Angular displacement is usually ex2(o-nuo.6yt5mgfyyw2 +am(aayy p :rpress in units of

  Angular velocity is expressed g;osp2z .p).qqxt pc+a+qjn nit5h;2 in units of

  Angular acceleration is expressed 5(s pm/a ocd51 iefo/uin units of

  A boy and a girl are riding on a mefdn,u(05s lt srry-go-round which is turning at a constant rate. The bodun0,s l s5tf(y 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 merfm;.ftjzq/, i ry-go-round which is turning at a constant rate. The boy is near the oz q/t;mfij,. futer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merrf m/ecsm 8 m((ht;qmj9y-go-round which is turning at a constant rate. The boy is near the out( ;9h8(m qsfmm/ tjecmer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is b3x-hrf) o 0k*hzo8s+xs crc,u(ph0y turning at a constant rate. The boy is near the outer edge, while the girl is closer to t sc )u * roobrs-+(0k8p, h3chhfz0xxyhe center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which o jo2um16mf k+is turning at a constant rate. The boy is near the ouk1j6+fmo mu o2ter edge, while 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 al/2 yt0vfccu)y3 5rp jn accurate stateme lur35jpvc2 y0tyc/)fnt?

  Rolling without slipping depe m-fd/rws ubb/rzduv (: +8qsj*)olo9nds on

  Two equal forces are applied to a door. The first fo;y sl7;mriv( krce is applied at the midpoint of the;(r vl7ki s;my door; 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 the doorknob. :a pa9j/j0tf yThe first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door.p0 :/jtaa y9jf Which force exerts the greater torque?

  Two forces are applied to ru2 (dq/t(l dga doorknob, perpendicular to the door. The first force is twice as large as the second force. The rt(ql2(d /rugdatio of the torque of the first to the torque of the second is

  What is the quantity used t g.sqq7:tr;a.y(4p n0ovu jzu o measure an object's resistance to changes in rotation:(7 r;4ujvo apz.ysqg.tu0 nq?

  Consider two uniform solid s; ncb;2w11qd- dxd7tyshl l8f pheres where both have the same diameter, but one has twice the mass of the 1 hsl wq;bf-x7 cyn8d;t1d2dlother. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same w1l/nuzoou45 mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of theu/ zw4nulo1o5 smaller sphere is

  Consider two uniform solid spheres where one has 89/ izyprn+gpc 1zg pg1yeo-+twice the mass and twice the diamrycpgg1e-gi9n /8yzo z+p+ 1peter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere hasn y0 -ip n;b-v40fvdnv mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inert 4vbf-;nv i-ny00ndvpia about a central axis?

  If a constant net torque is applied tnb x4k6znr 8dy ao(g-1o an object, that object will

  The moment of inertia of a solid cylindek,seq ) vyeg40r about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy ke e)s y,g0q4vto its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass o9hz 7urzu2*ad/2yw izr33n s4 ig; aeif 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translation/n g r3zuus2a49 i2z;d7wh e*rii3y zaal kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping da10.1 l slojjtown an inclined plane starting from rest. The linear velocitt.jl o0 ja1s1ly of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping do3 -s4g3jvmfyn wn an inclined plane starting from rest. The anv3ngs ym- 34jfgular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net exte7c 8 .g/x qbp+swgw6ifrnal force acts on the system. i .+8bgqwpfw7sg/ cx6" This statement is

  In what circumstances can the angular velocity of system of particles change , b4 ie0qeg.z*qbxg6l with.4gz0i,blb q*6 xeqgeout any change in the system's angular momentum?

  The Earth orbits the Sun in liil-3mm1 : uran elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular :l-m 3l1rim iumomentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth mov,ufyurd*ak -9es close to the Sun, then which of the following best descri9 -kyruf,ud* abes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling zyb.p8d-n+im in his outstretched arms close to his body. What happens to his angular momentum about the axis ofiy+pnmb.zd- 8 rotation?

  An ice skater performs a pirouette (a fast spin) by pullingiws dyr(,n66* gn9vtn in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotationg6yt6w,srndi (n9 * nv?

  An ice skater performs a pirouekpou64 m(y0ukqp :4nntte (a fast spin) by pulling in his outstretched arms close to his body. Whmo ukn:(6p4qynu k0p 4at happens to his moment of inertia about the axis of rotation?

State the law of conservation of angulye8n4oq 5t mj+ar momentum.

  What arc length does wa*dt(.nk,sp the Earth travel in a three month period in its nearly circular orbit abo a*kp(ts.d ,wnut the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 mcn:9, eeg--p jqf/d uh. What distance does the tip of the second hand sweep through in 3 minutes and 45 /q9e , fgj:h-dcnepu-seconds?

  How many rad/s is 25 revolutions pe m; lhln0+fn;er minute equivalent to?

  A bicycle wheel rotates unng.gi 2:jiay7uo8ges) +b9 .df zpq8 biformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rota7j8i9ugqfz pi+es)o8 nb:2bg.yg d.ation?

  A pulsar (a rotating neutron star) emits pulses at a frequency oale:29b3uvnqg d /e, sf 0.40 kHz. The period of its rotatiosaev2 eu/d: l 3q,9nbgn is

  A phonograph record rotates at 45 rpm. Through what angle does ito.mb -g p.eu9mht: eq. turn in 0.20 q9 beh.meo.:t mp.g u-s?

  A wheel of diameter 26 cm tu3)0+mvptoo-dyk /rj hrns at 1500 rpm. How far will a point on the outer rvp3dot 0 omkyr+j-h /)im move in 2.1 s?

  A bicycle wheel rotates un2u7av 6)u.m 0zjpl iqriformly through 2.0 revolutions in 4.0 s. What is the average angular 2q0v )zur7li6a p m.juspeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutic* mwmd ;.fse3ons in 4.0 s. What is the linear speed of a point m;*sfdwce 3.m 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The oqwhc h,-p7c) 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 the cable car to mak hc-7qcho) w,pe the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constanpltz v tgu*609t angular speed of 2.0 rad/s. What is the linearvg*lz6 90 pttu speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in,qlbjm g-62fj lo4)eq 4ml 1ta length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of m2f1aeljo,4 bl )g6l4jmq - qtthe cord?

  A wheel of radius 1.0 m is rotating wityfmvq ky93yuz a tma)6s7 .b44h a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point oumaa3m4)6zy yq btk7. vf9ys 4n the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of 1vpexy(wl:g 1 +y/ qiq6v;fys a bicycle wheel of diameter 70.0 cm when the bike is movinw/(ysy ye+vfv6xg qpi;1 :l1qg 8.00 m/s?

  How many revolutions per minute (rpm) must a circbjle(3 f/5 d5xutpz)vular, rotating space station (r = 1000 m) rotate to)3l u5(vep tzj/5xdfb produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat cir(9k2t38pe jm gl* esdvcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force t(93ek8gesp2 *dlj v m(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 os72yjavo yuf+my6) t:zs9j j 7f 20 m/s. The maximum j :mt)y97s jz7jy2fovsu6y a+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 string, is wh7vy/v6gd ,mdx 5vw6y sirled around in a smooth level table. If thvymvd6v67d /wx 5s,yge maximum tension 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 andj2nhmvd/.c7v 3pf b+ b radius 9.0 cm rolls without slipping 10 m down a .hvpfv+/7c3b bjn2 d mlane at 4.3 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 with a constant r sxx 0d1bj x-2l1v+pmangular 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 acceleratio+(tpr ossl jcd2kt13m i3u(p -n 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 nmvp1zs+(:(n6g o rdk radius automobile tire rotate after starting from rest and accelerating at aom sz6n+ rnd(vk:pg( 1 constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has i+m7cyanjbx. 81f1vh kh-l1zan angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/ eoud7gs(8hz *3spq (kefx7 )ls decelerates with a constant angular acceleraq8l3uoed(sxp(7z7hf ) kg*setion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angula0*org .a ucnm8r speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular arnc o.au*gm08 cceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s / pzgto 04ltm2to rest over a distance of 115 m olpm24/tz 0tg. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down u5brvw6 ,u.) u 9znunmnniformly from 8.40 m/s to rest over a distance of 115 m. What is the angu6uz)um bnv5rn9. wn,ular acceleration?

  A wheel of diameter of 68.0gslrx1 9rwp+d5g; )ng cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it takegdlngx r)+1sw9pg r;5 for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rov;)6f,3cn, k svufhdktational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a consckf, ks)uhv,vd 6nf;3tant 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 reqwc7zc 9;ne3: uyzixd 5uire tightening to a torque of 90 Nm. If a 30 cm loncuw3iczye5;:n xz 9 d7g wrench is used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. ne-a;90h6d+amko pdn If a 30 cm long wrench is used, what is the magnitude of the force ree6ndm0a +kpn; a9ohd- quired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of io-fzp ld14 tlf:d 6zc1)q)idjnertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is m twrk 1cgv;:+ unx61r:h:fxyi odeled as follows: mass m is at the origin, mass 2m is at::v+fxhr:g 6r1ukx t i;wy1c n x = a, and, 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 thought the 2wrajh fyu gp85uk- ,)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 a8-)a 2 ur,kjf5ypw hgungular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a friction774q8 c+tr2)mge j wey )kz7b1 jlrsqnless 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. How manq7 jqb 7)et7) yz1s jr lwm284+kgcerny 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. ba dic: /g.3-kup.ps *r uh9yl 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 ispblpkuuh/3. a-c *iysd r .g:9 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 cmdfg u;d. mf,h h84 cukpd*;d:i 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 achieve, assud8dphfki uu c,:;m;*h .g d4dfming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a fricti3gffv9p/ e5l2ei wjt9e9i1 yeonless disk pulley of mass 7.07 kg and radius 66.0 cm. What1/9epi9jfee5 2 vwyi fgt 9el3 is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pu*r zczi5uls3kl )wihb p.*3m 5lley of mass 7.07 kg and radius 66.0 cm. What mi)*5h3s*crbz.3ulwzpi 5k l is the acceleration of the mass?

  A rotating flywheel can be used to storsm3n ( n/r7/umpeif 2fe 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 inertia of adp ir:/6s59-gaotd r,epk aak/3y0h $5.00 \; kgm^{2}$ 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 rollvhyal*, eht .prg2*a/s without slipping down a 1.0-m high inclined plane. What is the sahlagy * t*,hev2 .p/rpeed of 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 cr):u; g8ygy6mt;ifj-o due8a speed of 10 m/s. How high umcud:-y86ft y8goi u r ;g;)jep an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass *4e)qi g ko 6s6 x0zi2v0 ypqzqkr95svof 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance oz6spvxi490kr5 q2 6 0ke)*vzgiq yq sof 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls win d.+jbis)h4:pdk-(jf w1bhn thout slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is givenh w( 4jkj+n .sn) 1hdf:bpbid- 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 momentum chghmpu;(t dc6z4c 6 4hganges 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 ;5mu6 (z kfq*59ujhl bjh4fso 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 2jq z/mf184 :sioqvdxc(wj+u ;w7qxc 5.00 rad/s with arms extended has a moment of inertia1x (q2wcx jswq;:z /cf8j odq+m 4vui7 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?