Angular displacement is usuz.sejas*jimm9i a l+ r (jf5*fl9vv-+ally express in units of

  Angular velocity is expreszj1okm ;6 njlmm(yx7 u 9ey13ased in units of

  Angular acceleration rze ffe4+nl t4/s,ze+5ggz p +is expressed in units of

  A boy and a girl are riding on a merry-go-roj( uws9r ww- 5+3vnvpeund which 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 angular disv(n9wvj3w+-we r s p5uplacement?

  A boy and a girl are riding on a merry-go-round which is turning at a consth5+oai x*;;t 8y2 h cl98 wg40)tjlejnocgsh bant rate. The boy is near the outer edge, and the girl is closer to thjo g5tcct 24; len8h*hw8yxaglo+ sib)9j0; he center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-gkg9d/1bzkkujp112txm u ) e) zo-round which is turning at a constant r)2gu1deumkt9/)k1 k xjbz pz1 ate. 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 ridinivup6-au4 5xqt57v.ts n6 eymg a merry-go-round which is turning at a constant rate. The boy is nearm nqet vu v4p766t s.ux5i-ya5 the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are ridingjork)yi .f y.wxc4) we8/mb)w a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center.r kwfww cx o.myb )j.yi)48)e/ Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. nx ia5abb :-9 4z()xtu e.wowsWhich of the following is an accurate statemenwb5 z.):9s4auoxae x-i n(twb t?

  Rolling without slipl /qk5 ;0uo7yy(b3zjfrx7 ftsping depends on

  Two equal forces are at 3hw hey:,k1ypplied 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 perpendiculahyk, 1hw3 :eytr to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknobxf4 eo/*)nq jm,e r6bw. The first force is applied perpendiculxq,4m/nef6)jre w*b oar 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 9wbafa(jfmze)/ es.) 0 j9ltpto 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 second isebj fj9tlfapa)sw(e/0z.m 9)

  What is the quantity umzun vqzk*p-vpwh8 *bi r5(y))z-zo /sed to measure an object's resistance to changes in rotatio5-wp*))oz nk(hr/ 8zvpby quzv *imz -n?

  Consider two uniform solid s3,.zz+f lfg-wkg-q ;gsh (t mjfaeo: :pheres where both have the same diameter, but one has qg.ltae3h ;f,sz: g-gkzj mfwo:-f (+twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have d9l;682j fh hu t;kgacthe same mass, but one has twice the radius of the other. The rati gla;dc jkt28hf6 ;9huo of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform soli k/r 2(lmnq:kh5hzxz+6tr r:ed spheres where one has twice the mass and twice the diameter of the other. e( tm2+r5k rzq6 n/zkxlh :rh:The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere irmxw u931w+g pre .ekhl+(l4has mass M and radius R. If these are increased to 2M and 3R, what happens to the spi3erh4lk9p.mw + wue1 r+xl(g here's moment of inertia about a central axis?

  If a constant net torque is applied rl/q3 ,fn5nmtto an object, that object will

  The moment of inertia of a solid cylinder gp5z;* at0:cslu,d p+ 1nucm zki8wi*about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ;8iz*1*glps 0k cudnpu5zm:aw it c,+ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has du5 w / qft*kw7fz0nt+a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the u+zkqn70tfd tf* / ww5wheels 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 rol91z b5dgn6sh)spu, ismeunl2ho o 387 ls without slipping down an inclined plane starting from rest. The linear velocity of the spn9 s )u 7i do,b3guzmle12o5p sh86hnshere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an apj 41ummhxa:(akke )u ()p7finclined plane starting from rest. The angular velocity of the sphere at thexe7 hk:fja(4pumap1 k ))mau( bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net externacs-(kii.j5smd;eo i 0l force acts on the system." 5se0ji s d;(k m.c-iio This statement is

  In what circumstances can the angular velocity of system of p iv((gjxt5 m 3z6k*dyaarticles change without any change in the system's angg(z x5ik* vdymj(6 3atular momentum?

  The Earth orbits the Sun;gfibh +*w) dl in an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about thi; h +*bldfw)ge Sun?

  The Earth moves about the Sun in an elliptical orbit. As they in9zqea+9w. Earth moves close to the Sun, then which of the following best describes zq y99we+ina.the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchesrziy9jun2.uw 5 :i v:d arms close to his body. What happens to his s2r9 5.j uz:in:ivy wuangular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) byk). d vzl q r 3wwq zsiy:oz269ew;0r1mgc98dt pulling in his outstretched arms close to his body. m:.e; tgyd r6 1 il2 cd z9930zowqkzv)sw8rwq 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 outstr-z82snsnw/ x 3t.6p14i svzde fxfo:c etched arms clos/ 2z cof6 f:zi-1wnst xex84sdn3s.v pe to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservationf-qhotac :b80; i b)ll of angular momentum.

  What arc length does the Earth travel in a thr (k0efnpal8x8ee month period in its nearly circular orbit about t0pexf88k(l nahe 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 dis-9z; derwd-6j ajdl j4tance does the tip of the second hand sweep through in 3 minutes and 45 w4ddje; 9djjr--6a zlseconds?

  How many rad/s is 25 revolutions per mi9+wu ,lms0jm )8v qnzfnute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whatvrv6qxl7 9agf4 5(rrd is the frequency of the whvf6g rq4rdx r57 (lv9aeel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.4 c0 d-z0zom xbetd;**nm)k5o y0 kHz. The period of its rotatmzt o0*d z0)k xcdnoy5b;- *emion is

  A phonograph record rotates aoryngwluuqn9u*2gm-ro t,z q+rd l0 ,( lj.2-t 45 rpm. Through what angle does it turn in 0.20 s?gojl dnqyo,. ,uw0 rn2-rl*2g qm-+ uzl9 rut(

  A wheel of diameter 26 cm turns at 1500 rpm. Hoyhvq0q,b : xqro*1s i-gm*z, .wlmox (w far will a point on the outer rim move in 2xg:hqrvlx ,mso q1wi* m q b*0y(,o.z-.1 s?

  A bicycle wheel rotates unifow 8f3s/w2llq qrmly through 2.0 revolutions in 4.0 s. What is the average angular speed of twqlwf2s/ 8q3l he wheel?

  A bicycle wheel rotates uniformly through 2.y; td du.hynlp(- *:rh0m( 3 4hre fgw+p)nyah0 revolutions in 4.0 s. What is the linea ;0 u4angdh3( wry:ymyn-ehf )pdp. t+lr(*hh r speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 k8,zacl(kh;4 ih fdin;m. The cable whichn;dla;zki84c (i hhf, moves 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 rotat/52 ptl1manip ing with a constant angular speed of 2.0 rad/s. What is thepna pt/i2ml1 5 linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter u , 2 ;c6kxa3gzjl5qsh,ojnm+ is 0.16 m in length. If the motor rotates at the rate of 20 reaoz5sl h 6,,g +x jju;2kc3nmqv/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.*sj v ;)th7g2nxq1tbe0 m is rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleratx sbv ;)1ehgj7q 2*tntion of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeteuhpfbu0 m jyjk.)(n1;r of a bicycle wheel of diameter 70.0 cm)buhmfjk;u1 jn (p0y . when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a/8,n fuk,f sae2+ yw1;gfzgcf circular, rotating space station (r = 1000 m) rotate to ,ngsa8ufk,2fw ;y+zfegc/ 1f produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 mu 3.2lou4l0p7dhthp:.1 k vcd 3ijpz m/s. The maximum centripetal forc3p m13zhhj d.c4pl2okutpu.7 0:lvid e (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating 4l;hr ifu-z8ea flat circular curve of radius 50 m with a speed of 20 m/s. u hel8;-r zi4f 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 to the end ofyl g +(vo-68ee8ofn4eab8 dcu a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear so g4(euodc8lfy8+e8-nb6av e peed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and ra kvgk9pxz*,dy )*p(ah;fawx; dius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m ydp vf;azw,ghxak)x( p **;k9/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 acceleration ofz9+atv5u.affml/ l/l $4.5 rad/s^2$. 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 consqz,w1vd /zhi *tant 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*4io ot9o6dhsy lyr/19 xk9bj automobile tire rotate after starting from rest and accele/ xdot9 9r*i9 ysbjk1hy64oo lrating 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 acceleration79)y.cbl f agm of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s z0mcm,tn -vafxh)n:7decelerates with a constant angular acceleration ofmnz,: a0ht 7xc-)vmn f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches a5 nqj:k7o:zpq 0yw3 ae6adp8 an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the avera3aw8:e6qa pnzjk p5 q07: odayge angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to 8vd:9(u+7ib hbdrupyl-aur3rest over a distance of8rv(3bhap9ury+ d-lib 7u d: u 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter ofe.:lw( ;m byge 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance e y bel.;(wmg:of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down unif)-e:tna u /,zrubnj)q2zb * wwormly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to nju2*w:uabr -t)e n/ ,w)zqzbcome to the stop?

  A centrifuge in a medical laboratory rotates at o:w. bqej++ l8u0gdhza rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at 8jgbw+ zo0+d:lquhe. 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 requin:8kz 7otv .1gg pweq+re 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 f vok1gt.nq:wp87 zg+eorce is perpendicular to the wrench?

  The bolts on a car wheel require tightening ta)a*t xs4krvje)cn5gytd 36.w tf(9go a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force rexa6 g3j)ds4r(w)t.tngk e* f ycvta95quired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ofp z z3c u8( /x/etbvcko7t(1:xhw5swa 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 wjl45ol tg *4r4u 7hjs+bkcf-is modeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origiu4bg- foj4+hc5t rl47slw j* kn?

  A solid cylinder of mass 10 kg is pivoted abou6e(kg a+ j;7i gsju0y-qv2hp lt 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 = 0.50 m(e s2;aukij -6l7 gq p0vgjy+h 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 frictcm43tv-play 5 ok,ag-ionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force c4 kt35-pvg ylom,a -aF1 = 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 ini*2jp jb*v pm3e 2nhy6stially held in the horizontal position, and then released as the free end is allowed to *h*jy mn6b 2jpesv2p 3fall. 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 30quj*9s,8 u i6pv9kkvq 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 4.1su*pu qk9j6i v9k, qv8 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 frictionllu9ygxj4yy,qy, 2 5nbess disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of thg,,ybuy 952qy nxjy4le pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of . y9iyjx0hf( smass 7.07 kg and radius 66.0 cm. What is the accelerat f x.sji(yh90yion of the mass?

  A rotating flywheel can be used to xt/7mgfkchs8;hz21 g 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 inert)j w6b4*hery aia 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 rolls2 gocw)jn3jn3v20luqn 7. x el without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the i23v0n u2ol3gjjxq.nenc )w7lnclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m a; .lg;dt;5wa0g)c*laxhi ewrolls with a speed of 10 m/s. How high up an inclined plane can it climb befor;c ai0w.wh *t;gg)a;xl d5 aele coming to rest?

  A hoop of radius 0.50 m and a mass o: vm8lubl4t3d 8z-l.4 b),cg njgyhv bf 0.20 kg is released from rest and allowed to roll ,.-mbjy 8 d3:u vgzth 8b4v clb4ngl)ldown 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 15 cm rolls i8j;srv .f hs82s+khbwithout slipping down a 35e ibh8k+ s;hv irjss28 f.ncline that 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 mqm40tt1k+8i uhwq;qq-gm.gm omentum 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 d8():hsoy zkp9. r gvumoment 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 arms extendwlvb 2dotw t*(- yxn+2ed has a moment of inertix dn2tbo2+-ywt*(lw va 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?