Angular displacement is usually express in unikm 4njs:cwg 1lsi +;xx5/klx8ts of

  Angular velocity is expresset2 z2bf1 /oonkd in units of

  Angular acceleration is exp9j6os jn-8kcb+z:cgl 5 fau:lressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a conshgy: d)a((j gstant ra (ygagd jsh:)(te. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a k;5;i5n s 8 1uozixtgumerry-go-round 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 greaterx;kgsi5u n;5tz 1i8uo angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a constant rf7 wz.0zg3 5fvpzm i+rate. The boy is near the outer edge, and the girl is closer to the center. Who hapzfw0v. r+f 7z 3z5imgs the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant ras2kn8htu *r,a32d6*wibof a rte. The boy is near the outer edge, while the girl is closer to the center. Whou t8o,da *knb*ri62h3sfw a r2 has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-roundivp)vk2i ew b0i 0zu5) which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to tv ivbzuw0i5)) ipk0e2 he center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Whijx.(c ),tqf0 vvj:d yrch of the following is an accurate statety)q(.f :r x vd0j,vjcment?

  Rolling without slipping depends 0n/id2 ;xqm+jk*z2o d3ukxzao0 y+lyon

  Two equal forces are applied to a door. The fir zwrroym4/i0pwi+ h+ )st force is applied at the midpoint of the door; the o/4+0+pirz hmr) ww iysecond force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are appq0pfbi1 5at 60c:s *48y qlzdf+djmkjlied to a door at the doorknob. The first force is applied perpendiculaqm 8dfcy5 q 6z *4i00s+jb pfa1tl:djkr 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 tu0 au8 vb(z,bw/dzaptk)j 5q-6lyq 6ahe door. The first force is twice as large as the second force. The ratio of the torque of the first to tjw)lp 0 uqztb/8b -aky6v,a(q5 6zaduhe torque of the second is

  What is the quantity used to measur2juez-qm+,h-av2z ,uol 2 rnm e an object's resistance to changes in rotation? 2eu2u--ahm m+l nz2, j,oqvrz

  Consider two uniform solid sf0w*vjr+x:wu .kduo 0pheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger mkj+r.w *ouf:xwu 0d v0oment of inertia to that of the smaller moment of inertia is

  Two uniform solid spher.njn (3hgfe zn0zo i4/es have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smalnhi0 z gn4ne/o3zf(.jler sphere is

  Consider two uniform solid spheres where one gtz9)-t ifkqe p-k+of7;yu: qhas twice the mass and twice the diameter of the other. eu-+9 :qoi t-p)fyzk7kt;qfg The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2M su t4w h7vaqic )/5uejv 3h2f-and 3R, what happens to the sphere's moment of inertia a3w2a i75uvtse-vc hf)/ u 4qjhbout a central axis?

  If a constant net torque is applied to an objeyqz,(f uoq rf -3bt0s6ct, that object will

  The moment of inertia of a solid cylinder about its axis is give(4zoh cs48 5)jtru0rm a;xvd1wxg )oxn by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic enerxvm8cdo (;tg 4 z4j )ux50warrs)x1 hogy is

  Consider a motorcycle of mass 150 kg, one whel1 o1fm+rg+x2weqttw sq:4* nel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of thmre l*:1f 4on+stw21xwq+t g qe wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of ak+ozqz4xq k gws::*9i1 sv f(mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear v:(okzssf i q+k 9*vgwza1:x4qelocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radix47cl*xa oms1ri+ynbuzb t7 ;l10g g8us R rolls without slipping down an inclined plane starting from rest. Ttx877sggl1ri b1 ;0z4oumycbl+xa* n he angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a 8h;*x.y(zc4s r link bsystem of particles changes when a net external force acts on the system." This statement 8zlh n*y4;xi s(k.rc bis

  In what circumstances can the angular velocixnfxg w h5* pk7g+l)1) ggmha.ty of system of particles change without an)g)hp .lmkf71x*gw+ hx gn ag5y change in the system's angular momentum?

  The Earth orbits the Sun in anj-53 oakrs4cou o0np 8 elliptical orbit. Ignore any friction which may be present. What happens over time to the-0on5pjcousakr o384 Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves4 swil(d9 et c/ohh5.y close to t (9ces 45dhyi th/wl.ohe Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirou0 3jz3tr )0i,eskk r) -jqg:aqoh8kdkette (a fast spin) by pulling in his outstretched arms close to his 8 z 0)r:kqstrkkj0oij)k3h , -qg3dea body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (uzcoo7ue 7ho:. k jh9 +ge*7nba fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kineg9+ju7 h eoz. e7k *:onbuhc7otic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulli)tupra 56ljb;pl.g3r)ezs ) wng in his outstretched arms close to his body.splrwu ))5gpe;b ajzl.t) 3 6r What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular mome/3hih pd;dl 2 fk).b-eb 6bgjjntum.

  What arc length does the Earth travel in a three month period in its nu8*e-v i x(ftes:nqi2 early circular of8 - *ie:i(stne2vuq xrbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clocxty 1a rs(c7 x74j0mppk has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 457y4 cs0 1xpx(7pmatrj seconds?

  How many rad/s is 25 revowhl 9nn 4.-:tov 6 iqpcrt12zllutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 p*c6g6;myb u bs. What is the frc; 66ugpyb *mbequency of the wheel's rotation?

  A pulsar (a rotating neut poe4a,ycz)b 6ron star) emits pulses at a frequency of 0.40 kHz. The period of its rotation isoz4ec 6pbya),

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.20)iw 2 nfkw0qoy88 c+xj s8qwojc)xkyfi28n w0 +?

  A wheel of diameter 26 cm turns at 150y+(om .:notw7 yw+ hxs0 rpm. How far will a point on the outer rim move x(soy:h nm o y+w7+.wtin 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whatqo9 rs/q c5ks4u/)l op is the average angular lp9/uoc4skr q)o5 s q/speed of the wheel?

  A bicycle wheel rotates uniformly t 1p2wg3jbxvm :( byp7r m22iiqhrough 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m fpr g7mmv2y2 2bx:1q 3(piji bwrom the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable whit2 lnzzy4l6i:cz2n6l :tiz4yl h 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 ro,(q jqvz f hjzr4ra9;5tating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheelr;f94v qz(j zr,q5haj's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in len8djzos- i s 9)c;wn -g x 723.ytlqokke3yib5xgth. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed gs)n 3wys-5-;i7otx2boix dlje.9ycq3kk8 zof the end of the cord?

  A wheel of radius 1.0 m is rotating d;ht l kdx)1xyk53gc2with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's 2th gdkxl5)k;1y3 dcx rim?

  What is the centripetal acceleration of a poimkk:9zw mr(8 d x;g2s bb ub26lb*6qyant on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is movzmr(2lx6b;kbgud* 2sqbk9my 86baw :ing 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space statx+jyr q*e 4+wdh53 87 vzzozltion (r = 1048ltw zz+dq 5yh* rox +e7zj3v00 m) rotate to 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 ofj l e/-e3d m-(so,wr(r8rii ri 20 m/s. The maximum centripetal fo-r(3-s(ireij e dirlmr,/w o 8rce (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating u) hc7pz5bp iulzp 4+/a flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (propzh)up 7zbil p5 u4/+cvided 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 str+qzey kkxg19i9o 8jw 1x7 wrip8uf ,o2ing, is whirled around in a smooth level table. If the maximum tensionyg+ejw117puxzr xwq if9 koi,k 88 o29 that the string 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 cy.xl6hp m;l+i m rolls without slipping 10 m down a lane at 4.3 mly.pxl+i ;6m h/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 constantm8/a zahn qk4 jb-/2gl 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 angular acceleraibcf rxeau -j3a((*u:tion 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 starz .2abx8tcb3jz2 1v bmting from rest and accelerating at a constant angular czb m 82bax.31tjb2v zacceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceler.3 wdzhm 15e0is ee/r.uep9mh ation of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating chzu tmo0n72bo q3m7mj: 44je at 20 rad/s decelerates with a constant angular acceleration o4mqzt:ecjnm4oj0b m3 2ho7 7 uf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 y/;1p4 fxlcg;emcfpe2i j 9 b7rad/s while turning through 2.0 revolutions. What is the average angular acceleration of ;f/ ;mx pg7b12iel 9cjcfpye4the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over a/3lo7 uzqxv9 o(twu m8 distance of 115 m. What iq/(7lw8v t3zuo9x umos the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68sf/zqblxz5uj,+fl ;r1 aww2 -rq x .e+ 8n+ulc.0 cm slows down uniformly from 8.40 m/s to rest over a distanl 5-ql+lxc,uf /wqj+s b1.enx2zraw z8ur f +;ce of 115 m. What is the angular acceleration?

  A wheel of diameter 4 * t/0ix 7o veo0kkj0qef1ecsof 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How o0cqo*e 40vt0/k exi1sk7jef long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of (ntq:lz(t5q f 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration befn :5(qtfzlqt(ore 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 requig: xtlk/1c y76;ju7u 9jzvws xre 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 force is perpendicular to the wrenchs1wgy9uj 7cu/t;7xk:jz v6x l?

  The bolts on a car wheel require tightening to a torqueib1y2mo9 8xu. r 5 7niahdiyzw-tj .:k of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requi7 i-ywh5z ju:namr.kd bxt.o12i9y8ired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerec 7 9fjikr-f3q*9gk+ ;rh4)guefrns tia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: m65( tfdyn*o s4rm ; xfc 24zf/gapkhi9ass m is at the origin, mass 2m is xp/f6oagfhsif9 ;tz n54k (y 4*cm2drat x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 i9p (5 kwqq*vdkg is pivoted 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 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the angular9 dvqw qp*i5(k acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pg*-l3z9j0xtw uv47ebe.aww 74oaw l jivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 uew4x.bat4lv77wj0 j- zg* 9o 3wael w= 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+ aik*ba)q8g/ae)/vgkkb0 to is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleratioav+)/ga ibq/oebkk )8g*0ak tn 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 ssy3j 5 hls89athe mass of th a8 s39yhssj5le 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 b x0zla)q,vz0 a rope wrapped around a frictionless disk pulley of mass 7.07 az0b 0qx vz,)lkg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrappe*5asii5a 8ledte6zf 1 d around a frictionless disk pulley of mass 7.07 ei5681 tld *ae szafi5kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to y xy,d9q-m 4wbc3- racstore $1.00 \times 10^{6} \; J$ 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 iners565wac z:(dmt)vcg. oa h(j otia 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 rolls witorw*ekq9c; qmat9s 7-hout slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclineqto;*k799ac remwqs -d plane?

  A solid sphere of mass 1.0 kg and6yxseweqv53s0 ; -l sg radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before s30qw e5 6g sxse;ly-vcoming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is rele csj/wejyn81 :ased from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical:8jjy1ne /cws distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolw5mvd/ a4du0pls without slipping down a 35e incline that is 7.0 m long. Assume it start/ 40p 5amwdduved 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 cjmh-(bqv 5 2wox:zx9momentum 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 i5n u3vw ekg::ucka 64dnertia 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 u5 pfd7l8ihjmif( 9z x bog:-2inertia ob(lf9ijx gmi2ph:f5 7u8od z- 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?