Angular displacement is usually exr u uw,cz+f 8c+n4+pg 7cqoa,cpress in units of

  Angular velocity is expressed in un6 ;6+ie pc7je: 9aqaqwwmuug*its of

  Angular acceleration is expressed in unitb +s2ufllac z +/6u4nks of

  A boy and a girl are riding on a meax:ufzvj;ne1 .hy / x5rry-go-round which is turning at a constant rate. The boy is near the outer edge, and the gir/f1:hx.a;e zn y5vx ujl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constaa,ahz,qhh/ 0ant rate. The boy ih0a ,,a hqzah/s near the outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merrecdq2 t8px68q y-go-round which is turning at a constant rate. The boy is near the oqcd26q8e 8t pxuter 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 wh :jyx(37vq3 tip:gtia* togt)ich is turning at a constant rate. The boy is near the outer edge, while the t :g t i3ovg73yt:xa)t p*i(qjgirl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constandkmae0b4yp 725 kvu:j t rate. The boy is near the outer edge, while th pydk4u:kae075vmb2 je girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the follow ghr5)72 jg4znc aou2ging is an accurate statemg)r2n5az4 cjghg 2 u7oent?

  Rolling without slipping dep(ac v-itehf65rgp v.0ends on

  Two equal forces are applied to a door. The first force is appliesi z,.z8ldjpm :a92 wmd at the midpoint of the door; the second force is applied at the doorkn zl,mmp2 :8.s9awidz job. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to 5t(net-:yqk g*a,m / iltwu l:+ql ,9tj.horpa door at the doorknob. The first force is applied perpendicular to the door; the second force is applied kto* tln yje/q,9tuw:ip+a-.hl,l:rtmq( g5at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to t(2 xojm,tgk,the door. The first force is twice as large as the second force. The ratio of the tor , tg,kt2xj(moque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to ;zthbmgx m. tv*wc11+ changes in rotatiztmg.xm 1cwb*t1 +;h von?

  Consider two uniform solid spheres where both have tq a0rmo13 (qokhe same diameter, but one has twice the mass of the other. The ratio rqoa1 (om0k3 qof the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have/) *faftfn, th the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the sn,t *ffa/thf) maller sphere is

  Consider two uniform solid spheres wher9qh;iz qw.bd9 e one has twice the mass and twice the diameter of the other. The ratio of the larger moment of ;i q9z w.dqhb9inertia to that of the smaller moment of inertia is

  A uniform solid sphere ha5soj 8w,i bo2vs mass M and radius R. If these are increased to 2M and 3R, what happens to thei2 owjo, bsv85 sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object will6 w5 6i cb)(iqnusss:b

  The moment of inertia ofie2xd73c d1 au a solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to 7a1ud 3i2decxits translational kinetic energy is

  Consider a motorcycle of mup1sv;pjg +u , 4tvnu;ass 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 whev s4u+u jp;;ptu1,gnvels 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 roll tn u-o dt10fc0+dg;apz)q5mje+ to2 ns without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the inn0ttj dn2zoef;mduc 51- 0a+p+g) toqcline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an i3:u ystithi xupe5//.b2u-w qnclined plane starting from rest. The angular velocity of the sphere at the botyiu /3 2 hx:suqwei ut/5.-bpttom of the incline depends on

  "The total angular momentum of a system of particles changes whccmcpe*5sg;q4l6 s 1k ,(tce(t/esbi en a net external force act(smec6 ig;(sc1s ct bq/c e5t lekp,*4s on the system." This statement is

  In what circumstances can the angular velocit,s8)tm x1 s7jbd) uzjry of system of particles change without any change in the syste jm)tz 7u),dsb8 xr1sjm's angular momentum?

  The Earth orbits the Sun in an elliptical orbizc3 vhm 9-p6z3ax.d u3vmrh;pt. Ignore any friction which may be present. What happens over time to the Earth's angular 3 3dvh a -zcm;pv3h.ur9pmxz6momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moj,) r4s5 5enpiubrm y5ves close to the Sun, then which of the following best describes the orbiting speed i54np,jb yesm5r) 5ru of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrp ,qpx jzem*-1w* iwcdvb8d4 2etched arms close to his body. What hq,bpwi8ejc4mv2* w*x1-dp dzappens to his angular momentum about the axis of rotation?

  An ice skater performs ak85 dxdngqff(ffgyq 0h86q;2 pirouette (a fast spin) by pulling in his outstretched arms closxdqqffdq2gh;f(n 5y0gf k6 88e to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his o-t:ogn 2,-v-wqw ry pzc sf)y6utstretched a z-)ynw rtpg2of c,s6-v :wq-yrms close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservaqthx-3js mn5/clb4ec-5r)tqb*td qm q xi;2 0tion of angular momentum.

  What arc length does the Earth tra ;2l )fp,vkf1wimy+mqq atzt5:n) o1 vvel in a three month period in its nearly circular orbit about the Su nf lm;5)1yqa)otvw2pm+i,zt vk qf1:n 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 does the tw*kye m3fber t4 lc:.id1sr7 4sp5(tbip of the second hand sweep thrrbsc lsr4i*4( 7.f:kb 15eyt3 wt medpough in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivale8 zi0gtmc )tiwz,54tlmw n 7n8nt to?

  A bicycle wheel rotates uniforml*)cnquqjf/gv(h pg n9l5i7 fcm )z20ry through 2.0 revolutions in 4.0 s. What is the frequency of the wheel'sv9mn (qj)z2hf 57u g/)q*lfcg0c inp r rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. ae7km gsq;x(a(gd r*1 The period of its rotation r(k7gd;ea (1x gmsq* ais

  A phonograph record rotates at 45 rpm. Through what angle does it 9:bt,q)qy u wmturn in 0.20 s?:ym, qwb t9u)q

  A wheel of diameter 26 cm turns at 1594acdzx h.5n2aw c jfcq;j,g gv;o: ,q00 rpm. How far will a point on the outer rim move i9acqx4jfv.g:nqd2 o5;w;, z,g ja hcc n 2.1 s?

  A bicycle wheel rotates pv2p 3 likvns(zkp((w l8y-)sg.v a5euniformly through 2.0 revolutions in 4.0 s. What is the average angular speed of th-v(kp 5zslli 2vkpy(vsg.nea pw8) 3(e wheel?

  A bicycle wheel rotates uniformly through 2.0p0f oz)h;l dm. revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center o)hmdp;lf . z0of the wheel?

  A cable car at a skii,t dd*t uo9e9 resort carries skiers a distance of 6.8 km. The cable which moves otte d, u99di*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 in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular b.qpquuga.p)ud 0 j/re, (q7b0d 5dmxspeed of 2.0 rad/s. What is the linear speed of a point oaqqgxepdjd70u( bq. uu.5 /,0r bm)dpn the wheel's rim?

  The cutting cord on a gas-p gvj35wut; ouq( 4uez( ;/owbnowered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the at;35q g ;nb( (vjuuoz4ouww/epproximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2(hiygf9 w t5:mpq4o3 n.0 rad/s. What is the centripet:9 ( i3y ong54phqfwmtal acceleration of a point on the wheel's rim?

  What is the centripetal acceop d i05(y,tpvv )dd(sleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cd5dp dvos)iyt, ( v(0pm when the bike is moving 8.00 m/s?

  How many revolutions peg,y1. 5 opm4wnnq n5crr minute (rpm) must a circular, rotating space station (r = 1000 m.npwoncy4n,q g 51 mr5) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curv(5 s2*vtgor8 xvqt7o1d i8ls (2 nxwbxe of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) 18vw ss8*to 27oxxvn5g2ixr( (lbqdt 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 50w112zc-e6e+uz-g6uoqx ,klk8no cp q m with a speed of 20 m/s. 1 zc6c, qk8qx2op+e gu16-ekn-o lwuz The maximum 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, attached t+pcfbqv80hl0l7fw* -(rnfqt o the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that +f 0lv0qh7p l-(q8t b*cwfnfrthe 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 sa,n2nf9 (wbvzw6 crd(lipping 10 m down v9rzf2bna( wn(wc,6da 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 constant angular ac+ k ))x jl6vvouukm94cceleration 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 cons(.fl9y thybe)tq 3 .grtant 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 tire r 1 ze5qswz) rmr0rtz*0otate after starting from rest and accele5z0q r r*0esr)ztz1wmrating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at res*b7eq0uti cam (5 0tzit, and 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 deceletco122dyr i2prates with a constant angular accelerat2c 2rip1doy2t ion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and rpof8w. +il /v *y.jaxovy3mbon :*v8zeaches an angular speed of 6.0 rad/s while turning through 2.0 revolwp:3b8./iox a8of* ymo*vyjzlv v+n.utions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.m ;0q.xbjh1u ,7oykgges+b*l40 m/s to rest over a distance of 115 m. What is the total number of ;beyhlsogk. ,0u1q7jx*m gb+ revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows dowt99x 9ypou t1cz tl.5mn uniformly from 8.40 m/s to rest over a distance oft9l9 9 c5mxtuo.ytp1z 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 ove(8hnqg c 8t*7 - iwrvem5p1zour an r o5-mhw8pg *tzeiqc 81vu7( distance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical labhb*z dj6 )n6udoratory rotates at a rotational speed of 3600 rev/min. When switched 6u6jdbdz*h)n 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 tightej6s(cr j w94ykning to a torque of 90 Nm. If a 30 cm long wresc(r4k 6j9yjwnch is 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 torj;qpanot)bm oz( ,+r.bd. z7y que of 90 Nm. If a 30 cm long wrench is used, what is the magnit( . o+pmjqyrzzdab7.n, ) o;tbude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of c(tys- s9nl 4vinertia $3.00 \; kgm^{2}$ 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 g:ljpu xd-+(or/ mc*bat the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia a(g: mr +ujx /-plbc*odbout the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought theq3wbe1vj dg)*4 mcew3 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. (See Fig. 8-1.) What is the a4jw3 mee3 g)1*cwqdvbngular acceleration of the cylinder?

  A solid cylinder of mass 10ole6,f 3-*,z qx9sva(5+a oerd svr ab 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.ofe6 (eaoq sa z-xa,r,* +5 rv3v9bsdl 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 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is init b.0 3knlyjthz5qss e23nu+)f,ceq)jially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is release +) jbseq yskj2f) th3ennu.q5z0cl,3d? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel tae09* g qpl;rpo be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sg p re*9a;qp0lprocket. 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 slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictioy *rybfx4j fn3n(n x6ad4k(; vnless disk pulley of massxf 6(krn x*nf v;(y3bn4dyja 4 7.07 kg 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 frig/c5 hxc,mx70e:tprg9zb 4ui.q ok9u op5g.z ctionless disk pulley of mass 7.07 kg and rhgzuge.cu 7co po4z:mtp9 /i.,r5k50q9bx gxadius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be usebf3dmuk3n g5- d 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 inertiul.nev94 93+rpe glvrvpd/m0 a 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 szuu .8)nmwj., nemq *m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the botn)mmusj,qz.n 8ewu* .tom of the inclined plane?

  A solid sphere of massr2 urb9i 99oyi 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How hbr9royiu2 99 iigh up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg ot sa hf7ro *-qy+2gk0is released from rest and allowed to roll down an inclined plane. Hoqt*ok+ fyh2ro sg -a70w fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls wi1 +s pklpe6o,lthout slipping down a 35e incline that is 7.0 m long. Assume it startll,e sp6k op+1ed from rest. The moment 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 mome9bel+d udhio 4ixo2sc8k*2 pxp 3im)7f v:(kkntum 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 momentm r3qfs7s2mjd 01wpq 2+(xznm of 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 arhyi*b/ dr v*sr4 qo:,x-ildd*ms extended has a moment of inertiar d/oh,:-*ib*xddlr4* syvqi 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?