Angular displacement is usually exprer-hz mpsd+8x fx(l*g) ss in units of

  Angular velocity is expressed in unit9uig aw .ve9dg6*gzo+s of

  Angular acceleration is expressed in un.dndk8n.c -u vxzl+,nits of

  A boy and a girl are riding on a merry-go-round whic, da:gdlz ,p)g4djl c-v4q7d tjwm ,ix1o+qu)h is turning at a constant rate. The boy is near the outer edge, and the girl is closer omu)x d,p)jtl ddc47 v q4d zaggi1,jlq:-+w,to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turniv3.uw.iejb+ y ) ucr)ung at a constant rate. The boy is near the outer edge, and the girl is closer to the center ruwv yuu.3)+j)iebc. . Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which i ga5 j)ds* cu:vgzwj60s turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the grea5w*jzgu6a0 :j)vcgds ter linear speed?

  A boy and a girl are riding a merry-go-round which is turni(*ehj93cpp 0eswe v 2jgi/5wo ukj :7eng at a constant rate. The boy is near thj5ce hsjwivj( p30oeep u:2g9e kw7/* e outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round whichzr ;ffy 2+t 0n4oj(pfy is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the cent+tyo p;zfnffy042(j r er. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the follope2 1kr3viwlk m4b: v4wing is an accurate statep4v3ib mvr 4kwek2 l:1ment?

  Rolling without slipping+ vnt p32kpal:hj 3ad+ depends on

  Two equal forces are applied to a door. The first force is 2j 2a +wqbfy6hn vd/5zapplied at the midpoint of the door; the second force is applied atqn+yhj a22 z 65vwf/bd the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force ixumpv-uoq, si)26-y xs applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts thiu6uxy mq -s),op2-xve greater torque?

  Two forces are applied to a doorknob, perpendicular to(*v3gwbu 89bkesnfw -o4rcza r : vz)0 the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the sec-ao0 4ebvwsg*8 znr9 c(3brvk) wfzu: ond is

  What is the quantity used to measure an object's resistaq jg/q/cu/ lbjck)7d w-+)de l)gwdu-nce to changes in rotatio )j7 -wg-qqubl)dek )/ djwldu+/cg/cn?

  Consider two uniform so-(j(3w+onyf vgu yhq3yue)j /lid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the largeq3v u3h)n+ w jf(o(/gju yyye-r moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but3p f8fkl 6;(0 oeywlly one has twice the radius of the other. The ratilp6wlfo0 (8ye fk ;3ylo of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform soli ktn63 3.kn7f4 cxydi8g nzqdc+ py:4fd spheres where one has twice the mass and twice the diameter of the:86.iynnypk4+4cxcf qtz3 d g3f7d kn other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R -6to r v:m. lqmsxix3o6g3+oe. If these are increased to 2M and 3R, what ha 33-o:6tm6s xoqiv.e mrxo gl+ppens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied tbg,+go8 ,dy3sw4 oko qo an object, that object will

  The moment of inertia of a solid cylinder abouko bv ru*:j1n 4)jyc.3k poje5t its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translationalncvej.k5:r )4oyupoj *1b3k j kinetic energy is

  Consider a motorcycle of mass 150 kg, one whl : /94kro55(t5u n)nelzqfejtjs *ka eel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kineticek)uf4 5az5tk q( j*5/ rnojet:9nl sl energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radiugja +u5)au/8 fkoof tx g2ay4k w-;n*is R rolls without slipping down an inclined pjo2xat-akog wa 5/y f8fg;iu )+4 nk*ulane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slih*vktpu:ud7ss -, 6ql pping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends onu-lst,7d6ksp h:*uq v

  "The total angular momentuufo8) iyi 3xt+m of a system of particles changes when a net external force actst8 3o )fy+xiui on the system." This statement is

  In what circumstances can the angular velocity of876i 49 5mb e xufeakg(dsjqs8 system of particles change without any change in the s au54mgk(ej8xb 9is8se6qf7 dystem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore mq2umcg.r9j* any friction which may be pres2 qmjrgu9.m*c ent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ajhe05ro*r r0 elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Ear 5*0eao0rhrj rth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hstlhnu +bf--a 1prt+ud1gd2dq,5 m 5ais outstretched arms close to his body. What happens to his ang5, uaa1hdrm52g1tu q -bs t+f-dn+dlpular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling/x 1c) r7 rrk(;vrxght in his outstretched arms close to his body. What happens to his rotatiot cr;k7r(h /r g)1xvxrnal kinetic energy about the axis of rotation?

  An ice skater performs a gw0587qjg:25enk dctun+ l gq 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 rotationqn 75gjqn g0d+lw2 eg85t uck:?

State the law of conservation of angular momj a9hbws;g7m4 entum.

  What arc length does the Earth travel in a three month period in its ne15ivf uckpx)2 )+f q0ibmd ed9arly circular orbit01 f9x5b2 dcim )+iqd)puekfv about the 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 distance luuk mq4 4khz):hi:w1does the tip of the second hand sweep through in 3 minutes and k:zhhi k u :u1lwm)q4445 seconds?

  How many rad/s is 25 rev0tg/zq wtjlb:1w9r76ieb9d l olutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revoluti6r(a(h g3 lgs ct4kr7jons in 4.0 s. What is the frequency of the wheel's jrcr sl 36 4kh7(tg(agrotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.l5d 1wla4( m4u wbm rc0c8fxa;40 kHz. The period of its raw0r4(l4fbl5m c8cx a; muwd1 otation is

  A phonograph record rotates at 45 rpm. Through what t4nj n:q-d:vw2 xv;t.f isfr*angle does it turn in 0.20 sqt4:vi xftvn *sj2 . ;-r:fnwd?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will -9zmqzs *1f2a hg 9ceoa point on the outer rim move in 2.1 * -z as9ezqfomc9g2h1s?

  A bicycle wheel rotates uniformly throug+tbt/s ycin*t1 .ulz37nk o7 nh 2.0 revolutions in 4.0 s. What is the average angular speed of the wheel./uy7n*oztt3 kcbt il+n1ns 7?

  A bicycle wheel rotates uniformly throug2( fxa yn:b2sih 2.0 revolutions in 4.0 s. What is the linear speed of a (2x 2 nsabfi:ypoint 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. ocssaue8/h/, The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must theco8/ ,ss h/uae pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotatingrd 9ijp 1f4o3mw8yvz l.xx8, 28vftr3ju ee5r with a constant angular speed of 2.0 rad/s. What is the linear speed of a point o l1 r vme2zi4drrtj59wx3 p8x 8.jo8euyf,3vfn the wheel's rim?

  The cutting cord on a gas-powered weed cuttereckt9(z y fbe 7za;swk( 04zp8 is 0.16 m in length. If the motor rotates at the rate of 20 rey;a4sk ez7 p(9f8e w(bkczt0 zv/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed b+.ptj-.)rz nv.h+v v,rr skv of 2.0 rad/s. What is the centripetal acceleration of avj+rr k.p,)vn v.sh-b zv t+.r point on the wheel's rim?

  What is the centripetal acceleration of a point on the peri5r 8jfgbxdbdu78 (zj4meter of a bicycle wheel of diametgr5 jb8z7d x8jb(fd4uer 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rota9hqx cz-ge a 6qi y(uj-o1.7eppo +6eiting space station (r = 1000 m) rotate to produce an artificial gravaihz.ujy-9pee 6q 6eq p-(ioxgo+1c7 ity of $9.80 \; m/s^2$?

  A car is negotiating a flat circa5)6 *dh qlyhz+jf m;cmbdd*k- )g8v eular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static a km+;bj6 ldgdq e)myd8hh -zc*5 *v)ffriction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular+q 84nq ,7teba2hsk miojxl17 curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (pro 7j8m+x kh4na1tl oqsbei,27qvided 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 0.7ozh7rrp447t 6m rmwj3dx5gc 0wdx7 8m50-m string, is whirled around in a smooth level table. If thexdogx0 3 w5z6 4t7jmmr7c47rmwpr8d h maximum tension 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 without slipping 10 mw xg80fn9 y-fu down a lane gn8-fuy 9wx0fat 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 an30z q k fak,kj,/lywq4s6r3 fkgular 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 acceleratmq7sls/teg qw5 ty197ion 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 tire rotate after starting-*y6 rj+slpyr 0ys n4rti0+idwt85 ue from rest and accelerating at a constant angular a+850ny dsisjrp6 -rr0 * ulit 4+wyetycceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration i3-vc )y/b szmof $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a constagnr:l)o5 yu;zj urt 6v.9n3u rnt angular accelerav 9jl6 t:n3grun)ruy .u ;zro5tion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from reb6as4qydj57 z3 (d8 1h.vmxa;sx cz xyst and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What ixa6yx .178a 4hsqz (xm3b dsjv;zd5cys the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniforml bcx +)30thspry from 8.40 m/s to rest over a distance of 115 m. What i)t0 sxpr3bc+ hs the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 2 g mxmwlk,,qm*dy47m8.40 m/s to rest over a distance of 115 m. What is the l*y mm g274xdm,w kqm,angular acceleration?

  A wheel of diameter of 68y2 mcc8q*wcr -g yi13m.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to the stop8iw-2gc31 myqrm yc c*?

  A centrifuge in a medim1 ,nqpurdide p2 5z,6cal laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accel d,2 m ,61pindzue5rqperation 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 9 4iho3fpyxb(4t: vuh tightening to a torque of 90 Nm. If a 30 cm long wrench h yiv:4t 93bxf h(pu4ois 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 torqu1tw+ku 79fx lme of 90 Nm. If a 30 cm long wrencu1l7k9twx+ fm h is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ofkua f ad+ii4 .fm(d+2f 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 mbf 4syw, 0; (-saohnb*rata,v is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is av,hbnb; a-w4*f,ostarsy0 ( the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a fric*4t0vf st rmc+ai:6zdtionless 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 wrappe+ fz: *i0smcvtrt da64d 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 tybi(tg htft12c le6-t3gnd/ gl +)q;uhought 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 secoeht;l ctit f(b163 g +lgunqtdg)/y2-nds, if it starts from rest?

  A 4.00-m long rod is hinged at on(-7gf o dnl.pu ahe,xu+(j k0ve end. The rod is initially held in the horizontal position, and then oh.7 v(x afn0uj-(,d gule+ kpreleased 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 ring of radnla8292y j hpe; cmssc5s.f(iius 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 ay5lc;ncm(.p2 i9jsfhs 8s2e slipping?

  A 1.53-kg mass hangs on a r x (0pt7l;aq6ylx2tzcope wrapped around a frictionless disk pulley of mass 7.07 7 xt2qayl(xt6;p 0zlckg and 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 pulley7pi-fnbz9* ju of mass 7.07 kg and radius 66.0 cm. Whati9z7ujpb-f* n is the acceleration of the mass?

  A rotating flywheel can c z00vec8t kbcuk,qxq5 7,ox9be 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 inertia of 9sayq4h62y2w1x7s6e hb oavj$5.00 \; kgm^{2}$ 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 anwiy*s c5oz*i-erop7 , d radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high incline,coiypswez r5*i * o-7d 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 rm fjb0 *sy)a)mt8lv j5adius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane ca)*j0s) mlv yj atb8f5mn it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and 8c21jvc* lmvw allowed vcv2w mlj8 *c1to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius:mvl ;),44 1whsx.fitkdwsn c 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The mome,:sdmwlc khiw;f4 )14.stvnxnt 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 momentugttvwmu; d m2s 37y34mm 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 inek*6r 27nxl(hyl;sbo v rtia 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 raw5guhdd ) 1u13o5mpfd d/s with arms extended has a moment of inertia o1w d5)dpmdfhuu 5 go13f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?