Angular displacement is usually express imhf)j9 ev *c z9.udinzqmfc++h2u p29n units of

  Angular velocity is expressedtlbbx5eb/ j.20iw b9z in units of

  Angular acceleration is expressed in un3dz ew t3b,w/*fx rzcdp 2;q(khe ko-*its of

  A boy and a girl are riding on a merry-go-round which is turning at a constant rws,;rb), wz ciate. The boy is near the outer edge, and the girl is), scbw;r,zw i closer to the center. Who has the greater angular displacement?

  A boy and a girl are wb.n0litr+ ym0pce gs 6*6,b kriding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has,b0c i6tr wskl bmn.*y+0 p6eg the greater angular speed?

  A boy and a girl are riding on a merry-go-round which isc)kcn4gj/a )c/u3shy- z .q kh turning at a constant rate. The boy is near the outer edge, and the girlh/ q/)4j-z h)cakc.yunkc 3sg is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merroo6ae7l4+zx-aut w l gf;.n -yy-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl i7-.g t4oanze 6yf - lx;uwla+os closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turgt i8ycrd1hyh-i0( 9k9pnob1w bc /t4ning at a constant rate. The boy is near the outer edge, while the girl is closer to 1/9t ir- tk91bgh(dbny04 o8piccywh the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an a*5q7quoky.j l+w mv 5xccurate statemq xk5lq yw +o.v7j*m5uent?

  Rolling without slipping depenp( lcy5q9 :p,gpa6pnads on

  Two equal forces are ap)u h9du uy/x6,y 6qtdyplied to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which forcu u,)t6/ dy6x 9quydyhe exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. sxms1/.wgi 1te14gb..fc/ffij ljq. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force execf jwxb 1 j1/ i.sftg4q.1gfm..l/seirts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The first fornuy )i z8+*sumce is twice as large as the second force. The ratio of the torque of th)m+* s zi8uyune first to the torque of the second is

  What is the quantity used to measure an object's resistanwcx1r 0h 7en 7cq83jx4+g ywjwce to changes in rotati0qj xw71jghr347e8cw wx + yncon?

  Consider two uniform sc+ vmydo-(ay.eg+2 p 1m( myoyolid 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 smaller momemm+y-c y1ev(ogma. d o+ypy2 (nt of inertia is

  Two uniform solid spheres have the same mass, butfy m.c rv0/ w2qn*zsyuw 2h-z6 one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smalzyrzw2 /mcu*2-6yfv0.h nswq ler sphere is

  Consider two uniformp+89 ;. e12keafc cjdxbo v7z*y4sz hm solid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of me9fzz8 2cb+ck.741 o v*yea;sd xhjpinertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these ae xx0o rznzi56)m3piyy69wy8re increased to 2M and 3R, what happens to the sphere's moment of inertinwyzzxo) ry5 ii6x eyp936m80a about a central axis?

  If a constant net torque is applied to an object, that q0rx,v1us8 d tobject will

  The moment of inertia of a solid cylinder about its axis is gu1rb b h -9kkb e:f+ 2qu6ugr1-.vlexpiven 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 has e t 5 loa7pbc(znn5,;wa 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 thwz75ltn,5e o a;cnb (pe bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radiw 6opwff5,+ajd4v45b2wsv+gdn.a bbkj)f2 o us R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bot5+.pvvafbba )onfww42 , dfojwd56g bks2j+4tom of the incline depends on

  Suppose a solid sphere.mp lyy qy-)w/ of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the )py-yw.my/ql bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net externaa s+/m 6omtdgyx0+5*ngfx -el l force acts on the system." 5tdxa0yeg6s+ +g/ ln- mm*xfoThis statement is

  In what circumstances can the angular velocity of system of particles (z/rle;lu e(n cl; b m4x j,:y/3arealchange without any change in the syr mar/3el4lcn :, au ljb lz((;;yeex/stem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which - l6jzfe6w9w gmay be present. What happensj9fwl6wg6ez - over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth movk ;agjfu)n)3ees close to the Sun, then which of the following best describes tu3;ef)jga)n khe orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in 3*)wm r42wrx4reymz c his outstretched armymre wmw4r43*)c2xz rs close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrev4y v- o39uq;p0pslyftched arms close to his body. What happens to his rotational kinetic energy about the axiqfy4l-3p;v s ovp09yu s of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchexltnf* +*r0zqd arms clolf *rx0n tzq+*se to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular ma-b bvn7gtg/grp 1j qd7jjr, l*4sw:0omentum.

  What arc length does the Earth t- epgam n6;sxz vb*rls308z *bjaj7z5ravel in a three month period in its nearly circular orbit about t0zsva lg7 na -pxs6 8jr*j;z5bzem3 *bhe Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a ab1l0i-(h4 g9tzmbr0egm:r ru4bi;x length of 0.30 m. What distance does the tip of the second hand sweep through 1i m;ulr-i40a r(m0 gz:brbt 4ebxgh9 in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions ihyoh0lb/, wk ,4vq)cper minute equivalent to?

  A bicycle wheel rotates unifodxjwco 9m4 ;1irmly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotati1m9j4 oiw;c dxon?

  A pulsar (a rotating neutron star) emits pulses at a f;l-vevab7qb32vsc g o2 4(wcylcgq5/requency of 0.40 kHz. The period o2vbec- bc gawvo 72gyll4v3(/ q ;5sqcf its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn ,apuph qdtrwhe:;mc r1);n1 7 in 0.20 s?u; 1)a7 w1;r,p:d hmp rqhenct

  A wheel of diameter 26 cm turns axidw- a,fys9)or 5*l4mq/c bot 1500 rpm. How far will a point on the outer rw-lqo* , bd4fscimx5 )ya 9o/rim move in 2.1 s?

  A bicycle wheel rotates uniformly througm5 tfm2y07ew4 wa6hwwh 2.0 revolutions in 4.0 s. What is the average angulaywmw6 ww eh07m45 ft2ar speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 r,/foeq7pq xyw0/q 7iq y*t l4zevolutions in 4.0 s. What is the linear speed of a pointz/*x7yqy70,weqolfi qt p4 q/ 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distancek myri 4ng+6j35)j 2f.5nlgeusloju . of 6.8 km. The cable which moves the car is driven by a pulley with diail.5 2n3o+)rl 5 jkjfujuemsg 4 yng6.meter 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 rotatins93kh3 iknan6q,v b9)0w,zqcx of c( xg with a constant angular speed of 2.0 rad/s. What is the lineqq 9 a9 63sohx,)nvnfzkikc ,b(c0x3war speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m iiapsq;6ypn m. xe h/7,n length. If the motor rotates at the rate of 20 rev/s, what is the approximate lmepx.p; n/i7qas6 h y,inear speed of the end of the cord?

  A wheel of radius 1.f2:3xk xpbsu/ 0 m is rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's :k/s u x2pfx3brim?

  What is the centripetal acceleratb :tl;g ox4a ,mg9+vlaion of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8. +l:;9tlgb,oaaxg m4 v00 m/s?

  How many revolutions per minute (rpm) mu*-rs6ykqd g8 ost a circular, rotating space station (r = 1000 m) rotate to produce 6rys- ogq8* dkan artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circulmx- a ygmx / j63:jiuxz.gkk72ar curve of radius 50 m with a speed of 20 m/s. The maximum centri:6jxx27kguamz3jik-gy x/ .m petal 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 radiusf aw yl+2jw8y7 50 m with a speed of 20 m/s. The maximum centripetal force28f7ywljy +wa (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)paam*lz/( 32wq d qfq.750-m string, is whirled around in a smooth level table. If the maximum tensiond* ql3 ma)q(qp/ azwf2 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 wscn y0(o9*/ z rt2m jsy3sz,atithout slipping 10 m down 0sr*oynay9 c32 ms,(tsjz /tza 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 with a ca;*ltbob v a4d4nf3w/ onstant 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 f dwl649(l4l gsshgp4a 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-mnn ev n893xkec(f +x7v radius automobile tire rotate after starting from restn( x8x+fnc3vnv7e 9e k and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has tu-n7il* ;*m0w kvysjan 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 const;.ti6y2q/d5n ;2hgg ga* cb vdbzupz+ant angular acceleration of zdc ;b+bh65ta 2vgyn* iup qd/z2.;gg$-5.0 \; rad/s^2$. 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 whk0*gmo8g okvq 36nt9aile turning through 2.0 revolutions. What is the0on69vqmk*g kta3 o8g average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly fr/ s gckfgjetcg95 bz5.(j ,m0eom 8.40 m/s to rest over a distance of 115 m. What is sgf zj,/ck cem.0jg5g9 bte(5the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cmbx+mu00+ p5 yrze9c z3+bfagh slows down uniformly from 8.40 m/s to rest over a5h+ ux 0b 0zbmeayzrpc gf3++9 distance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over q+8hz6gyn/ro e o s/g5aa0pc;2k5 jrd a distance of 1oq5/k 6a8 zpj rg;ny2dc5+hrag0eo/s 15 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rota +i0nc-4qdh y0 lu2uyydo85 hztes at a rotational speed of 3600 rev/min. When switchedh2-0nq yu+i5ddu480 yz ylco h off, it rotates 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 to a torque of 90 Nm. If a 3r9;1l k/ d3uc7ts+j ybja.yl q0 cm long wrench is used, what is the magnitude /q ya7;1 dbu.+yjclt9k s3jlrof the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require ah.ihfa0mp;d3i5(: +e lommitightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnit 5+pdlieoh f.(mmi3 0ma ai:h;ude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment om2 /vnh f c2o3tlqm53xf 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 o/o q5tb a;/9-a8dxca6byqnb as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moay;a9/nbdx c8at/qob- qb o 56ment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a friction+b(. t s4wv)a/hzh(+oi eclasless axis thought the center O. A rope w/lezc +vsih4 (s)a(bat+ w.horapped 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) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 1 8qb + uhp10bprwlivp(8 kx/m 05vwhu90 kg is pivoted about a frictionless axis thought the center O. A rxwub 1pr(q v9 /58 0l uw8phpmik+vh0bope 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 onbpru*fb 60rhak8u(s ; e 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 onebhrrkuf8u b ;sa0p* (6 end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1. k)4 qeb q+cf,)gpxd)q5 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,e fqq )gq4)bd pk)xcm 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 dis0hnyy 5cssh-vwqgixa /u. 1 33k pulley of mass 7.07 kg and ry0s-c/ gxahnqh.5u1s w3yiv 3 adius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs x q8lh3h 0lwoe:b0 j7 e(jsf8eon a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radijhebo0l(f8 lwqhj837 : 0ees xus 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy.ui emqns8.i/. .m /atm 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 inertia n,m frg9m)mfh30w,ml 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 stc;a 0orzx3m xc9isgl7g5+1ii 5 c*mqzarts from rest and rolls without slipping down a 1.0-m high inclined plane. What is xl7icoi1;*ri5g3 0z ga9qmc 5+xcszm the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and5m))jp bzjujpg)n.(4d jnj,y radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined pla j4j). pjy,(m jgpd)nun )bz5jne can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg snht +p .l)gt:is released from rest and allowed to roll down an inclined plane. How fast is it moving after dtl st) .hn:gp+ropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a 35e:z( aoqw7f2 +phzh 4 vp/h;yo mof,f2c incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphey fz;,paz+ wpf2fvc4(oqoh m/: h7oh2re 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 changk f;7t )wh wxyrm8nr4wysoa+ef)(4 y0es 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 1h *ui tctzk(9w a)sk0w;k/ qsinertia 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 x *pe/iq k3w/a 1bdzx65.00 rad/s with arms extended has a moment of inertiwqx6pa*i k 3bdx //ze1a 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?