Angular displacement 0jo:m p2 gzyc u54kry9is usually express in units of

  Angular velocity is expressed in unixbs6fm*10kb 8 w oes:yts of

  Angular acceleration is egdy) p*u*.q spxpressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a(csg x: :kwhhg.)qy,t constant rate. The boy is near the outer edge) x, yqsch:(k htgg.w:, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merrys/ x :vkv3bc3l-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 the:3 lbsc3 k/vxv greater angular speed?

  A boy and a girl are ridi fc6lqy72q xa3ng 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 the grexy6lf3q2a 7c qater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant ,jk s0bbjhz -r:tbkld v.*4z(rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?t0.z:*(kzrlkb h4j- sbv jbd,

  A boy and a girl are riding a merry-go-round whmscd )*ik77 ojuur7 5jich is turning at a constant rate. The boy is near the oij7)jkduom7 scr5* 7 uuter edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that if hnx(pe7f4m7s rotating. Which of the following is an accurate statementpx77 mnh(fe f4?

  Rolling without slip i;o 40h/p3ph1l,em w2 pjjggiping depends on

  Two equal forces are applied to a door. The first force is applied at tju)v 4oc+yh0 the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exer t)0ou4h+yjcv ts the greater torque?

  Two equal forces are ga9pu0 h gj3ou)*s.q lapplied to a door at the doorknob. The first force is applied perpendicular to the door;g lqho.0pu)3j us*9ag 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, perpendicularxt/ em0(pjocraqi ; l(ygpw-t; .7z.x to the door. The first force is twice as large as the second force. The ratio of the torque of the first to jtpp-q(cox;z(/eam70. .w; xgyi tlrthe torque of the second is

  What is the quantity used )3gvg4tcm0eq*7t nweet+p sipa*;5kto measure an object's resistance to changes in rotatio5e 03*tcgatmktvg 7pps*n+eew )iq ;4n?

  Consider two uniform solid spheres where both have thesik e)(cm jcn3 l 2w18n-cieu*3q ,yhk same diameter, but one has twice the mass of the other. The ratio of the larger moment of inerc )cul1nmw3-q3hc i iyk8,jsk(nee 2*tia to that of the smaller moment of inertia is

  Two uniform solid spheres hav gge72/y b6 tc(oc+vdse the same mass, but one has twice the radius of the other. The ratio of the largeg s6otg2 bc/v7ydc(e +r sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass anll:mm 4j i bt :m:t:vlp1x(:ndd twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inernltvjt:i:1ld(b:: l4p mx:mmtia is

  A uniform solid sphere has mass M and radius R. If these arerd z 65 bq,9t:s dlxc*pvu6m05jwl,gj increased to 2M and 3R, what happens to the sphere's mowqz5: xdmj9l,t bcj*5,vd ugl6r60psment of inertia about a central axis?

  If a constant net torque is applied to an objewr2ybqph28a2 a((,hdfe pl /nct, that object will

  The moment of inertia of a solid cylinder about its axis is bdrtl q -m8hg6k+rs6)given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic el+6s hb d8r6tmkq)rg -nergy is

  Consider a motorcycl .1kuweu0p-3z m6xvn:3kx lx 7mzh,xfe of mass 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 of6,mf xn w7kzxx .01-ke3pu3zv:l xhmu the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere rn26ibiqwk,. of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom ofk2qwrbn ,i.6 i the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping do6 +gdvlbi3(; pnuh0zv wn an incl3v z+hbv6 nuplid;(g0ined plane starting 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 w wr*,nlc-5,:/cytkpd4 vnwptek2d ;o hen a net external force acts on the system." This skt/v 2- t;cn,nrpddcwk:ol5 * p,eyw4tatement is

  In what circumstances can t-nfl bzb-m;yhkun;pp/ )gh+ *. q xfs3he angular velocity of system of particles change without any chan 3pf )hy*f;n+-/zpx b-k.lqhus m;ngbge in the system's angular momentum?

  The Earth orbits the Sun in aaltyeb io6)h 8 h5zq;*.zkvg4n elliptical orbit. Ignore any friction which may be present. What happens over timev4.8*)6a zbyg e5oz;hit lqkh to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Ea y sxt7e45np0;n) w pqfr*ztl5l mxj;:rth moves close to the Sun, then which of the following best describes 05zxnynmp;* 4; j5qtw:rl7l sxp)et fthe orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretd9c e:9y (f**hx jud4:hhwx qhched arms close to his body. What happens to his angular momentum about the axis of rotatif9hc uh:w: 4 xd*x9j(d*q hhyeon?

  An ice skater performs a pirouette (a fast sq v 0anbszy0/g j)w(x)dbd29cpin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the g)/vy(9cn)0ws0 jz bx2a dbq daxis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched f lbr8a ): ,a+c lovah8rv+mg;arms close to his body. What happens a :g8oc8hvfr ,lr+vl)+a ba;mto his moment of inertia about the axis of rotation?

State the law of conservation ttsx 4/rnl9f c*w1hn(of angular momentum.

  What arc length does the Earth travel in a three month period r/o61 jq-ngkr in its nearly circular orbit about thejnor -/gkr1q 6 Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What rqe6p0 dary+in :ju1 sc756u hdistance does the tip of the second hand sweep throughq6ucj 1pra:ni 75e60sur hy+ d in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute*h ,n 7nvesgd5 s8kp-,ud.owy equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. 4 m6ii:ud+yqk What is the frequency 4+muidq 6y ik:of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequencw 7z k-6zyl+uv .fn,hny of 0.40 kHz. The period of its rotatnl,f vy6kz7u +-wh. nzion is

  A phonograph record rotates at 45 rpt/: d h4o 6s/te;dtdntx ,yt t9i2m3ntm. Through what angle does it turn in 0.20 s? n /:xd t6o2td tt3,het9; snd/m4tity

  A wheel of diameter 26 cm turns at 1500 rpm. 41/uz9sr7fsqv(+be -ly uui j How far will a point on the outer ri-(/rbqizjf4yu1uu9sl 7 v+sem move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What ism2 lm*,3ns lgnjpem ,8 the average angular speln,* m,mn2p 3g8sjem led of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is th e s7+ghnlbcd -,zd o79nq6a.se linear speed of a point 0.10-c6be hqz.dlsdn9, onas 7+7 g m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cg vczud5ohv08107+tadaxa lb4 .neg9able which moves the car is driven by a pulley with divbeh na1 5gugxaa0 9 04clo8tdzv.+7 dameter 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 constant angular speed of 2.0 rad/s.x:e rs 2/o kg2ebhxu5; What is the lin;2rhxg xs5k :ebeo2/ uear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 mb yd0u r*(pvl0f;fh5m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of theprhu(bl;fv50d 0ymf* end of the cord?

  A wheel of radius 1.0 m is rotating with a co-l qjli1-gz/ f w:ytj) qv*n)a5y)hijz cq6: hnstant angular speed of 2.0 rad/s. What is the cenq-tv:*qy)hacy) j6g jhzj5 ) iq-wi fz1l/nl:tripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a pointzs8w2aivo 8v pkl5)d chx87 u qqd64/d on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is mow6pax s hkqvz)v78cdli82doqu 458d/ving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating gt arz vj0* -g- +d4ikggh(/opspace station (r = 1000 m) rotate t-zdgv* prig4/tk 0a -goj+ (hgo produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a fla7j:q y- .swkwxa uvpq39add4(t circular curve of radius 50 m with a speed of 20 m/s. The mvd9s(q3wjya74u-p a:dxw qk. aximum centripetal 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 radius 50 m with a speed of za, u)/pwp)d+j : mh mvrf+de;20 m/s. The maximum centripetal force (provide ,pmevdad)m+;+ f whpz)r :/ujd by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to jiy 4litb9e p-p/dqx :1hi52d the end of a 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 maxhe-j tp51bd9xp q iid4i2y:/l imum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 c-jncd2t wvfp165xa5 kg and radius 9.0 cm rolls without slipping 10 m down a lane at 4vxcpd1 2w556jt fc-na.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 *e rmnu9:ginu ux7:c 5a constant 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 constant angular acc krr8m,ur6pku ,otz.7,* kgdleleration 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 .0p w k -ap6l(w)vbvorradius automobile tire rotate after starting frowrpa(wo-6vk vp.0 b l)m 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, andmc.e;bnu)-o z 2zx,fa 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 decelerates with a yhsmr eqjm 5*2d6h.b0vl5k6d constant angular acceleratio 2ey56.5m dk6rhdbjsl *m 0qvhn of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed 67jf 6ahyiba 15bsa5rof 6.0 rad/s while turning through 2.0 revolutions. What is the average angular ifh157aj ar5ab6 bs6yacceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly frob.rk0t/tca mb+z -o9x m 8.40 m/s to rest over a mazbt/k+xtc. r 90 bo-distance 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 slows down uniformly from 8.40 -4 7n mco0l9-ftr yd30 rgdzfk wdz*m(og3t3x m/s to rest over a distance of 115 m. What is o- 0c*lkt3r gdmwzxg3n40d-ofmd 97f ty(3rzthe angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over a buj71 s+pqwz*,g s2lu distance of 115 m. How lowsb+ u jpgs7zu12lq ,*ng does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotas;z:lc ax(d,o+ vh0aites at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleratiov,o:aalxz d+i(c;sh0n 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 r nrafhm;u+f6kif8 94 kequire tightening to a torque of 90 Nm. If a 30 cm long wrench isi+auf9m4k h rkf; 68nf used, what 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 tor iekf+5j8fxl*v*n c n)bbd()rque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the5b+ 8(r) jblnkx fdcne*) *fvi force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of in:a :cyxeap.2n 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 follo:e,jz nrs0 )ldc: humu+xx f-5ws: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of in +x:h,r05xenfc sdumul zj: )-ertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis tvfld(fn 9n6ub wthau90 p/ )6zhought 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 secondanfdvzf hn0t 996pl u)b 6(wu/ 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 of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thongtl.h:*z lucd 0;qzeh )0 h;gf.b t6fught the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. h;fnhcl;*dz gehql zu0t.):t. b6gf0A 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 initi;c62iivp5, m,lwq fslnp z.d(p q:i9fally held in the horizontal position, and then released as the free end9cv.(p;s62 zlf pliw dfqim5pn,i,: q 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 ring of radius 30 cm and maslkeo .0jzyq zj/q baurj.3-9,s 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,o, z qubl-a ./q rjkjjz9.3ye0 what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs o /g,+am byphg3n a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 g ,h+pg3/yam bcm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a ropx1l5i x( a3szdyay;4d1u i/u me wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 ym1d a(syuz5xi 4axl d3/iu1; cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If i5qh2hrg zbv m /6v*lf2t 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 inereqr4;3atx9 99pjb khltia 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 radiusa7ae( fvx;gbf8 mx-j2 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the-bjf2m x7av; gafx( e8 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 9te; nh5c fx:vkhh;sng6jl ju5g4., a m/s. How high up an inclined plane can it climjgc lte:hg5h 5nkn,v 9f;6 hx;a4.jusb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released fwf+g,os-,xn*5efa5mzyh x(-shkb q, rom rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical dist,*hs( abfehs o z-xgq, -,fy xn+k55mwance of 3.0 m?

A solid sphere of mass 10h -foa7u/h ynkl 2ci5.5 kg and 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 i0ulnihk/cyfh 2o5a -7s 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 mc (nd+i1pv)e comentum 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 ofw-bt-oa6 l: b,67pzl rg ljrspw7-s- j 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 with arms extended has a moment a +g) 3(u)/x.qc8det d c tfi(;xvcalxof inertia ox)e t8gat vx3c(iq)dd/ + (;lu fac.cxf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?