Angular displacement is usually express in unitc4q-b xx 3ms/ lunc8zk.h*58 hub mp2us of

  Angular velocity is expressed in units hyuj j st)uk.;4g(o d.d d)l2yof

  Angular acceleration is expressed v 6db;tezz(z4b,/:q0 phioees :8 syg in units of

  A boy and a girl are riding on a merry-go-round 2mkiyn-isot(xue t9 . s0nq96etnp45which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greate.qkt06s 9np mu25 -eeo( nitt ix49synr angular displacement?

  A boy and a girl are riding on a m ow- hvy:ma(0berry-go-round which is turning at a constant rate. The boy is near the outer edge, and the gir :(my hv0abow-l is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which7rk6 cd2 ec/xju0pfu, wrv9 rj.q g*2h is turning at a constant rdu.c*0wxqh7 p/2 2r ,ckjevgu jf69rrate. The boy is near 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 wh 9a yuqxgid*5:ich is turning at a constant rate. The boy : ui* x9q5dgayis near the 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 which is turning ay)85f)y+mms+e/su zh/ fr v1kzg gar.t a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acvsfz f1gzka)rgmy /)5m yhr+es +.u8/celeration?

  Consider a rigid body that is rotating. Which of the following is an accub33 jz)kcpa(9b hrk q5rate stzp)abh 9 35k (b3jcrkqatement?

  Rolling without slipping depe(uj )a7aji l2mnds on

  Two equal forces are applied to a door. The first fe9k kckb c )k;0+si; fiovs,6dorce is applied at the midpoint of the door; the second fd,b9)i ve+kscs;ok 60i k;k fcorce is applied at 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 doorknobco 6cv,ii;+ ycpsz45t. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the gre,pc ;vis 5oci+4yc z6tater torque?

  Two forces are applied to a doorknob, perpendicular to the door.jgpe)w,svqu-o,mgt. m 4 ,y 8d;xno8r The first force is twice as large as the second force. The ratio of the torque of the first to the torqu vg4o s-odjpw8rq,te,g,.mnx8 );um ye of the second is

  What is the quantity used to measur2 x6a0t)nzidyjzqu2.m4 dj + . ooj9wxe an object's resistance to changes in rotation22 o qdn 6ty+z4j9xzxio .jw).md a0ju?

  Consider two uniform solid spheres where both have the5w,jj y 39fn j8lu*kih same diameter, but one has twice the mass of the other. The ratio of the larger mome j59 i,ujly3fwhnj* k8nt of inertia to that of the smaller moment of inertia is

  Two uniform solid spherph4 u1(ir av:ees have the same mass, but one has twice the radius of the other. The ratera1 4: hui(pvio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid sphe duv-u/m)k 9*e:mrww lres where one has twice the mass and twice the diameter of thwmrd-uk*luwm: /e v9) e 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 8/ /z*sl0mnf*myf;0bayrzuzvbl3-z and radius R. If these are increased to 2M and 3R, what happens to the sph*zbffb y alz3sl 0y/z0 r*z8nm/;uvm-ere's moment of inertia about a central axis?

  If a constant net torque is applied to anx38-tvao l ,jg object, that object will

  The moment of inertia of a solifbdciow:szs nw/. w : 68beh,7d cylinder about its axis is given by 0.5 MR2. If thifsb :76 : owhww8.,ce/z bnsdis 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 wq m3 )osv ;b:bxar 4-*qi.brhphich 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 4mr.ih3)xq q o;v ap :bbs-rb*translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M arf4 w;pgvzcftv9p-(q 4+2kbwnd radius R rolls without slipping down an inclined plane starting from rest. The linear velocitpkgft(4vpwqw zv4b2f-;+ r c9 y of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass Makr3o3m/ n 7) glnfop. and radius R rolls without slipping down an inclined plane starting from rest. The ang ookfm 3).ln3/ rangp7ular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of k7:. h7niwswxwj3dzc 96n xv9particles changes when a net external force acts on the system." This statement is7nvwh xcz 9j7 3 k:wwdn.6x9is

  In what circumstances can the angular velocitysj a6o5 8/9mx 9vqnt *z5krwpx of system of particles change without any change in the syswrampt9n 8x9*v65soqk5 j z x/tem's angular momentum?

  The Earth orbits the Sun in an ellipticadi+ n t0mhb sx.b hz+/+j2jfz6;)tpccl orbit. Ignore any friction which may be pr)j hmt/+pzt0csh; xc+.bf zni b6+j2desent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in g cwlkd ,z30x-an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbitin -30kg cxz,wdlg speed of the Earth about the Sun?

  An ice skater performs a pingx1.3 fde(nd rouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis.dx( n fdegn31 of rotation?

  An ice skater performscpn na-(vpy l66mo,:c a pirouette (a fast spin) by pulling in his outstretched arms close to his bodynv6 aoc :mny,p6lpc- (. 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 ox7vs,tubl 3b/u9wl6dutstretched arms close to his body. What happens to histwvxd6b 9,u slul73b/ moment of inertia about the axis of rotation?

State the law of conservation of angr(j2ms9 kfxey/p ) upx1/gz+xular momentum.

  What arc length does tmh-e e:6b0kc z;s7s pohe Earth travel in a three month period in its nearly circular orbit about the Sun with a radiusspso :ec7 m-ehzb;06k of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a leng+tcu 5)q 2ag4c )yekzxth of 0.30 m. What distance does the tip of the second hand sweep through in2cueq)z)tkyx c4 a+5g 3 minutes and 45 seconds?

  How many rad/s is 25 revoluti8ebqxv6 .,-+kmjvq act0w;,d c cq) kuons per minute equivalent to?

  A bicycle wheel rotates uniformly tsji6dr3l 08vb ni:7achrough 2.0 revolutions in 4.0 s. What is the frequency of the 6v07ab:rid lijs83 n cwheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz.bq+(o n/q ,lyt The period of its rotation i oq/qny,t+(l bs

  A phonograph record rotates at 45 rpm. Through what am7cm ;4m*il 75tgsm z-.fyorrngle does it turn in 0.20 t-gfsrr7. cz*lm7m4 mmo;5 iys?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point zk-w1f kuu *a;on the outer rim move in 2.1 sw -;u 1ukz*akf?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.;a6ejsj+u o d4 ge3ss* What is the average angular speed of the wsd*esge 63 sa 4ujjo+;heel?

  A bicycle wheel rotates uniforml:h u2whqk pe0 ,uabyu3bgk ob)4. 6t;fy through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from ty okb30wuu pku ;hhg):t.6bea b2,f q4he center of the wheel?

  A cable car at a ski resor+ojg)*m4 ff uvwhvi.5t carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must*m 5vow4 +hvj.u)fifg 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 r2q 786xxtwmi sad/s. What is th8w t sm62xi7qxe linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter bd5)j6 ctk0rm is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of ttd ck6j rm50b)he cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 h o;c7j*0 movz* x,fbpw s(u8rrad/s. What is the centripetal acceleration of a puj0w8rsbf ;*( ov hcxz ,p*7mooint on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicyc 2o5wc ley:z6(y(ry*ndiar-mle wheel of diameter 70.06y*oyy a ez ((- 2lridwrmc5n: cm when the bike is moving 8.00 m/s?

  How many revolutions 7ajkfpl;2j1qc 8a o9z per minute (rpm) must a circular, rotating space station (r = 1000 m) pj;z7k2cl 9 qa1ofaj 8rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a fnrja j,2- ptn i9.po45kzlx0 g/kn (djlat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) is .(jn2nlrd ,tx59g4/ip-k j kzaj0nop$1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curvoo8yn4xe4x/ e ;*cq lme of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by xl4*oyeonxcm8; e4q/ 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 uxn8q i 3(tpkuzwi5 fy.-c;+q0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what mak ;q(fi.c3u wp -z8qtuiy+5xnximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius6 otsd: 9fxf)v(ijo0w 9.0 cm rolls without slipping 10 m down a l0djf(9 )ft6 s ovixo:wane 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 accelerai-ey (/rlw 02 t,schrgtion 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 c1u* hd5 yrzmeo0 (qck5onstant 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 tirey-lkt l.. miw 5 rwhess,.7pd7 rotate after starting from rest and acceleratl.5lw-7.7id wm kssph, rt.yeing at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular afa(5m vh o4r.d s*fzz.cceleration 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 constant angula 0fz z*q13 pge pbn-nd*5jtvh(r acceleratione50dqz-bf v1j * ph*3p(g tnzn 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 5bi 6h0myop-fdzj.n fzbg 4ddz5c)82speed of 6.0 rad/s while turning through 2.0 rdj85 nofdpbzg6 -chf 5y bm.z4d i02)zevolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slocoe.gbk 1py lc+3glfd 1x;4-1ts ; ivxws down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in comin 1yocd1.xc; b1v43pf-lxl kie;t g+g sg to rest?

  A wheel of diameter of 68.0 cm slow2 vq;6v xbq0ezs down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular accelq20v b6qvz;x eeration?

  A wheel of diameter of 68.0 cm ps*/8kjk l.w cmx0agy,yla .4slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How longa/0g k..4 l,apxwjs yyc8*mkl does it take for the wheel to come to the stop?

  A centrifuge in a mediff.;yn tq n0k4 mxt9-vcal laboratory rotates at a rotational speed of 3600 rev/min. When switched onkn49mqt ;0 xt -v.fyfff, 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 requiree59*lewd3 mi6e.o ec w tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the foele e3wm dc.iw 5*o9e6rce is perpendicular to the wrench?

  The bolts on a car wheel requihy73fvji *8r ure tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the forhj y3f 87uri*vce applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia 06ri:2l m)mbtvk2skf jv1na1 $3.00 \; kgm^{2}$ 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 )+;m6ib,f pnd ta6tl dis at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment;li6+f) tmnt ad,6db p of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis tabr2u ::)fdiu hought the center O. A rope wrapped around the out:b2u a)ifdu:r er 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 angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionlexz .i fy7wd,i6+ lqo9kss 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 i.,+ziflw xd9o6q 7yk 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 t)2jlgw /vvno 8; w/vlhinged at one 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 acceleration as28;go ) /nvvwl w/vltj 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 mai+pt6qd 5i d8dss 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of rad85 +dd ti6idpqius 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 frictionless disk pulley ofx7a1eqh+ h1g,ye( hxh mass 7.07 kg and radius 66.0 cm. What is the angular acceleratio(eh +7axqhhhx1yg, e1n of the pulley?

  A 1.53-kg mass hangs on a rof9d 3 u,7bvm8;mdt mzj7o5jrppe wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Whmdrjjut,o 9z;f7 8m35p dv b7mat is the acceleration of the mass?

  A rotating flywheel can be used to store energy. in c1grh88bn v:,uhu5 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 h x8l+x245lao u0ic1ozyp u;j inertia 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 m starts from rest and rollscka.mm.xrz-9ruyf h vi5;v 2( witho.m(2.ryfak-h9cux vi z v5; rmut slipping down a 1.0-m high inclined 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 radius 0.010 m rolls with adgiqm 7(hvjk :(wfq,2 speed of 10 m/s. How high up an inclined plane canm,(2:hwi(qdvg 7fj kq it climb before coming to rest?

  A hoop of radius 0.50 m a(gyp;jvcc3iuv5;, qb56b2 vxh .dzzx nd a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 mgz2icxu 55; (dx ;,byvzvp63c.jqhb v?

A solid sphere of mass 1.5 kg and radius 15 cm rolop7 ;ktnq99tj ls without slipping down a 35e incline tqj99 7;tpnk tohat is 7.0 m long. Assume it started 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 momentu pu,2ae)ql;kqm 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 of t(o7j s h6l(b1bivkg z1ghx07$5.0 \; kgm^{2}$ 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 extendtf1g d;oq.anvyz g.t *x(1ae,ed has a moment of inertia o d1aaq*t(zn;x vg..t,o yge f1f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?