Angular displacement is -ni1.v :eam4h aw9 m5b0nceamusually express in units of

  Angular velocity is expressed in units o/ ,dms:o:aq m7ethr9l f

  Angular acceleration isfw e 6k0saar4,/;.i anphzh 5c1quf 9l expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constant j(/i,ik/vau8+ v+v(uciy6g alo z1cv rate. The boy is near the outecu( a+8o /vvg1/,i6jyilia(+kvczu vr edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-rouo 334hg;xrlhv nd which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the olh;g4 3r3x vhcenter. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is. hcowdu*ap 3 8p9ecd-p87bzo turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Whoz9doh38uc87d a* weppb -cp .o has the greater linear speed?

  A boy and a girl are riding a merry-go-round bxb qjxn-jcd 3,(s2( 3gy(pm cwhich is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greaterjmx(x-p,32b n(d cgs3y jb (qc centripetal acceleration?

  A boy and a girl are riding a merry ,fva-zy3 8xbn-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 h8-,zxvf ay3nbas the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following(ilth; e9n io3 is an accurate st3ielt(i n;h9oatement?

  Rolling without slippinggu4ku j7bvs r /0shrb9/1g kuusijrh6 9y) k1. depends on

  Two equal forces are applied to a door. The first force is applied at the midpp-:0kmzqaf 3fud + e.goint of the door; the second force3kf0gz+-f.a:qm dupe 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 dooen0 /zf:ot)ac2j ei*4 l1keulrknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?z)l lu2/fe*njo4et0 a :ike1 c

  Two forces are applied to a doorknob, pqn 7,jf3xs:f7ic:qh aerpendicular to the door. The first force is twice as larga:if,s q x:7qhc3 nj7fe as the 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 resistal yx jmn*nrewn1 4(y w(;ryp(1nce to changes in rotatioly((wjrn*m1xenw ypy14(r n;n?

  Consider two uniform solid spheres where both have the same diameter, bupk j 6n4 8/gbimtw2 edg1)xwj*t one has twice the mass of the other. The ratio of the larger moment of intw1k x 46j pbj/emd8*nig2g w)ertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but 4felf 7u5jwjkz*p1i pkytjvy. s0,:* one has twice the radius of the jjf :7w*tk, i5p 4pzl 0s 1uyyv.efkj*other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform z iol y) uqta21bgqn,e-e*:;lsolid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of yb1 2,*neolzaug qte ) -l:;iqinertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M andxi3v:c4k zsf0 radius R. If these are increased to 2M and 3R, what happens to thv4 0c3xk:sfize sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wilmga +9 pt/yd/;xikd8 sl

  The moment of inertia of a solidxka 7 (+82v7qzt vzheej*px ll7v80sg cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic 0alvetl7 s(j7z7ev+ h*q k28x8zx pgvenergy is

  Consider a motorcycle of mass 150 kg, one wheel of weoeu/zfoor vmg2 4.x * y36 l53syaedc+cxz17hich has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheelcu3rf7o*+scel e .y3o /xdvgx4o5zaz 21 ey m6s 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 rolls without sli5 6r kan2twataz371nspping down an inclined plane starting from rest. The linear velocity ztw1 5an 62staank 7r3of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slippingxu fo,n0o6*hqx2cj, q;8e rx dnnh)s- down an inclined plane starting no*no6hfqe j2hdxx08;)qsr ,uxn,c- from rest. The angular 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 exte/jla+jp l / qk laz9)nd/65jgdrnal force acts on the system." This statement ijl6 dad9jjz/+pkq/ n5l/agl)s

  In what circumstances can the angular velocity of system of parti2o3d+w3 joq-hfl w8ht o, aob3cles change withoutl3-h2a +bqww hooo3ftoj8 ,d3 any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frict: ( qgfguj-.bdx)pw-le kji 7)ion which may be presen- )fgw7q:k (i -.eup bjxjldg)t. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an u.wrcbf3y* cq5s sf:d+q4rc0elliptical orbit. As the Earth moves close to the Sun, then which of the 0 wr4burq5cs: cs+cy .d3*fq ffollowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchjh :l a3/mux.zed arms close to his body. What h:j /zxu3hlam. appens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullin0nac2wfr067l px* . kyhc,wvxg in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis ofwc,6h 2wx7alr .nxf*00cpv yk rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrgm wmk, vohvdq(4.g0:etched arms close to his body. What happens to his moment of inertia about the .wg :(4mkm,g q0o dvvhaxis of rotation?

State the law of conservation/(o7jbzi/tu*qo 7 r gr of angular momentum.

  What arc length does the Earth travel in a three month period in its nearly cbw)bp(gr-8 (z wwmlw)ircular orbit about the Sun with a raz )bwlb8wr)(w -p( gwmdius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lp/ (yd- y*:umgy38 /xqz xpdolength of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 seco8-/l dqgyd(xuo:y/ yxp3pz*m nds?

  How many rad/s is 25 revolutions per minute equivalent to?9k;i ;joqj/m q

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whapswehor1;xys79h w wuxdb;d 5yd/*+ 8t is the frequency of the wheel's rot8u;wp hre/y15os9* +;bdy x dwhxdws7 ation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Thl*yf-i)ifna:0 qqv upd tg;58e py 0:;u-i ila8q)5d fgv t*qfnperiod of its rotation is

  A phonograph record rotates at 45 rpm. Thrtlu:bj znmqd/.9mp7 .ough what angle does it turn in 0.20 sm9u.zdp ln :tq jb7m/.?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point5 lrwr-.o8fcz3m;xj s:-t wg z on the outer rim move in 2.-zfrt-c: 58m ;zwgx wsolr3.j1 s?

  A bicycle wheel rotates uniformly througkk5j oh224jveh 2.0 revolutions in 4.0 s. What is the average angular spee42 hk5kje voj2d of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Waw2d p/g:*3roxi 6hlj hat is the li2:6 irx3 gwha*jl/do pnear 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 km. r 4a7a uymn w;g1cq6wyh8f: 4wThe cable which moves the c4;8yww g6uy1a mwr4 an:q7hcfar 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 rotating with a constant angular speed mg2y i54rdn/xhq la4bi +sa: 2of 2.0 rad/s. What is the linear speed of a qh yaba/2sx g244+ mldr:i5inpoint on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in /5e3 uqiye.8q/ yop;nqyp,dtba q71x length. If the motor r.p qpo;813txynq,/qyiy/ be5eau dq7otates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constahguu/0xpyf,7:zb1a u t18dii) b rn9mnt angular speed of 2.0 rad/s. What is the centripetal acceleratioaufx17d )gn9buu 0iz,8th y /1bpm:irn of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the peri4 mjsate2sn+ lw;c /m5c7/oexmeter of a bicycle wheel of diameter 70.0 / s a stj/4;mcc5n e72emwolx+cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, r+yzvm0nf5spx. q 6a9botating space station (r = 1000 m) ronm0 q.+5a y69sfpbvxz tate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m witc v peu5r l3wm-y8*3twh a speed of 20 m/s. The maximum centripetal 8*5r pvtuc-y l3ww3 emforce (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 /j jux 2a3po8u/t vak/+ab /vcof 20 m/s. The maximum centripetal force (provided by static friction)acau8jp3 t/2k obuj/v va /+/x 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 whirled aod4y u3 hmc9x8ctpm1.round in a smooth level table. If the 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.pt 39ccummho 418 dxy?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls withd yi8jr1z( 8ioout slipping 10 m down r1 jioy(dz 8i8a lane 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 angoeu7r299oez/gh6: of*;rkqlc 7i f uuular 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 c*l5 m pt4gju7hvyb9+r : ix-axonstant 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 automobil f+w8xmrv-cdm7me92 rv) kb.le tire rotate after starting from b.l2 ex)vc r-d9vwmr87+ mkmfrest and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, w+7jmu:ks p q.2 l8urqand has an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a connp3qi5hr:zrvqz4p;::l nk. dstant angular acceleration of 3nzrl5ip.p:4v z:;rqk :dhnq$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad:)w.dx-z0y yaui ys4r/s while turning through 2.0 revolutions. What is the average angular acceleration of 4:y)xd iy au0w-ysr z.the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ove rq mdfz(az -0; 0un9tslwziyl5685bsr a distance of 115 m. What is the- miyr;l08nz(szlz au9q5 d 50btsf 6w total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/btwp 5, j :)ptd:p+p *zwebub;s to rest over a distance of 115 m. Wh5wup: *: btz+j)be ;tw,ppb pdat is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down unifpwq a0erhcvx-km gfys2+2 6o7a g8a(8ormly from 8.40 m/s to rest over a distance of 115 m. How long does i7fv2gag h p8cw m60ro-ky(ax+s 2a 8eqt take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotationav*7 utuq,. cnzl speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to ru cn,q*v.t7zuest.
(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 require tightonv--mac b 37hening to a torque of 90 Nm. If a 30 cm long wrench is used, what is then73a-m c-ohbv magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tiq+k4(mk7isj mzq(69o ep pkhn3t7r+ cghtening to a torque of 90 Nm. If a 30 cm long mkr+7eckk93ipmzo ht+spq7( n(q4 6 j wrench is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of idm)ww62 fz* zcnertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as foll*kn23e , slmdtows: mass m is at the origin, mass 2m is at x = a, lm32esnk,d *t 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, 1qzm (29jx , v4dydjgk-dh/.ticr7kdb.ef j about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 , q1dcdvz(4 xe jt2gm7r-.yk/,9b ihjfddk.j = 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 angular acceleration of the cylinder?

  A solid cylinder of r6l6:g8 fry+ qie0 alxmass 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a for6xyqir fg a0rl6 e+8:lce 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 hit-4/p4 tsrmy2c1 yyw8 t(u jecnged 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 yjpcutmy8 /( cwyetr1 ts4-42is 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 12kxv) ) gx)8gcwe bb,p;dzgb7.5 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, assuming )p8v ;d2 ,)ebxgx g gckz7bbw)it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped asd;5klv5yzvr g / 9xr*round a frictionless disk pulley of mass ;vydg5*5rk x 9slvr/z7.07 kg and 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 disk pulley of ma x4 *l5y( plxowfk24clss 7.07 kg and radius 66.0 cm. What is t*4 pl2fxcyx4o kl5(l whe acceleration of the mass?

  A rotating flywheel can be used to store energy.2)bo:1 xwvl el5imze/ 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 inertiagq+*l9sifma .jxah * 9 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 sawc5 ct+t/ iqz hwm+hu4s 1x90tarts 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 inclixhcw95 uh+ac si 1tqmw+/ 04ztned plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a spe1y ymdwa mmdt.t0( k()ed of 10 m/s. How high up an inclined plane ck)md( m.my0ywad1t ( tan it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg czzn48pixk3;dwkn* aq.(; ja3ktc8n is released from rest and allowed to roll down an incline(k p;ankcqni.x8w4at3d z j;8n3*zck d plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of maoe hml+e bag1 ss. vv* v8vzeo8ll438-ss 1.5 kg and radius 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 aelo . sva-v 3 ee8h8+4v lglmv1zos8b* 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 moo8 l dwmh;sy0 a(:t 3e3fzui*fmentum 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 moy(fxo 0, *x5c/h jzqtement 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 extended has a momqy 1 cmv wa4- gazel7r7 w29pmoe7(;ly4itt l-ent of inertia ofr e;v 9 lmloi a24qza w4e7m1wytg7cl-y7-(pt
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?