Angular displacement i*4qu,z/biwa 1 o (0hrouols 4ts usually express in units of

  Angular velocity is expressed in 6dq kl-w5xc ,k3jb*8uy;2umfifs y;bunits of

  Angular acceleration is expressed in uni; 05 gqagl/n5dhnv0 sn8anry8ts of

  A boy and a girl are riding on a merry-go-round which is turni 4o:czqlu)go3:n4g y b3)eukh ng at a constant rate. The boy is neh: o)g4 cnkybl:o3u4eq3 )z guar 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 whic-+uur qyos*n0z- v yp-h is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. +qvr-*zn- y0oyuspu- Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-o hx, 1hy:al(ne, (nr7f. 72lfenomrpround which is turning at a constant rate. The boy is nea l hn7ynx( elrh17 ape2f,fm,:o r.(nor 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 merry-go-round which ;18p ctfvj. twis turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripef8 w1vtcj.;tp tal acceleration?

  A boy and a girl are riding a merry-go-round which is turning ajdcjlae3 43e3 t a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who dlj33j43ceeahas the greater tangential acceleration?

  Consider a rigid body ay0 6,kqam4kg that is rotating. Which of the following is an accurate statement?qkk0a ym4a 6g,

  Rolling without slipping depends : +hx;k2 whcr6/eqsa bon

  Two equal forces are applied to a door. The first force is applied1x*xs8el-utx, 7r yc bd2 f)bt 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 the gt)7xbrs1x2, fty dlub - ce8*xreater torque?

  Two equal forces are applied to a dob ,yqeamn97n )blgl(; k67g zziusmz:i 79a8mor at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force e97;eyb(ml nb68qm)sg 9 uakzgi,7 m: znlzai7xerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. Th:m 82+ puzdhcve first force is twice as large as the second force. The ratio of the torque of the first to the torque of the secumzvp +2 8hd:cond is

  What is the quantity used to measure an p+sm yb t(zb1*ooik6,2kri5 xe:8lm+d:r t lkobject's resistance to changes in rotatio:ye i+ kd56 k b2li+k(rx:z mo8brt1pt* lm,osn?

  Consider two uniform solid spheres whe93x+5om0veb bsnqf00 3o d -cvyb v3glre 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 lo v0s930b3v 0cx+dgvm 53eqbbf n- oythe smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one httx+cw ,es*,aas twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller s*te,a w,cs t+xphere is

  Consider two uniform solid spheres where one has twice the m//+ycp x nvo+n6d rzg8ass and twice the diameter of the other. The rat6g 8zndpy/ r+xcv n/o+io of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and rar( lnz8ji: xlmz213q vdius R. If these are increased to 2M and 3R, what happens to the s328v1 xr:m l(nzq lzjiphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wd)l,5pihn(po d-,yf oill

  The moment of inertia of a solid cylinder about its axis is gib:ehdy ; pdis e*9km 3mee0h9.ven by $\frac{1}{2}M{R}^2$. 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 a mass of 1x kf52:j)db(qpazt:g 0 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? Assume the wheels are uniform )x2zp:bjt q(d:5gk fadisks.

  Suppose a solid sphere of mass M and radius R rowdg7yvau , *eyl qd ;;h0 *(kakf85ynflls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incy0w;n(;a dydg57lykkq,v *u* h fea8fline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping do t;)ahmyyni 8ho8 *ef,wn an inclined plane starhiy;m)y8t*oe h,8fan ting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when.e 06bdoh. sqvu(o.ty a net external force acts on thv0 es.uq t6y.bo(ho. de system." This statement is

  In what circumstances can the angular velocity of system of particles change we*1bp *ppple(e( p g9ud)rum.ithout any change in the system's angularpdu e e)*m .g*ep(u (p1rbpl9p momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictio(v2s j1da9a /ivtt c*in which may be present. What happens over time to the Ea*/vd j91acitt(s vi 2arth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. w/,z/ dwk*0pulew0n nAs the Earth moves close to the Sun, then which of the following best describes the orbiting speed of t0en,0zdk p w/wn/uw* lhe Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in huuh u (3bj /p7v) fwza ahp-ne(78.dosis outstretched arms close to his body. Whatpvh3(fuu e/8(jznd aw7u.o)-sah p7b happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spinrxg v xp:5+fd iu26k,+lb.rop ) by pulling in his outstretched arms close to his vi+gd5, + ofurr:6klb2x.p p xbody. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pq. n2vfj-y ndska.6i bt)l-v4ulling in his outstretched army nf-) ktb.4 vqs26dvn-ilj.a s close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular mome9cunwdr x .9p0vay8y 2ntum.

  What arc length does the Earth travel in a thrg)lzr 66y)x + .kdlhproao.0m ee month period in its nearly circular orbit about the Sun with0lxr z6.oomy g6 l.a)h+)kdrp a radius of $1.5\times {10}^{11}m$?

  The second hand of a clock hasfyklno/:+(q;6d,ynsi s5 jrx a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minu idkyj6o: ,s slqx;+nyr/f5n( tes and 45 seconds?

  How many rad/s is 25 revolutions per minute equim,9z+ qcta4 j b6r8zy1hr xgo-valent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What xqbd s;12/zc9y hyx)iis thez92;x xqy/ih)c s by1d frequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequen9c3yd w qykxk bqk acf371l;6*cy of 0.40 kHz. Theyqk3wlc9 b;d176ka k*qcy3 xf period of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.20xo tpx2oo7 2irnqepj4g 0q-++ q+jron42+te 2iopg x0 -xop7qs?

  A wheel of diameter 26 cm a37e)zmzq2-mf/ng hjt-. gc i turns at 1500 rpm. How far will a point on the outer rim moghai /z2-f)-3.qgemtz njcm7 ve in 2.1 s?

  A bicycle wheel rotates uniformly throhh8 rakd,kz 5/ugh 2.0 revolutions in 4.0 s. What is the average angular spee/ h8k ,zkdhr5ad of the wheel?

  A bicycle wheel rotateyk8wre b. .st2s uniformly through 2.0 revolutions in 4.0 s. What is the linear speed o.e.rys 8k wb2tf 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 mn*qa mfr t/.s-f3h-*pkjr 8n which moves the car is d h-prf8tjmfa3msnk/* *.r- nqriven 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 constantk(2al9ror(v ocfbb ( 7 angular speed of 2.0 rad/s. What is the linear speed of a pointa72lb9k r(ofc(borv( on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If tge;s6ya)n z9z he motor rotates at the rate of yz);s9 nez6ag 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotatinq6 9)ydaw:k: zf-sxq9 tz d(ltg with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration o :y f qzzt-6qdwts9dl)k9(: xaf a point on the wheel's rim?

  What is the centripetal acceleration of a point on the pus vgw dz-sxx y;dd4 1(;1ci4ferimeter of a bicycle wheel of diameter 70.0 cm when tyxd -(z c4xus1ig;d; vdfs4 1whe bike is moving 8.00 m/s?

  How many revolutions pe hvvfujnr8/:l: + wvb-r minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravity lrv8uv: hn+fv/- bwj:of $9.80m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a spd+jb j2(s x1sweed of 20 m/s. The maximum centripetal force (provides 1x+d2s bw(jjd by static friction) is $1.2\times {10}^{4}N$. What is the centripetal acceleration of the car?

  A car is negotiating pwmz ( k2:z6,b(,psff.ep weqa flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) ( ,6(mqeew: w fk ,pbzps.p2fzis $1.2\times {10}^{4}N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.750-m string, is whirled around in-h, ok;1/ u.vfsyr6d. zrgcwnp; 3nw1ei,bwq a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the ma 3f,;nbw /6gwwrdqs,.c; r1yoine h zpv-u.k1ss have if the string is not to break?

  A bowling ball of mass 7.5 kg and rvs,epct3i u558r*l jmadius 9.0 cm rolls without slipping 10 m down a 5lc3sj,e 8pu v* m5trilane 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 acceleration -.mtxlb 4)kqs of $4.5rad/s^2$. 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 ,prj0bmvy4xo:7ld6a angular acceleration of $4.5rad/s^2$. 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 aut,. rs)szk5elq3 2)zq y hvz:nzomobile tire rotate after starting from rest and accel sy2zl z z3qs.5q)zrkhn:),everating at a constant angular acceleration of $2.00rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angularj:v82e4; dfvpau wd4e acceleration of $4rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a consta1a*;my,yxymbn +f g5d*-.rx ns. lfxnua).st nt angular accelerationr1 f .ys *+*x;bmsalytnngd)a5u. fm-n .y, xx of $-5.0rad/s^2$. 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 txtz/ 3,n4 4fjspaktl6 2ib2vburning thsi4tnt,6 42 vbbjxz/lfa2pk 3 rough 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 6ki nf2j3m6isbal.) .d8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the whee.n3l6s. b)df2 a mikijl rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s: vayssit. nq) nuu/r,d;5t u5 to rest over a distance of 11 d,5s;vrunnut: )tua5/q y.is5 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to restql0ie30byll 8 ,j(qbox:w n i- over a distance of 115 m. How long does it tak80qx,lb3 eib:- (0iw ql jnyole for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 3/vi 1m kmg getg(yhpnu;3.7 urev/min. When ;/3y(mkg it3u hmggev.un7 p1 switched 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 Nmx q4k3 h9cn)rm. If a 30 cm long wrench is used, what is the magnitude of the force required when t4m k3r9hqc x)nhe force is perpendicular to the wrench?

  The bolts on a car wheel require tighten) uuyf;;iema. ing to a torque of 90 Nm. If a 30 cm long wrench is usedeaf.; u;uiym ), what is the magnitude of the force required when the force applied at ${53}^{\circ }$ to the wrench?

  A wheel with moment of 8b8hte/z q3biinertia $3.00kg{m}^2$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mass3fowy*ws-i2yvd m 8;v m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What 8 fmyvd-s*;v iwow2 y3is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought theoi-v ,n+yk.wz center O. A rope wrapped around the outeo.y+ v-z ,kwnir 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 10 k pphzma24 l95tuk-x13qfdg b- g is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer-p53 k9ufqxtal dp214 - hmgzb 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 od:w/r dlv :*zane 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 accelr adw v:ld/:*zeration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius9*e-zdcx- 9sh, sdhm g 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 whe- ,g9dezxhmsdh -9*csel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frii2n 04cfvbo c.bhqb3f0hp b,2ctionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelerati.bpf2b fh0q bi3 4h0,bvo nc2con of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionm/ nc9vbp5lppp3/ 0x oless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the ma/9pvb x/lpm053cpon p ss?

  A rotating flywheel can be used to store energy. If it is re( xi4l(fg* wc+clk/qj quired 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 $kg{m}^2$?

  A wheel of moment of inertial/9.lyaej5 jl8al g8 h of $5.00kg{m}^2$ 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 rest aehd, piior 3:.38jm fhnd rolls without slipping down a 1.0-m high inclined plane. What is the speed of the3joipfei8,:hh .m3 dr 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 spaum(4 sh51 4 amki/f2ai zkt3veed of 10 m/s. How high up an inclined plane can it climb before c4i 5auks2fvha/1t(mai 3m4kz oming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released fr uae)rn/ ;)rzugec- 8hom rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 ahergzu-;n8u)/re )c m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a 35e3kz.m am1/y+n q 8y,hszpo; vd e+1fxm incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is given,mdq a;.h+ py 8x1kfv+/mos ez 3mn1zy by $I=(2/5)M{R}^2$.
(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 c fc 0w7yb41ly zm3j9rrick; h/hanges by $20kg{m}^2/s$ 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 momenk2- 3vbkxxp8vj3 e g)r pnhfytu*p+ *lv;( z4bt of inertia of $5.0kg{m}^2$ 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 $2.0kg{m}^2$, how fast will she be spinning?

  A figure skater rotating at 5.00 rad/s with arms extended has a moment of inegql gj *4i(hb 6uz8bh-rtiq4bh- j8g*b6 (hugilza of
$2.25kg{m}^2$. If the arms are pulled in so the moment of inertia decreases to $1.80kg{m}^2$, what is the final angular speed?