Angular displacement is usually expb3)xrn19aw 0q ppa v+9q,x2 nn bbi;gpress in units of

  Angular velocity is expressed ( 0 koqra,7a+bpoq4cba.e,d ain units of

  Angular acceleration is expressed in units.82e,(jcv, ybn qrenw of

  A boy and a girl are riding on a merry-go-round which is turning at ahb0 1 r+fw84cbykxs9t s i1/cb constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the gr 1 skr1/bf0ibstxw9bc +ch48 yeater angular displacement?

  A boy and a girl are riding on a merry-go-dlb 3g 5ux3)o3 yzvc7eround which is turning at a constant rate. The boy is v)3u7byexolcd zg335 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 merh g r 0x6bic:h4ly 8bop4+6bxhry-go-round which is turning at a constant rate. The boy is near the outer edge, and the +xy46h bxl6b0:pc hb grh o4i8girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-gfr- 5 v0 hmwszv mf)7hmc/71-bsu kjw/o-round which is turning at a constant rate. The boy is near the outer edge, w0hvf//m7z5)7c m -hsvw ubmwf 1jr- kshile the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-roun::l78r (b(;ac6dcplu9lr dtreep vt3d which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Whor trdv6raeclcu; (p7b lpd:t ( 9e83l: has the greater tangential acceleration?

  Consider a rigid body twtp3zbev /g8i/:l nh 4n88ytkhat is rotating. Which of the following is an accurate stan n8/w 8 pkhyb4g3:te8i vtl/ztement?

  Rolling without slipping depen 3f5k*he:0ew qx t6wxnds on

  Two equal forces are applied to a door. The first force is applied at the midp n c):z0zho,n;iu y4choint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts; z0cy,unzi :cnh o4)h the greater torque?

  Two equal forces are applied to a door at the doorknob. *a9b*eh6 :onzo3*gn- ky uwfeThe first force is applieg*y3u waf 9ok:-*bho *ee6 nnzd perpendicular 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. The first fo6wbnhgh. 55wc rce is twice as large as w5bwh.6cng 5hthe second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to ch cu l)o-:7 7ktxsk9jvjg-wp4wanges in rotatisoxt p j) k7-4g v7:9l-ujwkwcon?

  Consider two uniformr5r:cr4z bz6w solid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to:4z rbc5rw6zr that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radfs elo)9nt5vfh 8q2;jit . zno/ 86ywjius of the othefy6tj8 o seof9nq/l5 z2;hwin8t j v).r. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one oxq*mm , 5j5xrhas twice the mass and twice the diametj 55qrxx*o m,mer of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has;emvl4t 2 1 otf2 :6kt ohux0ps8x:red mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of ine:lf:6t o h2estuxp x8 1oe02;mrdtvk 4rtia about a central axis?

  If a constant net torque is applied to an object, that object w25ne (cgc*pa12mi; m3; wwomv jsup; dill

  The moment of inertia of a sol52;wda2+q hk7nx fnkb id cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to itsb nw 2fkh5d ax;+k72qn translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 10 kubq0)0 5hrve:c+srd k g and a radius of 30 cm. What is the ratio of the rotational kinetic energy of khs+r0 0):buqdr5 vec the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mas5vsjr740*+- jkhwmw ;qsp-qn tyydzj5pvj /1s M and radius R rolls without slipping down an inclined pljhys/1w5 - ;pydjtsq m0qwjprj+vkvn7z * 4 5-ane 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 slippinj,lbtt.ner , *50ncgfcv8 qb1g down an inclined plane starting from rest. The angular velocity ofrf5vbg8c.nn t0*tcjel, bq, 1 the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net exr8jo/( p f*5hegg xz8 s-rssb*ternal forzse85g g rs*/ b-(*8hxs opfjrce acts on the system." This statement is

  In what circumstances can the angular velocity of system of particles c zk:lv98 bbpk2hange witho :b9zvk8blp2kut any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any fre*9xx:y- k y o4m9pyqbiction which may be present. What xpek 9y:qx o-*b9my4yhappens over time to the Earth's angular momentum about the Sun?

  The Earth moves about knp7qh+ 3umm1i ikn7x6;x6 zn (xutm9 the Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting suu6xzmm;3 k9pxn7t hm7k6n1( ixniq + peed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in h+.x l2y8t++ rr ng.o8ynd t 0p.gpznaxis outstretched arms close to his body. What happens to his angular momentum about the axis of rotpy+g +. o n.+ pat.xld n820rzn8rxgytation?

  An ice skater performs a pirouette (a fast spin) b 72gmuq02-j 9odcja y,xdq g fd1ml*j.y pulling in his outstretched arms close to his body. What happens to his rotational kinetic ene,c q*dgd2xd j712 y9qu-jom mlgj.fa0rgy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pull6pefps)w 8k -+ ohhn:kip/ uy9ing in his outstretched arms close to his body. What hasfh9 ouye6h8kkppw i/+:)p-nppens to his moment of inertia about the axis of rotation?

State the law of conservatc a z99 zv/jg,-qqar7+jlcw7yion of angular momentum.

  What arc length does th9ek e8 ;dyt)frb;(mx ,skjob/ e Earth travel in a three month period in its nearly circular orj;,kkem9; sfyt) /xrb( b8d eobit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length ofgu:kk g/cp 6g. x64rsc 0.30 m. What distance does the tip of the second hu66cc kxggpsr g: /.k4and sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 r1l vlqpc4 ,bonyo341a 6;n rzbevolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions inpfnl;vbssb/ -78 mhg0 4.0 s. What is the frequency of thb870-nbvl/f ghs smp ;e wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of (ofr+4hgy len8r4 nb2 0.40 kHz. The period of its o48n l 2h nreyfgrb4+(rotation is

  A phonograph record rotates at 45 rpm. Through what angle jb1*vkhq*; st does it turn in 0.20 q1tj;k* * bvshs?

  A wheel of diameter 26 cm tur.i /3xh bav5syns at 1500 rpm. How far will a point on the outer rim move in 2ash. iy35/vbx .1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in+h xb p abyu)35,nq,lu 4.0 s. What is the b b+ 3)ynx5hua,q lup,average angular speed of the wheel?

  A bicycle wheel rotates uniformly thro7*5nitr9cier+fy s:y ugh 2.0 revolutions in 4.0 s. What is the linear inr 9 s etr*5:yfc+iy7speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski rlc6dqj:tcf0ykye -/pt ;n q0 ;esort 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 the pulley rotate for theq y:n -ct6k0d/ t ;f;yp0jqcle 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 r h0oge,e/ e2vcad/s. What is the linear spv/oehe0 ,2g eceed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the ;en ti9e l.8tal 7,lgtmotor rotates at the rate of 20 rev/s, what is the approximate linear sp,get87nla9.ille tt; eed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angula*d lw(f m.4euar speed of 2.0 rad/s. .(*mfad eluw4What is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimetm o:uyb b) s3;6pmv7lcer of a bicycle wheel of diameter 70.0 cm)buyvpb6clo; :7 mm3 s when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) m(ry4elej75qf ust a circular, rotating space station (r = 1000 m) f5 y4erjl qe7(rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a 8o+r;kim7t -fn f+vdb flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripbn8;kd +ivm fto+7r- fetal 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 il2h (h3 ;jzn6-eltw b20 m/s. The maximum centripetal force (provided bel2jh(3-6lbt hnzw i; y static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the en2 e-vblwba:x9 8niic/d of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the stringx: n2 iive-bbl8a wc9/ 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 sl;4o .xkp.6i4abl*d8n j ltgxn ipping 10 m down a lane at 4. 68 axl .4olnk4pj;x*ign. dbt3 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 witho/x7 p6 p+bxup a 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 ang emcu2 q*fixo2 :2nq0pt-5:qfzgepk5 ular 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 ra9tkplv::r fj* dius automobile tire rotate after starting from rest and accelerating at a consta9 pr:jtf l:*kvnt angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, 0y8u ajjmv,8tth(xhk2;uql1z ;qc /eand has an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating ay cvzczh2k+ q ;rx0bco39 ;ac)+fqe c:t 20 rad/s decelerates with a constant angular acceleration of r0;+:q y;3ck z2cf qac v)cxh+cbeoz9$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular scggp vh 0zhps6lg3jjj,2 am :5c, i)y5peed of 6.0 rad/s while turning through 2.0 revolutions. What is the averijhl2cjgv, ,cp6ja y sg30 gmhz)p:55age angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down unifoprqr3ff6 jballn6 t 4li .7;(vuoy27d rmly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheelryiu6(6;lao72qpl 3rf7 d ntj4b. l fv rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest oveh4-s5lj8gzn/d 9 wdaor a distance of 115 m. What is the angular acceleration?89al/-4swn5hd jzgo d

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s x gori.m5 gm03to rest over a distance of 1xm.ri3go0 5mg15 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 r akk3m-q:qcwkq.4 hx 5ev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming cw3mq-: kxhk.5qqa 4k 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 wob b.v5 /a-eg,r;: n 4m.wduvw8dyqlaheel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required whee8 mu:bq v;/vgo.l -wdnar 5a,db4 .wyn the force is perpendicular to the wrench?

  The bolts on a car wheel reqx+e8ig v 6+kcceknvxl hs jvzt;z m,*w0:)m03uire tightening to a torque of 90 Nm. If a 30 cm long wrench is utg+x0nv):ehms 3 ; lv,jwk*z c0ivxc8k6ez+ msed, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia 93wpb;scu(xj 6uh adni0z4 9r$3.00 \; kgm^{2}$ 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 at the:h b v.ew( u*lco;(zlg origin, mass 2m is at x = a, and, mass 3m isu (.(:cbw gv oe*h;lzl at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionlessgn lou t-tt3 n;09t4ry 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 =tu 4 r;lgoy-0ttnn3t9 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 pivywpiiq qb 0/0a jlaw*,(*w,vx3 h,qiniik+y3 oted 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. A second rope wrapped around another section of radius R2 =al i0, /y*h3wwp3w0q,i n i(qix+qb ,aji yk*v 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,c z;db,y yy2f held in the horizontal position, and then released as the free end is allowed to ,,ydy2;yzcfb 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 kb)mf9uu u-xmh;d (4p(l :fb hradius 30 cm and mass 1.5 kg. Neglect tfhu4u;b(mbp -x:hf 9 )m(ukl dhe 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 slipping?

  A 1.53-kg mass hangs on a rope wrapped around a fri 1fn * ft+mivu;t:hwxt3t7hu0ctionless disk pulley of mass 7.07 kg atw *mitu+70 ;utn h13vx:fft hnd 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 diskl0dbj1 s4 *ffk pulley of mass 7.07 kg and radius 66.0 s*0l f1kd jbf4cm. What is the acceleration of the mass?

  A rotating flywheel can be ekok;0)xn5ah )vp lt0 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 inerlku6 +6 .w yh os8wden.e(pm 1wgnt5(t.o a5xxtia 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 pbfh- 2v79uj ws*sc;feacj0 :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 bottom of the inclined plane s;c0v9spch*-ejwf7 jfbu2a:?

  A solid sphere of mass 1.0 kg and radius 0.0+c;fjtz( 6qs2zx-hy *kd xo) z10 m rolls with a speed of 10 m/s. How high up an inclin ;xq -cx2 f zyt)zh*+(jod6skzed plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is releasm h 6kqvvcnf; +y)-re:ed from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distac; fyh+- q): nvvrm6eknce of 3.0 m?

A solid sphere of mass 1.5 kg and radiup e95hq3yp)t4yom h6 er*(t ljs 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 5tero hpt*6 qhe4y3p9yj(l)msphere 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 momentumwk (pod2d4xm25lz o; o 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 of7ttr (sg+gbm 0q n:4ml 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/sl),c;b *oev cs with arms extended has a moment of inertia oo), *scevcbl;f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?