Angular displacement is ox3gi +o09ejimksj.m jo1c rj(8g1 6pusually express in units of

  Angular velocity is expressed i4uh9bas7gpf0 bn ;. son units of

  Angular acceleration is expressed in ua,cr q(+gx.gprnyi 1 ,nits of

  A boy and a girl are riding on a merry-go-round h.ux8mxj.pdk(tu0- m g- n vs2which is turning at a constant rate. The boy is near the outer edge, and the gixgmtnxv shu p-(j2 ..dum k80-rl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round whic.lr.76fdq ,oje 4us ahh is turning at a constant rate. The boy is near the outer edge, and the girl is clhar 4s7 ej ,df.lo6q.uoser to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-ron 5x0n*1sbhx) s ui7n(hdo(bw 6a0frfund which 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 linearx0 fnoh7b xsd )nn5sf 1*awr(ibu0 6(h speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant esd jfuf99vj:. q bnz:o6r./u rate. The boy is near the outer edge, while the girl is closer to the 6o f9.q9e.: b rzd/nufjvj:sucenter. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round whiw2t +;*jq8vvbw (uxubch is turning at a constant rate. The boy is near the outer edge, while the girl is closer tov 8utv uqxb*w ;+bwj(2 the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the fo zqsa19*acbc 9llowing is an accurate statementb 9aaqc9z1* sc?

  Rolling without slipping depens4l8f1v ads-hds on

  Two equal forces are applied to a door. The first force ,n+h x-q7a vs3z)tb ziis applied at the midpoint of the door; the second -q v7xnzs,)a 3 hbit+zforce is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are ap ,kqhriy:sdbhov 5+56 plied to a door at the doorknob. The first force is applied perpendicular to h :y5d 6sqkr5i+bho v,the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a do77rl.euc9e9s2;e uztjnlm vx iw(1 r4 orknob, perpendicular to the door. The first force is tw9e72trlwn1zsu79 ;u 4ie.e xvc(jrmlice as large as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to changes in rota9esipce9p+sls 1 z0)a l( ye-ntion?p-p9ye0+ ls(e)es nl19s zica

  Consider two uniform solid spheres where both have the same diameterbh68i(1ybi)6 yo m bbc, but one has twice the mass of the other. The ratio of the larger moment of inertcmb(hb 61o i6 yb8b)iyia to that of the smaller moment of inertia is

  Two uniform solid spheres have :gw a;,xyzjoi 7b7y:uthe same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of ii: ;gbwa7x , zyu7j:oynertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass/t t l4jeqog(7p-jb8r :f m)ae and twice the diameter of the other. The ratio of)jm:7t/ fgp -at( 8ebrojq le4 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 inca9p0hi s74o9f ;1vqrshh0kp dreased to 2M and 3R, what happens to the sphere's momen9spidsf o 1phqh 0k;arv9470ht of inertia about a central axis?

  If a constant net torque is applied to an object, that v q 345qc+k0vmkmz,dl object will

  The moment of inertia of a solid cylinder about ityga+k:lrn-g+ maud . .s axis is given by 0.5 MR2. If this cylinder rolls without slipp:ng.ry-mg .+l kdaa+uing, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of masq9;o;s p a 6;x g/t0g6/l mlktuxcny7os 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? As x6l/coa7u6x/gk;9npy;ts0 mlo ;g qtsume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slqs):s 3rrk5q;7sertvz p3 s0lipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends ot)s53k rsspl 07:qrv3re q zs;n

  Suppose a solid sphere of mass M and radius R rolls without .;:icfvl kwzw2,l h1p2mv o5eslipping down an inclined plane starting from rest. The angular velocimwzi2:,vlch 25peowf.k v1 l;ty of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when59djtxa q ;:nr)s mf4e a net external force actf9m;tr j): da5 xn4seqs on the system." This statement is

  In what circumstances can the angular velocity + 6xxi8;bgvmmof system of particles change without any change in the system's angular ;vx bm+68gxmimomentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore atwmq0f 0 tg3.5fz qe;efx7pa1,nl/ dany friction which may be pregl f;wa d mf1qp tq7a0x/f5,0.eztn3esent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. Assa 5r1lwedh86a1i8 m+ajbg9x the Earth moves close to the Sun, then which of the fom5j96 e i+1b81r saxd 8whlagallowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hibqs)(j,t+ ki is outstretched arms close to his body. What happens to his angular momentum abouq)s , +tjbk(iit the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulli1 . 4wqt b9ceaj2mk0d3czgu6v ng in his outstretched agaut z j.12ecb0 d9q64k3vwcmrms close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater perform9pe1.v8pr* o3 hxws1p97iq ggyg+htis a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of rotati1v9r8iqw i+ gtp*9x1pos hpgg h. e73yon?

State the law of conservation ofe 9 wv6,s/dxrh angular momentum.

  What arc length does thwoeq*)wj, :azfa( ius a) g,q7e Earth travel in a three month period in its nearly circular orbit about the Sun a 7j( :sq fzau)q*eg o,waiw,)with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. Wha1itap 6ht;n21w *:fs yl a2kqtt distance does the tip of the second hand sweep through in 3 minutes and6tythk:t 2anqs2 ;1pal *ifw1 45 seconds?

  How many rad/s is 25 rejy vp/qh9; w5tvolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. W shnl- ;6ajh6ahat is the frequency ofnha l-66jah ;s the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequenc4 sq ns4nw;9 mhaqe( r6ita94by of 0.40 kHz. The prninhs9(qwmbs 4;eaa 6944q teriod of its rotation is

  A phonograph record rotates at 45 rphj/ jg,+jy. pvm. Through what angle does it turn in 0.20 p,v+jj/g.jhys?

  A wheel of diameter 26 cm turn ;mqu(fbdy) v:-vg5 jss at 1500 rpm. How far will a point on the outer rim move in 2.1 f() ;5ysgd v jv-buqm:s?

  A bicycle wheel rotates uniformly through 2.0 os:t+6ia rgw:revolutions in 4.0 s. What is the average angular sg+a :rits :6owpeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What isjqbkc1z s:pd:t9u 2o/w(+jmf the linear speed of a point 0.10 m from the center of t 9bzqu/cko:j( mdfps :w+tj21he wheel?

  A cable car at a ski resort carries skiers a ulr*494 sz;r*8km cai c6 ibqjdistance 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 the pulley rotate for the cable car to make the t4i*c6 b8rm k a4cz;u i9*sljrqrip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant af.sez6wg2 av gz3*g37aako 4b ngular speed of 2.0 rad/s. What is the linear speed of a point on tz3zg oa742g* gafe bs3a.wkv 6he wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.c*2s; ez:jix zxlp f/216 m in length. If the motor rotates at the rate ofsx2;lzcjx :2pzi/ *ef 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating ww p18dvip o69hith a constant angular speed of 2.0 rad/s. What is the centripetal acceleration odihvp 96pwo8 1f a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeterz2 9rz a(sqj9b of a bicycle wheel of diameter 70.0 cm when the bike is moving qj2szb 99r(za8.00 m/s?

  How many revolutions per minute (rpm)7yiit f9eoa) 4 must a circular, rotating space station (r = 1000 m) rotate to produce an artifiof9e7t4 ii ay)cial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a kw; egs/hci82 speed of 20 m/s. The maximum centripetal force (provided by static frks2we8 hi/; cgiction) 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 56rmr* ml26xe h h(2lvo0 m with a speed of 20 m/s. The maximum centripetal force (provided by static frictionermmolx 2rh2 l66h* (v) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of aa:z( h1txx ,;h*-yeaa,gdqko; -ryj f 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mass ,( f:dhxz oy -;*e taxajghy ;kq-r1a,have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm kh)u*0tbtng 6 rolls without slipping 10 m down a lau0httgb*)k6 n ne 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 with a constant angular iop(,zv24b 6g kivz/qacceleration 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 withbyq*6 sns)xje 9 sc:t0 a 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 0.300-m radius automobile ti5dl i2 ,f7uf)7ohwf mcre rotate after starting from rest and accelerating at a constan7wo uh2,fcf7m lfi 5d)t angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acctjtc1 q3en*q 3zwc64t eleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s deceleratesx)e(u51eviwl y.lo:i with a constant angular acceleration of 1:l5wvuo.(ey ile) ix $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s while t n76 jxek x2680xhr0ubm3- sjolu2qdwurning through 2.0 revolutions. What is the average angular accele2sq- ubrj8 3xo 020jmk6 w 67nxulhdxeration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 oh wbt)*xi;u: m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to res:x ot;h*wbi) ut?

  A wheel of diameter of 68.0 cm slows dodb p-gx 9sp1dzuh+:o4 zf*oo5wn uniformly from 8.40 m/s to rest over a distance obxp*p 9 5s- g+o4:u fozddhzo1f 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows dowzj7pjmhr 1t) 4n uniformly from 8.40 m/s to rest over a dirht) jp4j 7z1mstance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laborat t+ml;mk4z5op+:- mrprs ytf/ory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to rest.rpoy/m 4r t zfs:-5pmmkl+t+ ;
(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 tor)lc -dt i/vz*muypf*3que of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force rev*ldy up/ fz*-c 3)imtquired when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torquemj3lpoo ucs 1-t3* e:e of 90 Nm. If a 30 cm long wrench is used, what is the e-lp13os*3:c ojmutemagnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of vrtm7abj3*g) 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 modeled as follows: mass m is 3jjq*/gbui s.at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the momeniu/bq.3jjs*g t of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictbi gko+;a npy ,/m:.qxionless 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. 8-1q+;ing y,/.m:b xp oka.) What is the angular acceleration of the cylinder?

  A solid cylinder of 0ht7;pimj rsf:ect )4 yx(rw4mass 10 kg is pivoted 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 wre;fw i r(4xc40tj p)hr7 tyms:apped 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 the horizs td5gweo1 l0r69 lxhg/r.q,wontal position, and then g 1g,l .6hxs0 e/9lt od5wrrqwreleased 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 end is ML2/3.)

  Consider a bicycle wheel to be a bkmc6a) p8i gw9io (we4zqn.2 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 c ac9ow wb4mk.( 28egzi6 pn)qim 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 aroubux( 4/w4b3 a,sb9(/ j xouwxy vvhd-end a frictionless disk pulley of mass 7.07 kg x 49,se(-34(vjuxbd/a/ y ho ubbwwv xand radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley ojep 0fp da;d xsf958sm(7+euif mass 7us a5xd9d; ppf sfei8e(0j7 m+.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can bezg 6xw9,f :mz-zjm:jz0 f*ea z used to store energy. 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 inerti m4kvuw,u;,b qa 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 0.010f.,evmoi hgk8xhh6bi+))f/o m starts from rest and rolls without slipping down a 1.0-m high incli+fm8io )h ho,/6ifgb.hkx)ev ned 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 o4f w;+s*mj8: frixir hf 10 m/s. How high up an inclined plane can it climb beforwrf;i84xim +hj: rs*fe coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowe3n o:ihgu/kb /h3cpi ) :avk5ed to roll down an inclined plane. How fast is it moving after dropping a vertical chpba):u/: 3eo /niih3kkvg5 distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down +( 1bfo/t i;uj+ytc.tfn4 nam a 35e incline that is 7.0 m long. Assume it started from rest. The mome aj+btt ;fto4/(yunmi1+fc .nnt 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 momec13vd pklkelyd3 :4 8+hp o,elntum 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 momesb 8 fi b5)zsje2b)el5nt 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.)d5t a 6vlw.r;vqlrv p55um5h00 rad/s with arms extended has a moment of inertia o;5dv vl5r)6h 5uvm5 .aqlptrwf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?