Angular displacement 0z0r6 4k)7i sy dvrf e8rid2ojis usually express in units of

  Angular velocity is expressed in o ;z0.w8 oq,zff- qnghunits of

  Angular acceleration is exwstngtm ,26 i /bc:8uxpressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a co qlb) 5i9hg9apzn1tk7nstant rate. The boy is near the outer edge, and the girl is closer to the cept)79 9iaqz1bln5 k ghnter. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning5ylg;y/5pnx w at a constant rate. The boy is near the outer edge, y/yng5 l xw;p5and 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 is turning at a constant rd+x k 5cw/1uriate. The boy is near the outer edge, and the girl is clrk dcu/51x wi+oser to the center. Who has the greater linear speed?

  A boy and a girl are ridingmq syt/;39m vzj3 a7gdq ybt19 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. Who has the greater centrv q931b ;tgm3ta/j7mdyy zqs9 ipetal acceleration?

  A boy and a girl are riding a merry-go-round which is tu :jbtvvp r7 y-s,w5s t2e4vsd+rning at a constant rate. The boy is near the outer edge, wbe+vrvtp4ss:-,dw vs t2 7jy 5hile the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurate sc o nomizm*h2ka1jw a3 r6-l 68ye.*jctatem j*hj8m6ykz ncroiala3*oec2-6 .w1ment?

  Rolling without slipping depends on wuzvv9 h wq(h22irex8 fk+d-x- ob84k

  Two equal forces are applied to a door. The first force is appliedg2vpx2 3b,5nh.yt kdm at the midpoint of the dvxnh. 2p,3btyg2d5 mk oor; the second force 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 t(fr9ne4zrbc +he doorknob. The first force is applied perpendicular to the door; the second4 zerfcr+ n(9b 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 zy fj 6*s9y4yjq p)b-ovhz6k7force is twice as large as the second force. The ratio o yp)jvh9jz 467*6 yzfkyoq-bsf the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistah,hy8 c+ei 3cfnce to changes in rotation cf+ei8hy ,hc3?

  Consider two uniform yvwhk - s+ct2q (4lu3csolid spheres where both have the same diameter, but one has twice the mass of the othe2c-( lu qh+4 w3ckvtsyr. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have ther9noa: dc8ytnz e 1pf3ql:5 t: same mass, but one has twice the radius of the other. The ratio of the larger sphere's momen85e ca3dz rn l:t:nop1qty:9ft of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the mk nmkbd(jew 7822c-hdi -w2e m 82nhkbkmj(cd7ameter 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 mass M as5 p0fjo s/t:r9slhr2nd radius R. If these are increased to 2M and 3R, what happes2hlpo5r9:s/ rf jt0s ns to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that7+wqbs,g/ d+ qtyxj8v object will

  The moment of inertia of a solid cylinder about its axis is given 4ibp cyn 4nk1*by $\frac{1}{2} MR^2$. If this 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 which has a mass of 10xhm.pe zj40d0 kg and a radius of 30 cm. .z4h0djp0 m exWhat 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 ana 5m(hd 07rdi4 xjmcizv c4.4id radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bott5 jrxvch04m7d cim4 d(zai4.iom of the incline depends on

  Suppose a solid sphere of mass M an0e j.4q t* rfx* ltxfdofo7e75d radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the t 5ooet*j.0 *7frdxfq7le4 f xincline depends on

  "The total angular momentum of a system of particaj*rf2+ r cmqqm r7qo (eef265les changes when a net external force acts on the systrq5+ rj*e 7r26 ff2(qo caemqmem." This statement is

  In what circumstances can the angular velocity of system of particles changeh2k:m29rowm3vpuap(tv;st + zry7 dn 6 ./t ge without any change in the syster9:.gra2 mtktp+ t2/wh 7unesv v;6(ompz yd 3m's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictionz(ps4ufwsc,3sn,3 10axi mfs which may be present. What happens over time to the Earth's 0f431ipux,zswna,ss s(c fm3angular momentum about the Sun?

  The Earth moves about the Sbm*gkj mn (9z yjp4a *(b.h)vr,uo d.bun in an elliptical orbit. As the Earth moves close to tr.)9 4j *mbob(z vuhpymab*,.k jdg(nhe Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performsn*1gl 8vj/yq oeqa765 ebc2 lh a pirouette (a fast spin) by pulling in his outstretched arms close to his body. q c eblv g7o*1j2nhl/56aq8y eWhat happens to his angular momentum about the axis of rotation?

  An ice skater performs a piro316d7e ytdib dll kibnc /0g-0uette (a fast spin) by pulling in his outstretched arms close to his body. What hap icn0ly0glb ib3t1de/ dk7-6 dpens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouc6fcl8yfy/7ill /pgj s0 uu 59wlw t+0ette (a fast spin) by pulling in his outstretched arms close to his bodypl7c6i/j/wcystul +08wl 9f5u0flg y . What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momen*nk zwoqr2r d21nt- 6sg/w hi8tum.

  What arc length does th*g2i4ozgy68uovlt v5sh9hr,e Earth travel in a three month period in its nearly circular orbit about the Sun with a yoghvr zt vlog8iu 49h5 ,26*sradius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lengtk7 ppi xe3t8og:swy/ 4h of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 second4:3g ipwox s/yekp8 t7s?

  How many rad/s is 25 revolutiokia+ g e8dx-o9z l9rz/ns per minute equivalent to?

  A bicycle wheel rotates uniformly throu2l08 x5hkl.gb;ysz-wy mu0ril 42pkugh 2.0 revolutions in 4.0 s. What is the frequency of th42wslyl u h8ikp0gz- 2m u5ryx.lb;k0e wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 g-kymqp ns85 bh8 ri6-kHz. The period of ismry qphk-b8ni g658 -ts rotation is

  A phonograph record rotates at 45 rpm. 3b7 dgmyi27xmq8 ktjq2z k h+9Through what angle does it turn in 0.20 s?k 2 htjqgmzi+7m8x 3kq92dyb7

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the ykh z0 jz. znm izb2l9cc g9)15g9f;vuouter rim movy;9zhbzz) 29gf vnk10l cmg9uizjc5. e in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whgdg 5zjml i 6;t/c j -f8m8psk;xre8veh-p)a6at is the average angular speed ofspmgm)86t8;x; r86eh -f-p5kicjzl ae /g djv the wheel?

  A bicycle wheel rotates unale,q +i6:2iykqab ;aiformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m frq yla;b e,q:+kiaa26iom the center of the wheel?

  A cable car at a ski resort mc nc 1wd*x*6mcarries 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 fas *mw1cx *dnm6ct must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 ,xxi xxv6*c n.f: x kjc495lmrm is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel's rim.xx 9 *cfxi5v64x cn, x:rkjml?

  The cutting cord on a gas-powered weed cutter is 0. 7ibqn 5c,roap p13tc916 m in length. If the motor rotates at the rate of 20 rev/s, what is the approx1o patrciqncb ,p7359 imate linear speed of the end of the cord?

  A wheel of radius 1.0 m ebe 0kvh-) msnyy9o3 (hde0b7 is rotating with a constant angular speed of 2.0 rad/s. What is th3dmb)0 (e h 0synkeh79yvobe- e centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle wh uob eogz45x;3bt o9j,eel of diameter 70b3jgb; ,z9eo54xoto u .0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circ8c97f g/o urfr )svq9-,bt 6.uze/xo*i pptuw ular, rotating space station (r = 1000 m) rotate to produce an artificial 7c9f. r,p/ p9vb) xz8 ugq/fuwt oisr 6-oue*tgravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a qkv*4fia f(6q speed of 20 m/s. The maximum centripetal force (provided by sta4vaf*ikq (f6 qtic 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 20 m x8tlf2 z,d; n dgejh8u)k;,n/ n0jhli/s. Ti)l ;jx,0zhnhjk 8/;2ef gnlnd,utd8he 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 of a 0.750-m ovs7o :cn3*ugstring, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then wha7os:*u3ngv oc t maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radiohh* gyjw79v7y e4fg5us 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/s. j9fh7vy*hg 5oye 4g7w
(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 of 0m)qgldi;w)c $4.5 rad/s^2$. 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 angular acceleratkbtows+t -/ul m+h( 1b97gc sjion 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 rotate after starting z3utf8o t8)wu mzk9y1 from res9 uwmt z3of)88kyzu1tt and accelerating 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 ogl3;w ( 07 malgftgjl:g1w8 eangular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s dl)cv ( wzeo :mxo c2/)4zyljw-ecelerates with a constant angular acceleratlycz) 2wo-lw )(co z/v4exj: mion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angularoac 2w3m,rxn u7c+ q;n speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleratio 2xanrwnoc +,qum7; 3cn of the wheel?

  A wheel of diameter of 68.0 cm slow m av.z(;/q4uf qkug(t5my:zs s down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the ;m zumkt q4 u/(v5g(yzs:.a qfwheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uni i6 p9qkawkev b34(.a ster/goxm (l(*formly from 8.40 m/s to rest over a distance of 115 m. What is the angular acce(xpvta(63 4 bema(w g e9. s*kk/olriqleration?

  A wheel of diameter of 68.0 cm slows 1gllvjfzh xbajz302;7e p4kjm 95o0k ej9r:m down uniformly from 8.40 m/s to rest over a dmzgfemj l j5lo1khjrz2p9v; 0:9 a7 x e40jb3kistance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medicax0o 59y9 wujwal laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times ata5owu0 9 9xwjy 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 requi8 cn.r/l* b/ s1wvb8nhvw8b ycre tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force rc18ynl8 b/h. v /w8bvwnc*rs bequired when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a g hptd sdo,/ia/p3 u3m(.sfy330 cm long wrench is used, what is the magnitude of the forsy sh3 3 apuoit.f3d(d ,pmg//ce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inert:906f) d m7,6wk ovmme lxdmoria $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mas6yd*f zv+ ia ep07x4hbs m is at the origin, mass 2m is at x = a, and, mass 3m i*4bvd e7a ixfzy +06phs 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 thoug7 r) s*ze oaxmj6s163wi/kow uht the center O. sk7x/w166a)om ojuswr 3 *zie A rope wrapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 *yjdq0:5z 2prb/mznj kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer raq z0m*/djnzj2b 5r y:pdius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 hinged6cnq,-jeei -e xz64 py 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 as it is released? (The moment of inertia of a rod about one end is MLji, cee64-zpynx 6e -q2/3.)

  Consider a bicycle wheel to be a ring of ra9/ zu,.xkynp bv,)ltfdius 30 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 4.1 s, what linear speed does the wheel achieven,uk/vbl fz.xt,y)9 p , assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley+ oy2y7xarw3j of mass 7.07 kg and radius 66.0 cm. +xo27ywr3jay What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless . x9) hnfvrudfij,r98 disk pulley of mass 7.07 kg an r)n.hxr8f9vuij fd,9d radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energye-5,ywzewd ,p. 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 ineerv :/5r yczn8rtia 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 starto:yl1cv 5,bv3rda vif9vjpu h:h/7 2js from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed odvuyjobpvfhv ra3i5c,9 l h1/ 2:7:vjf 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 a speed+r 3zxnpb-n.c,0;7y2 w uclw m* shssh of 10 m/s. How high up hc3 ncz,p;wn y0r wbs7m .usxl-h2*+san inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released froiis.(.qyxva6, i vq/r m rest and allowed to roll down an inclined plane. How fast is it moving after dropping a (6y/v . ar.v,qisqixi vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm r.aenzq;,np j ,c5zjns65vgxmhy4r5 7 olls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia orvqxhnzanjnz.4j55, 6 gcp, ye7m 5;sf 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 momeny9d *oxrkp68ua )r8n otum 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 i ;f rrhptc/so2ls;.:j nertia 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 extended has a moment of h0aplei2dy6d3wd. d7-1fl l q inertia ofh3 dla-.pliyw0q dd76ld1 ef2
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?