Angular displacement is usually express in units iv/wp:8dnghsa or:r-)np3 t7xi(y.mr2 hn m .of

  Angular velocity is expressed dpjre1*-2 a4y0 cheicin units of

  Angular acceleration is expressed in unitsqg4 n d a:*)8 2xkk4lzxat)tgp of

  A boy and a girl are riding on a merry-go-round which is turnl.qug bc)9ka82ek8 aiing at a constant rate. The boy is near the outer edge,ul88i q eac 9ab.2)kgk 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-rou +*soxd8 gsp7tnd which is turning at a constant rate. The boy is nd 8s 7xop*+tgsear 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 merry-go-round which+2,bk,4ev poz q ,jota is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear speed?qo24+oek,, jtva pbz ,

  A boy and a girl are riding a merry 6:kb hfnt7m1d-go-round which is turning at a constant rate. The boy is near the outer edge, whi: bhm6tn 17kdfle the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry5o iy5 (7b-ot eq1a; s jvlq*1eopo*tx-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has theyebvsixto ;1o1 7p(* 5* loeaq-qtj 5o greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is 1)geicbiy9hjq6kh7 /bu( 1o qan accurate statementko)1jqgh bi(6 q/1chie7y ub9?

  Rolling without slip2htx23e-l skxping depends on

  Two equal forces are 9 gzq,v9vr( yxapplied to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force y 9x9 rg,vz(vqexerts the greater torque?

  Two equal forces are applied tbdl+lv,)vmqn 35x nv **z o 359avhbwqo a door at the doorknob. The first force is applied pex* v qwv)+zdq*3lnnvm 3bb55hvl o 9,arpendicular to the door; 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, perpendicular to the door. zdye0vwceqd6sx, y 0oqdi7f0z8o *39The first force is twice as laiozwe0dc 03 0* ,dsyd 8zfv7o9xye qq6rge as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity d l(g2oph*s t*used to measure an object's resistance to changes in rotatio t h*pdg*sl(o2n?

  Consider two uniform solid spheres where both have the same diamet n c9rr4k2wt5xm5 bh)oer, but one has twice the mass of the other. Tx5knw924mt b5h rcor)he ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the je4u si-q( *ebradius of the other. The ratb4ue* sej(- qiio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres wherei,h7x 7peycb.;g xt1s one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inerti1 px 7h7gtcx.s ,biy;ea is

  A uniform solid spheu ut2s2:b5nlx.nr3w fre has mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertiaru25lsun 2:wf.bx nt3 about a central axis?

  If a constant net torque is applied to tta2 (,d,qha zan object, that object will

  The moment of inertia of a solid cylinder x.ou- xed ya:)*g,k knxs -qo/l:i-tqabout its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kin n/ts)q kdq:kxg oxix.*,-ue ly:--oa etic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 10 kg q 3pb6 j-gy;o 7zb4j7tb oqzv4and pj73z yq7q6bo;4 -oj zbbtgv4a 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 disks.

  Suppose a solid sphere of mass M and radius tze-) zdapkm0uxv: (nx5zl 6:,8cqhb R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere a (dx8nqtak)vh- xeup6m:5 z ,zcb0:lzt the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping ;a nz*h xlm-22so.(sq0sriqjh *xnz2down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline dependsqjhxx*0ln*a2;iz ( mr -nh. 2sso2z qs on

  "The total angular momentum of a system of particles changes when a net external+2 ai;v ,nqiqs force acts on the system." This state nis vqa+2,iq;ment is

  In what circumstances can the a9 fw* ng3:zs3r9cghnvnq o zgr*d0 z+3ngular velocity of system of particles change without any change in the system's angz3n9qsr+093zvcnnod*g :*fw hz 3rggular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which may ;2o0o9vfi aefbe present. What ha f;ife20a 9vooppens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical or*oh;wv(oq 9 aqbit. As the Earth moves close to* 9hwoqoqav ;( the Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrexpb4mr tjp 36+ ;a25p7)m,rorgwy sqrtched arms close to his body. What happens to his angular momentum about the axis of rotation ;4,)m rp6j q5sawxgptpry2+o r73bmr?

  An ice skater performs a pirouette (a fast spin) by pulling 8xupqrm u 2q96in his outstretched arms q 82pmqruu9x6 close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouettb q g .kn*v6hl/,bk8mye (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about t lmh*b6/8,qn yvk.kgb he axis of rotation?

State the law of conservation of angular mojv)vr v1qxx.( mentum.

  What arc length does the Earth travel in a three motp 2j wyzqy6+8nth period in its nearly circular orbit about the Sun with a r z qy+wjt8yp26adius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has psxb zytua;p2 p6s+86a length of 0.30 m. What distance does the tip of the second hand sweep throug 6u+;xspa s t82ybzpp6h in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalentjx7rzmt xkf// m1px+6 fyy4/y to?

  A bicycle wheel rotates uniformly through 2.0 revoluf/,te4n1; ok7 wxyeictions in 4.0 s. What is the frequency of the wheel's rotationfwce;7kty4n,x /e o1i?

  A pulsar (a rotating neutron star) emits pulses at a frequency of i jbvx:yv iu99)x8rrmfp84, p 0.40 kHz. The p48:yjpf8ri pxbuiv9,m 9 vr x)eriod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does ite* w eo .yhew)0o.2-w0slt ntx turn in 0.20 s?wy* e swon.o-l00).x2t heetw

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a8ii vg0kbaqnej)q3) 5f 4ja0k ml0cu v(sqw38 point on the outer rim move in 2.18qi(3 aql jk)wbj03s) qvnfmevu05a 48kigc0 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is the( ,xz4 f.txn2tm,abxvnhg / c3 averag xx4n , hxzt.g2b3c(vf na,mt/e angular speed of the wheel?

  A bicycle wheel rotates uniforbwgm(kff kp;w9m y65:j d2ri7mly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m frkmkg 6p: w;yr5d jf(bi 97fw2mom the center of the wheel?

  A cable car at a ski resoral /4sakqdh.d vl2qi9r6wu44 w z3;oot carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.4akzlw4 wh au2odv6/;qdo34.9lirs q 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 spg0r(cw yw cjah4xcb(i-t5. fl0t() cl eed of 2.0 rad/s. What is the linear speed o4hcb xcfgt r w(ly.(c lwi(c)a5 0-tj0f a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter rp4rd w7hysg5+* e5bbis 0.16 m in length. If the motor rotates at the rate of 20 rev/s, wha ypd 55w+ebsh47bgr* rt 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 of 2.0 rad/sb/gqm1.p 6c -bm) 2rvgo2q pt7bs9yv (g.gs iz. What is the centripetal acceleration of a point o.m sboz/ p 1qbgtgg -2v6qri) y2(.7mbs9vpcgn the wheel's rim?

  What is the centripetal accelm b-a.,if. ldrg s.ja;eration of a point on the perimeter of a bicycle wheel of diamfr.i ag.;m -a.d ljsb,eter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minutev x- v9q xkh 5jcsg.z/jnm1r.jv 8h/*n (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravity o8 jn/gs9c z.*vvnxm 1 q /j-r5jxv.hhkf $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m v8(6 q- ey.zbcsqei3t with a speed of 20 m/s. The maximum centcyb (6 et.qzsev -83qiripetal 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 1i fl1cqv8bi4 r0,wbm50 m with a speed of 20 m/s. The maximum centripetal force (pb b 4qc,08lii1w1vrm frovided 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 0.750-m string, is whirled around in /x+zn uf5,ow ga smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mass have if the stringogzn5wu/+ x f, is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without s(4- wdy3s+1n h0 nuixx5ev6 nijl.meo lipping 10 m down a lane at 4.3 mmnn(lix jho +y03nw vd546usie 1.e- x/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 constantte3;lpf* 85ceo (z yox 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 jxwo 6drb;lw; b8(thlzu,:z6constant 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 t5,0is3 v eytumire rotate after starting from rest and accelerating at a constant angular accelerv3ys5ti0 m, euation of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular a;3vn uvge7 bgdfq. o6d:po w 69j3f1xwcceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelksa3u+ ;/m 3mf:eotrp erates with a constant angular acceleration ofa;smu k pe3+3/ m:ortf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.09v shllw, o0d) rad/s while turning through 2.0 revolutions. What is the average angu,9ld vo )hl0wslar acceleration of the wheel?

  A wheel of diameter of:2)jwboemb sgi +f3d) 68.0 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 wheel rotates in coming to eid))bbjg2s o:w3mf+rest?

  A wheel of diameter of 68.0 cm slowx 1n *zlkq,i7vs down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular acce, 71lvzn kiqx*leration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 h+h 5* yppl(j xc+a; -jjrik1cm/s to rest over a distance of 115 m. How long does it h5 1 l(yajc;-kx++hpirp*c jjtake for the wheel to come to the stop?

  A centrifuge in a meibh ,pw;3;oay dical laboratory rotates at a rotational speed of 3600 rev/min. When switchap,w bi3; oy;hed 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 tig5o2,4*x3hj hbb ik isghtening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required w5* gx2s o34bki,h ijhbhen the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a t vdz3en**vco0 xb 9cyylpq0 43orque of 90 Nm. If a 30 cm longpd4b9 c0o vv *l qcn0yex3y3*z wrench is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertij- yn wmx8 (ktv;m*fe(a $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mz7va5j+u z1lpao,4vzk:n :lv bt/rej+ e)3 mmass m is at the origin, mass 2m is at x = a, anj, 4z+ev):vkzr 37bjpumo/z tnla5 mav:+e l1d, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thoughj6 vqbss-:tk48 9y rnrt 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 8qsy:r-vsj n t4rb9k6d 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 kgb.)bh- r h2co (ybhqy y1d2a+f is pivoted about a frictionless axis thought the center O. A rope wrapped ard+-.(hh2 f)b2oyq ha1 bcryb yound 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 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially held in the hr5cro 4td6.bd3+m(liyv7t* ,p cyzrd orizontal position, and then released as the free end is allowed to fall. rt(65yod4 m7 zd*l+vrp 3cr,tyic.bd 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 mass 1.5 kg. Neglect :ad6c8)tc b+c i8t-o/ bnvl l q(/kskqthe m/ s6 -b8 tki:8qlvn ca(lqob+c )/tdckass 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 slipping?

  A 1.53-kg mass hangs on a rope wrapped arobcs 2t+cbf( a(q4 .nmbb*da3rn3y6 qmkbc:;pund a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelsn3n+mqa(k*:cfyqp bbc6rb(d3a b4b 2;c m t.eration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a3 a9ch,.ly7o-+jnrlx2p ra /qsgm4 jv frictionless disk pulley of mass 7.07 kg and r947vh -jr a32+xma.lj,lg rpcqyo s/nadius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be useh.hgw 19oy*ood ( i1w6ggfzv 9k4sdu3d 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 inertij, /cmk7 .v,hwri1oxs7 thhy .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 m starts from rest and w43crbapai np)31)ck1y)n f a rolls without slipping down a 1.0-m high inclined plane. What is the speed of the spa) ncw)1yaf ab3p3irckn)1 p4here 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 m-etn7v cujb: kbyh,ki nq8(.3 bt*fp9/s. How high up an inclined plane can it climb before coming toj9.: tyb k(-*ucbnfe8pk7vh3n,tqi b rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is releasedf6+h/5;tkeyb9 uyap h from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a verticfkp6 5be;yt hyu9+/ahal distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slippizmkj,9h;z1 h.8hji wp ng down a 35e incline that is 7.0 m long. Assume it started from rest. Thjp , wzhih8 z9k;.m1jhe 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 mo/c qktwp2bd(c; tni7. uq44 mymentum 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 momentk /ysv3c*wgz55x qu9 f 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 r ndi hz1;b 3ejn 545nc4auqi.dad/s with arms extended has a moment of inertie i53d.;dj4iah4 zu51n cbnqna 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?