Angular displacement is usually express in units o kz,.au4 j7-w+rva hdwf

  Angular velocity is expressed in )ozlln p7y;*f d :5xlqunits of

  Angular acceleration is e9rvij97p)by//p o qkagde/ bpz2 1k4txpressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at at:cq g),z;stqa zh qn1;.qi o* constant ratet qz g1.,)o;qq tq;asiz*h:nc . 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-round which6hpg ujl31+n m was;() ar1uer is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greateru); r3umg(16 pelw s hja+rn1a angular speed?

  A boy and a girl are riding on a merz;g s 69byxt,ery-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 tt6,z;s gxey b9he greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning t *t.mv6d2 g idarh0+cat a constant rate. The boy is near the outer edge, while the girl is t6dd+t.r0im ga2* vc hcloser to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which iv: 7 dpzxux+) /eegpyukn-/h :s turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential accelera xzhegv/ ud+ x pp7:e-):y/nkution?

  Consider a rigid body that is rotating. Which of the following is an accuratep4qd,6 1;fl kacmtcgs:0: x ua statemefg4 cq: 6u at;xmsa 0cl,kd:p1nt?

  Rolling without slipping depenuspe-f db;ve*:k 9a 1kds on

  Two equal forces are applied to a door. The fi9mp w.kx dgv8r3 0iw7srst 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 force exerts m3gdvkr0w7i8sp .9w xthe greater torque?

  Two equal forces are applied to a door at the doorknob. T n: d6bto8gh1lhe first force is applied perpendicular tg 8b:1l dhon6to 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 doorknob, perpg+ ae2v1w cry(endicular to the door. The first force is twice as large as the second force. The ratio of the torque +r(vew cy12agof the first to the torque of the second is

  What is the quantity used to measure an object's resistance to qlcz6gsvytoog 2tz*-xm0,( a 3 4tox u3b ).apchanges in rotatio zoq320ox4p zg 3 aygbm*stt ,6-axu)tlo (v.cn?

  Consider two uniform solid spheres where both have the same dirj,iyw cvek q,cu47z5c .* 2bcameter, but one has twice the mass of the other. The ratio of the larger moment of in4i*kb 7eu5yr w c.q2cvj,,z ccertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the hfx c2f 0f.dki:b(l 5nradius of the other. The r :cf0n bhfflx5i.2kd (atio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheriy)f/+ou aoy. q9i55bctzf o hz5h,;c2jw7uees where one has twice the mass and twice the diameter of the other. The ratio of th9 w ;5t+zf,c/u7j5c)uz y.ohiofe a 2q iohyb5e 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 ink+ c zz/2(cauqcreased to 2M and 3R, what happens to the sphere's mom kccq+2(zu/za ent of inertia about a central axis?

  If a constant net torque is applied to an object, that oqt n02v6i(ivt bject will

  The moment of inertia of a solid 1wi+9 u;khiq gcylinder about its axis is given by 0.5 MR2. If this cylinder rolls without k gwqi1 9uih;+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 o2o *vxv1uj,ibf 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of tji,*v1u v2ob xhe 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 downc+ s -gw+pou4cjb )h6p an inclined plane starting from rest. The linear velo-4)6wuspo+p h cj +gbccity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls withouvn 02pr4,vy6 7jzb1q1f hyrljt slipping down an inclined plane starting frqb j6 r y7rvf,lynv0zp 2j41h1om rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particleujv8odx5 8vhi)(jxa9 s changes when a net external force acts on the system." This statementvaujoh (9i8 jvx85xd) is

  In what circumstances can the 8.y23 b;1xbd els 7d nvufiwm3angular velocity of system of particles change without any change db;.u7xyb1vd3 s mw82 l 3efinin the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which5 vycr3zedc)* may be present. What happens over time to the Earth's angulyr 53)*cec dvzar momentum about the Sun?

  The Earth moves about rxdc0lc 68v 0+azm)h8*zzoty the Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the folloc dcox+z8* yhz068mvtr0a)l zwing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstre jbttms0i2cfnx vm91(fm-(y b7lk39xtched arms close to n t9ffxm(3j b 0-1(mlcik27 9t mvsbxyhis 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 outstretchs:l4ahw .c xh:ed arms close to his body. What happens to his rotational kinetic energy about the axis of roths:c x4a:h.l wation?

  An ice skater performs a pirouette (ah)1v/,+1np0po3ntapqy. m b+ fhv s xu fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the anpo sy+p1n3)1 pvauhhftqmb x+.0 v/,xis of rotation?

State the law of conservation of angular -t; )dski 9ltuyc ,i(4yo pkr2momentum.

  What arc length does the Ea2- evd9oqd5t pm0o3 zarth travel in a three month period in its nearly circularvotm-5z e3adq2 p9 od0 orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock h)8g yt--acsazas a length of 0.30 m. What distance does the tip of the - a8a-ysctz g)second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute ot(:edtu8e f;equivalent to?

  A bicycle wheel rotates uniformly through 2.0 rw 05iy8sl;gqew y5ob 9+bzr(nevolutions in 4.0 s. What is the frequency of th0bg y+i rbw8n;9sze(5 yqo5wle wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequeh j;xi 4ko qaw3of,y+)ncy of 0.40 kHz. Thekhq,);x jo+fw o34yia period of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn tl5k jdk(okal6(+ +zsin 0.20 sosltlz6+akk+j( (d5k ?

  A wheel of diameter 26 cm turns at 1500 rpm. How far h()1cjcy. 1hotxwp a 5zv60vowill a point on the outer rim move in z j.wcpooy1x(t0h vh5cv6a )1 2.1 s?

  A bicycle wheel rotates uniformly throu6k:ovm 1k5ey rgh 2.0 revolutions in 4.0 s. What is the average angular r v16m keyk:5ospeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is the5m-m1m+mv1b tjbgj3p li tm mbg5mvj1b-3pm1j+near 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.;4ez6 nj gu 47kr /yg4mfnaho( 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 trip iu44gyoae( kmrh n46/ j;znf g7n 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant apsvubt 3nt9 )gfj-z8 v*/svj(ngular speed of 2.0 rad/s. What is the linear speed of a points8 t-p*jvu(3 gz) tsjf9/ nvbv on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the mo*cn, zyo o7a5ctor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cor ,cy5zac*oo7nd?

  A wheel of radius 1.0 m is rotating with a conxiqij6g,q /ue*d+o. wstant angular speed of 2.0 rad/s. What is the centripetal acceleration o.xu+6 q oq,gd*j/eii wf a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimbc.wvg a;uib 1h4t( 0dug*f+r*omc k: eter of a bicycle wheel og om;*af1vcu0rkw (db: u. c* b4hgit+f diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating s g9rl0 ;mxaysg*xtz (5pace station (r = 1000 x 5(zg*at; r0lgm9yxsm) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular c86qri mc)x65sdgu oi* urve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provcgii8 6*)sro 5mx6d uqided 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 radius 50 m with a speed u j. ffv5/q(io u;ceu46g*tpgof 20 m/s. The ojq u5if/4g6t.;pc f*geu (uvmaximum centripetal force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attache vmu -l)1oqn,xd to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tensivnmq1-xu l)o ,on 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 withoefuml0 jx5 bdf-b. :h7mj2us1ut slipping 10 m down a lanejbl1muf0.7 sfb jud5he2-x :m 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 cq7(2veda2tv v 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 a cona8xv: p exl+1 uys.dhwl7ru 75stant 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 t6.mpah5i9 h :e/lai qdire rotate after starting from rest and accelerating at a constant a9dhle :6ia5p/ i.aq hmngular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has phi 9 nkmqy1/gnx +obpjnu(8;1)t9p ban 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 de aoc,m: unhf. m5hku atq,8p-/celerates with a constant angular acceleration of -k5n m,:hou, tcmu8faha.p/q$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angulu 7tk n9l gh/.jt(xh3f,sf0arar speed of 6.0 rad/s while turning through jshut(/t0ka .7lghxf9,nf 3r 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cmfz k: 0vduk5uk9.ut /m slows down uniformly from 8.40 m/s to rest over a distance of 115 m. Wha:.fvu /kd09u kz5m ktut is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s tolisotife:: d-:r j/*t rest over a distance of 115 m. What is the angulri/t:*i f:d-o e j:tslar acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s t hls5fy6wjx .3o rest over a distance of 115 m. Hyf .sw6j5lx3h ow long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 7 holu6uy9-e pyco8;r vwb v(;3600 rev/min. When switched off, it yo; 9ewh p7ucuv;l8v(6-orb yrotates 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 tifs k8lam jo8(:c0h1wdghtening to a torque of 90 Nm. If a 30 cm long wrench is used, what8:k 8ldwsma (j1fhoc0 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 torque ofey8(w xws6,g(jbrxf(n2koo: 90 Nm. If a 30 cm long wre:oo(,wb 8yks6xg 2 x j(efwn(rnch 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 inertia0l 4e8sp,/jk5iqqd q grrz4j6 $3.00 \; kgm^{2}$ 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 at.:ki ihqvq/a c 6cnt1+(z;emf the origin, mass 2m is at x = a, and, mass 3m is at c /qv6i+:maqkc z (f.it;hne1x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivote7jm2 xp*iswf2 xd o3h9d 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 rop of7x* xw93 2p2sihjdme 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 massvffn (s -lqc p0(yhw5xu2:cq9 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 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 second2(5wvhxf(f 09c qlun y:cp-s qs, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is wp.9,rzucm) yso 0)s ainitially held in the horizontal position, and then relysarw)c ,m.zup0)o 9seased 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 rin y4x el cqv7,z2*ri.-:jexux fa.k ob:g 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 does the wheel achieve, assuming it rolls without skuex. :4ja :x27-cvye oxqilr.b z*,flipping?

  A 1.53-kg mass hangs on a ropyjfme 0h8a7g0plv1aw3 +.bk ve wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelerat1ebwpmy+0 v vkagh0.af 87 lj3ion of the pulley?

  A 1.53-kg mass hangs on a rope wrapped a s-rk ryv)eat0 -tgzs0f6x+y *round a frictionless disk pulley of mass t06y- f+rk rxgvass*e0yt) -z7.07 kg 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 stos1w0ev r seyzw,2t6xru-w, /dre $1.00 \times 10^{6} \; J$ 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 inemq ovac 2rlgs9v2,0qj5b**smrtia 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 mas 04ur aat*;eogs 1.0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the aotr4g*a ;ue0 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 of 10 m/ c sb*x5 y. 5u8byb9gme*i/gans. How high up an iab8bg *m/s9yg* u55neyb. i xcnclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 k)z;;sj8 f2 onm9p/hf6qnvmbpg is released from rest and allowed to roll down an inclined plane. How fast is it moving afte9p/fmzbmh;fp jn2);8qsn 6ovr dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and 7sh ,rohie :z yx;gn.(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 is given binyhrg:;h, sxoz. e(7 y $I = (2/5)MR^2$.
(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 n+ aq52eqrq1be xst gz,4tg1,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 moment of inertia w)o6jvn7rt) oof $5.0 \; kgm^{2}$ 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 5.00t oymhx + wmqqm8u,0jt5pi5(/ rad/s with arms extended has a moment of inertia o ,5o mtuqxj ywm/t5+mqih8(p0f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?