units of

  Angular acceleration is expressed in unp6 yiy 54rpzpw/a+lu8its of

  A boy and a girl are riding on a merry-1ks y/cn x(ee;go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Wnes( ecx/ky; 1ho has the greater angular displacement?

  A boy and a girl areq9,wbz9k ; 0ga5 ojuli riding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl ;, k9 lujiwboa5qz0g9is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a+vfcmvu +9;g lwv3rx, merry-go-round which is turning at a constant rateg3x, ul v9v; wmrvfc++. The 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,r58 vfjbckgoe.+ y 5h 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 centrre5k5. fco+8gjy v ,hbipetal acceleration?

  A boy and a girl are riding a merry-go-round which is tur95i a l6/t6,hga6wcvfay2 jzbning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tava59 zbf2g, t/ j6y6a6awiclhngential acceleration?

  Consider a rigid body that is rotating. Which of the fjlm .m a*xgr,*ollowing is an accurate statement?l*j. rxm*g ma,

  Rolling without slippi0p 5 9pjcr+,t)gk9ddfbp jtjbn0)2x cng depends on

  Two equal forces are0cbs(o5s-6,e9qe hkeo jwy/m r/t q:p applied to a door. The first force is applied at the midpoint of m0 ocyq j9 kp/5-:rs,hwto /(qebsee6the door; the second force 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 doork av)-fq,4 1hwj-tq+ mwhciuy -nob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the u 4 ) 1yfa-,mj-htciw wvqqh-+door. Which force exerts the greater torque?

  Two forces are applied to a doorkh0cymq:71 snzt zp3o *6o fy9nzud3k,nob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the q3ynoytds1 um6:07zp zz ochnf *93, ktorque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to ck+ev 36,qu hxuk tam hr)n-c/+hanges in rotatio + ran-tvhu 3hex/m+q6k,cuk )n?

  Consider two uniform solid sphereslgga1+ nb nuo6/5j tp8 where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment opn6lngu8j 1 b+tg5ao/ f inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius of thevng4oz.uv : hcnm 321f p:b5we other. The ratio of the larger sphere's moment of inertigfu n n45mbo3v.1zpwh:2cev: a to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the dia q vn2z6k1k8 e(w;rwbameter of the other. The ratio of the larger moment of inertia to that of the smaller momenn kq68be (wr; vwk21azt of inertia is

  A uniform solid sphere has maz)l5fj/an7d c z1o/ isss M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia abou sadzco5 1f /iljn/7)zt a central axis?

  If a constant net torq0y 4suwpb i wei8 .kt5ti9fi27ue is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given byt)-qu;a ((td w)gp wmf 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its tram))(q;t-ugwdp w (f tanslational kinetic energy is

  Consider a motorcycle of mass 150 kgw(;t/9gmx+8s re 1v tbd:jklq , 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 9mr1wlsxe:tt(8k/d; q+gb jvthe wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M-7g b*aous*+0maohu ri ,xi7a and radius R rolls without slipping down an inclined plane starting from rest. sbau-7 *i,xi*0 ugrao+oa 7 hm The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere 9sk p96lkhu2bof mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of thp6 bs9hk92ku le sphere at the bottom of the incline depends on

  "The total angular momen9 b0xak a0jg8as0 -vjvr ces3,c .rrm9tum of a system of particles changes when a net external force actrvjm x38ek a-0 9acrs0vjag0b c.,sr9s on the system." This statement is

  In what circumstances can t*/udh- c6fwt5 mz 0kqlp+2lolhe angular velocity of system of particles change without any chpw2tl odl-k5lh+*/0cm6 fq u zange in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any .s :tzbqu uu h7)7odqrdv ;*7lfriction which may be present. What happens over time to the 7 *zv;q lo)uh:ddb sut.7q7ur Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As t7 pj,4b ;nbku4p.jzdrygo r67he Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about ndpg; buj46r7r 7 zbk4,oy.pjthe Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in.9f ;vq f gt*4oy7ivbm his outstretched arms close to his body. What happens to his anguvb o9m.7 *fy; v4tfigqlar momentum about the axis of rotation?

  An ice skater performs a pirouette (a kb)n6x87( n: jkskddp fast spin) by pulling in his outstretched arms close to his body. Whnbdn p67 (xkkkd8 sj:)at happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirour v2fm an.b:u8ette (a fast spin) by pulling in his outstretched arms close to his bn2 bmuvrf:8a.ody. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of aniw8(8beq; m h851sa ejk*rdnjgular momentum.

  What arc length does thyv12rex e au8(e Earth travel in a three month period in its nearly circular orbit aboa ree281(uyv xut the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a l, -lr: yballc6ength of 0.30 m. What distance does the tip of the second hand sweep through in 3 : 6r-lll,acbyminutes and 45 seconds?

  How many rad/s is 25 revolutions gx4 9+rvk0 -mm/, gkzr 0ruxhdper minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4:gk1divty w.*c hl82h.0 s. What is the frequency of the wheel's rot 8yc 1hg.i :k2dt*wvlhation?

  A pulsar (a rotating neutron sta*dvt 0rf en9d-r) emits pulses at a frequency of 0.40 kHz. Thedt0f- d*v 9ren period of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn inp8h,8 bzbj,/a( xw bou 0.20 s8,8px a(zb,b uj bowh/?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a poinn4dfj otc19u.xb :fd -6:afb 6e da7qlt on the outer rim move in a14dqjf7cl. 6nd9 :b fefb:u x6a t-od2.1 s?

  A bicycle wheel rotates uniformly through 2.0 re:iv ;n*to rsr1.wh r7mvolutions in 4.0 s. What is the average angular speed of the whe1 ors:7tvw*r rn h;mi.el?

  A bicycle wheel rotates uniformly through 3i2 :+p;far;bk01qsnq 6 z)ubak ki un2.0 revolutions in 4.0 s. What is the linear speednnq+ u1askuk2p;a:bir q6i3 ;zk0b f) of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers crfvn3, )78h nq6jr 8lc0. jfdgmdb3ca distance 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 th7 d8mff3hrd,.lcjgq cn0v 6jb )n3c8r e 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 oi ye+n +x;g/ef1 /jlovfj/*lt f 2.0 rad/s. What is the linear speed of a point on the wheel's rim?vfel/je; +tjo 1n*/g+l if/xy

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If th) n.m:zsosn6q 1n zeqz-m 5 t.6bej) +d4cvaoqe motor rotates at the rajes . mcnq54.et-nqobd:z on 6+m)sq6vz )az 1te 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 angular ;9egd k9 d1ymtspeed of 2.0 rad/s. What is the centripetay ;dt d9g1km9el acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bi udg:5b -elu1mcycle wheel of diameter g:1bum-l 5deu 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular,n226lkbi; 3 kmu em9bq rotating space station (r = 1000 m) rotate to produce an artificial gravity26eq2m3ik ulmkn;9 bb of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve ok6:pnsp+, oe zf radius 50 m with a speed of 20 m/s. The maximum centripetal force (propk n+poe6zs,:vided 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 curv;u i1giu m-+vce of radius 50 m with a speed of 20 m/s. The maximum centripetal force (pro ;cv-mg+iiuu1 vided 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 whirijksus /9 (vbcdkq q* zkydcl+x/27 2,q 2ov0kled around in a smooth level table. If the maximum tension that cq/2 2* ykv ud,0 7sqvq92/l(+szkd kxojkbicthe 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 radiusq *6 r4 maob0ezes(foyb- v0k* 9.0 cm rolls without slipping 10 m down a lane r64 -*sb*qe0o f b0omakve (yzat 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 *;eh1gt2.)v c8ktsv cs j+jmkangular 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 ak1up u)6i:7 u 5tqn3kai+pmy d constant 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 0voeuv m5:k/:iwt ty)7 47dtig .300-m radius automobile tire rotate after starting fro5t)t ov evwgi7kdy74:i um/:tm rest and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, anql35sme h* f6n0okw tl5a8l+ v4 vpny9d 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 deceleratoe-3oiz,x)bk 0 zwz h)es with a constant angular acceleration oz xezb,oh0zoi-)3) k wf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reru : c u)h7j.8qt5pr *q(qinmiaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acch qrmt)cuq:n (5q8irpui*j. 7eleration of the wheel?

  A wheel of diameter of 68.0 cm slows do tgwvb0fsp2w xcl:+y6:6 ntb je +o.7mwn uniformly from 8.40 m/s to rest over a dista.s2bfleb mj0ww:76nxyvgc:+ +o t t6 pnce of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm y ei(/ ys;6popslows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angula pysy/o;6p ei(r acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to reshow x34z5td;s6uucr cn,z; z)t over a distance of 115 m. How long does 6zo5u43 wut,cz;rzcnh ;sd x)it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 36h5//d01 uyzj 3knpn qrc44cpu00 rev/min. When switched off, it rnyj4 uh uc/k1zdrnq/3 50 c4ppotates 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 whld ai*36 xk3t3;cxgkveel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitlxkt63xv;ag d*3 ick3ude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tighteaa / nd6sms3 j.9zkrg safq-5n+-gqg2ning to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnisg qzaj 29amn dr+s-s/ gk.6fg5qna3-tude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of in-urovvpiv9/s(h0 i+ o ertia $3.00 \; kgm^{2}$ 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 arfpyi-a .8a3qt the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about theipa8f 3a- rqy. origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionl ky)nht *wub s7l(1)bm v*ne,sess 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. (See Fig. 8-1.) What is the angular acceleration o(b)wk ,u*7nytb)v *e mlsns1hf the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionpfv2l6 8efb90c2owg6ghy l05qyxd /qless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts0o/e fp6x 859wbd6qcly0 f2h2 v lyggq 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 f;-q)1iskeja in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as i- ) 1a;qfkiesjt is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle whe 3i,wzl)u/4 qwde ng1jel to be a ring of 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 radius 4.0 cm for 4.1 s, what linear speed d/ zji)u lqg,34endw 1woes the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on zwxtqk+: zm)i oa6v75 mg:e x4x.u pr8a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of mk.o)547qw u8mx+: vtp :xrg6x azezi the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pula;)c q whaob-6ley of mass 7.07 kg and radaow-q) a6c bh;ius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is require(8.erg.jks5j lc)a)r z 8nnmwd 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 /( zrwcyx- qb*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 h)ve:4vdbk(pn6aq5 pfrom rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reachesdp(pqkh v5)v n4e 6:ba the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10 m/ 1t6(twmif0 vps. How high up an inclined plane can it climb before coming to r6(mpwttfi1v0 est?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and fqzs8da-a,shhhu)b1y,5 4vv allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 hs8 dz5fah)a,vuh s-,y1 bqv4m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without s.i m)knk+puw pk+:tvb74,xqilipping down a 35e incline that is pui)b kiktnq +w+ :.74xpmk v,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 m0rfzbyj5s7s xr wy hp7cp)61jk5 t; (bomentum 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 mom/of kk-tw;bgsaj4,k( ent 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 x x6b*p nkl6bu;r:uh8 with arms extended has a moment of inertin6xbplr xh;b*86 k:uua 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?