Angular displacement is usually express*m k8xkjrlr8/4o 2u venp+ru- in units of

  Angular velocity is expressed in 3)/ip z twircx82 1ldmft80oqunits of

  Angular acceleration is expressedgw3gwp 4v q8qr *1sf5d in units of

  A boy and a girl are riding on a merry-go-round we;0o71a ezuv ghich is turning at a constant rate. The boy is near 1o;0aeze vu 7gthe 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 m5;ke fkcsu,e5,q mm5perry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Wh,fe5, mq ck5uk;pmse5o has the greater angular speed?

  A boy and a girl are riding on 7dyug2bg)h3 0; x yvyga merry-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 hasgxd 32ub 7gyy) vgh;y0 the greater linear speed?

  A boy and a girl are ridin0z bus( fqb/719jn jv,o xap gmke-;t(g a merry-go-round which is turning at a constant rate. The boy is near them9xz7b-kojp 0q1 ua,v t ;(fn/ge(bjs outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constantz/fxgb( o+) fk+mvfr9 rate. The bo m+f rgvko(xz9+)fbf/y is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Whic;rpuy iv4.qz4h of the following is an accurate statement?.ru4 qz;iv4p y

  Rolling without slippi5rcpir4szst8,vuny to,r)3+ 78n yki ng depends on

  Two equal forces are applied to a door. The first force is applied at the midpr(x2x fvm7c: boint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to mxfc2vx( 7:rbthe door. Which force exerts the greater torque?

  Two equal forces are 0.d eaevgvw -ag2+*mml :nf5r applied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which forr.ggv 2elmw0a-am: 5vfen+* d ce exerts the greater torque?

  Two forces are applied to a doo85;yfo .cc ebpne7gl.rknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque75;epfg el8yc.ob.cn of the first to the torque of the second is

  What is the quantity j*h*xp l,nbyzl7x oa kegl.8r0),a:zused to measure an object's resistance to changes in rotation?.7bxl8* ,ky )o ra0nhpz l*lae:x,jgz

  Consider two uniform solid spheres where both have the same dia vzh b6 eh)3/zdev0hea.c79 t7dtb7tb meter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment b0 dvhhe 6avb9e)h7dzte7/.3bz 7tct of inertia is

  Two uniform solid spheres have the same mass, but one has twiccr-4wq rkd ux g()69/dc3oazce the radius of the other. The ratio of the larger sphere's moment of inertia to that ofox3(rc69- )cc a /gkzrwdq 4du the smaller sphere is

  Consider two uniform solid sphb(1;rw n(czv:ohc6g fn 1dp6reres where one has twice the mass and twice the diameter of the other. The ratio rcnb nzrv(6pd(6 fgc 1 1h;o:wof the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M a.7.pj 5 x2v)cehgqgd l:qrj6and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a ajp56.c :rlgq gx jh)q72.evdcentral axis?

  If a constant net torque is applied to an object,c g, szkze:l j-17x,og that object will

  The moment of inertia of a solid cylinder8 u/y4v6b qrva about its axis is given by 0.5 MR2. If this cylinder rolls withoby8u4 a/6vrq vut 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 oadoscjyc/:q h -ab; 1.f 10 kg and a radius of 30 cm. What is the ratio of the rotational :s;bh/ cy qdj1-c.aoakinetic 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 and radidu xq dk0(*3fvus R rolls without slipping down an inclined plane starting from rest.qxuk(* v ddf03 The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls di1 l,bmgn+ vfkw,11o without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bobwm+vd1 o in1g1lkf, ,ttom of the incline depends on

  "The total angular momentum of a system of particles changes when a net exterv * ht3fagf(z )s0p7phnal f tfzvgp)0as 3fh7*p( horce acts on the system." This statement is

  In what circumstances can the angular velocp9znmz4,lb- vity of system of particles change without any change in mz bn, -zlp9v4the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction ,ad65cm/v a s4gg3vvawhich may v6ac/, v4gv35d s magabe present. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical n7lws;w3njvfe szw*/ns bv/0 7f c9e*orbit. As the Earth moves close to the Sun, then which of the f w *wsb97w0fsencz7lnnvfj //s e;*v 3ollowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrettzz4t 6l6lfv: ched arms close to his body. What happens t :tfz4tv6 lz6lo his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling ly;yf,u b rdu+b7.zads )gj 9c;/qc/xin his outstretched arms close to his body. What happens to his rotational al9dx; ccub//jfqdgu .r,ysy;+z) 7b kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fasy gioo9 a/y7(at spin) by pulling in his outstretched arms close to his body. What happens to his moment of i9i/7o yaag oy(nertia about the axis of rotation?

State the law of conservation of angular m99xd /2vu, umtcfs ;f5za8jkoomentum.

  What arc length does the Earth travel in a three month period in its nci)d gdi58e k/early circular orbit about the Sun with eidg/5 i)8 cdka radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the tip89c3k x7x v*+vt l 7(xmtehtpm of the second hand sweep thr9t3txc x7ev+lh (p8k*m 7mvtxough in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equival/vl*r*8fn7idgrbt /6dtu6 i8 at0ae eent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is vc9:u,rkqnu06,u cqg the frequency of the wheel's rotatiorkuq:,v69 ucng, 0 qcun?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Thjnv83o r.bh97du jx4 ce period of i3obrjn4j7cu9hd. 8v xts rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it tj1q/ 6bv3 b7;kskq r 0krip3pyurn in 0.20 s ppvyqk /q;ib k337 r6rs0jk1b?

  A wheel of diameter 26 cm5q ownz6w, 4bm turns at 1500 rpm. How far will a point on the outer zqbm,o 45w6n wrim move in 2.1 s?

  A bicycle wheel rotates uniformjvi(nlu:m(:hknh)pf8;x d ; qly through 2.0 revolutions in 4.0 s. What is the average angular speed ofj ;m: x dvun flnq(ki;):(p8hh the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thevlz 9*ftmddzlnl 3,-6yg d54w linear speed of a poz 6d- l3g4*md ltyfln9wv,dz5int 0.10 m from the center of the wheel?

  A cable car at a ski resort carries nrf0fv h*4d9oskiers 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 fast must the pulley rotate for the cable car to make the trip in 12 mh9 r0fn f4d*voinutes?

  A wheel of radius 1.0 m is rotating with-ohse bj ggd0cxeycr* 4 9bk)8.6x*qr a constant angular speed of 2.0 rad/s. What is the linear speed of a poinyd*8bjh)srge o0rqbkx6c*4 xc.9 ge-t on the wheel's rim?

  The cutting cord on a gas-iibqv8 vl/l(z, 9lui3 powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed 8,zv/bl(q9i iil 3vlu of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0d9a,s yx gxd7vk*i6 0x)w gj9z rad/s. What is the centripetal v)0i 9wgx,s*x jg967dza kyxd acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle w* cz*tc4x4yv0x g r.zgn+,n aqheel of diameter 70.0 cm when the bi,*r 4xgnnzatv. + 4xz0cqcg*yke is moving 8.00 m/s?

  How many revolutions per mi 9-k*p0 b.w d .v5d mk/ydn0erq5mvv (glfai-nnute (rpm) must a circular, rotating space station (r = 1000 m) rotate to pv-ydiw ka.( v-f g/ 90 . *kvr5bddl5nmpmen0qroduce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a fdk bz0 ,gczi33t;nu m2lat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fri 2,c3tni3d;kg 0zz bumction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a ftbnu nc;n ,xf7fdb;2g pg-, (elat circular curve of radius 50 m with a speed of 20 m/s.ungf- bbxn ne(,,t7f;d 2g;cp 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 of a 3eozw/(i us;k x+2vj w0.750-m string, is whirled around in a smooth level table. If t2u+ svoie3w (wk /xj;zhe 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 and radius 9.0 cm rolls wnyli-m 6d2z9k x itd*b( 0h(lhithout slipping 10 m down a lane atn-tl0xhbd(z (92 i*hikmd yl6 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 angular accel4hjk4sj 4dwq xwnfda c;a.,6*eration 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 accelerationn6etuc3 -v t1o 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 kg5jxy;h7z5m tire rotate after starting from rest and accelerating at a constant angular acceleraxy 57m5j gkzh;tion of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an fddzb(r 7fw/w:1;6 pvtrt5 ou 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 decelera7kh7wf x4cgx2 tes with a constant angular acceleration 2wkc7 f 4xhx7gof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s while 5i)n:yxg+ 4,aaurn tn7d - sbhturning through 2.0 revolutions. What is the average angula nr+7n5dh4a ig)u xaysb-,nt: r acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to r-tp*4s1 :h dziic95d8zg)xfm8 ohqahe: xn 9lest over a distance of 115 m. What is the total number of revolutions the wheel rota4n:8h*d8mox9i9hxlt:ps -df )q z hc 1g z5aeites in coming to rest?

  A wheel of diameter of 68.0 cvw5/z6a,hzfe8 ar cqw(2z b h2m slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular a(2f,va25 zz/rahwb 6h eczq8w cceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over 50ua9dff ;8h6m uwkx3ir e+jharu6e53u0;kj +hwmfh x a 9dif8 distance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed ofc ubt6z*.c1,(kbmy su 3600 rev/min. When switched off* czy s. cu6kbb1(u,mt, it rotates 50.0 times at 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 require tightening to a torque of 90 Nm. If agfq22gvm ) f/mgi2jec 30n a;x 30 cm long wrench is used, what is the magnitude of the force reqxfc2 gn givam2f/03 ;gm2jq) euired when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90t)tb dggc5vl + 13fz7k Nm. If a 30 cm long wrench is ugkc+bgt 7f1z)l t53dvsed, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia 79)6l+ukjcb y)owrf l$3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mass m is at the origin,5zi81)w9v lzgf y0 zznc2kv7v mass 2m is 1zgv 7n9)y izlz508kw f 2vzvcat x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kdb+y 30 9ut9bpssi c7pno/z.u 5ocq; cg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force 5ptdy9o+39.cc ucz;s o/i b sp u0n7bqF1 = 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 mass 10 kg is pivotc2 yd-wr idr53ed 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. How many radians does the cylinder rotate through in w5 3d r-cr2yidthe first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one wii3.ya 3mc /b.0ap0 uue1qr tb+0egjend. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleratioi. bt3pqa0rm u3e wg+j1auc0ey/0ib.n as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a rind(yy s32vrj1py/c z1j sl(b6fg of radius 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 radiusy yj 1j31 (s cbs2ldz/r(pyfv6 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 a rope wrapped around a frictionless disk pulle7zy0os2 1e qcby of mass 7.07 kg and rade1ys20 o czb7qius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped ar ;vvifkrogk5 74ra w od4rk,14ound a frictionless disk pulley of mass 7.07 kg and4 144vkivwoo;rrkd 5g7,ra kf radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energ m.edvow yb3sax4q*08y. 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 ofcjbv*8(1 wc5g sx as:2xlnh4 x $5.00 \; kgm^{2}$ 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 roll :6e*6s mwis585yaax6 cxc svws without slipping down a 1.0-m high inclined plane. Wh5xsyv x iw: 6c6wa 68m5e*acssat is the speed 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 qfa5a2y ;pqiqvm0*n.nk u 6:t a speed of 10 m/s. How high up an inclined plane can it climb before :yvt;502qm n. 6aiap qnuk q*fcoming to rest?

  A hoop of radius 0.50 m and a mass of 0.2094v3qhw s+d dapmz8-o kg is released from rest and allowed to roll down an inclined plane. How fast-38h + sdm4oq9vadwzp 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 without slipping downe 9iwem aeg0*m5v:/9bno3v j)f(t ov k a 35e inn09k oev5aw *9mejt(geb3i vfo:m/v)cline 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 mo* 8 rw( mthl(uk,;irbeh,i+upmentum 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 inerfe ; r0wc2xsw a8ddj :-efm+/ctia 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 + lkz.u)umn84kyjd5d7v apz f1 s7mc(5.00 rad/s with arms extended has a moment of inertiam(a+zc.ku d)n87 uv7fz5 smk1y4lpd j 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?