Angular displacement is usually express in ui8norga9 n 2x(, .8ujycuxx1jwagt 63nits of

  Angular velocity is expresse./l ov .dhbcsgp3m3 v;d in units of

  Angular acceleration is ex2 t/;ehlt4 y:b ezla2kv7xbt:pressed in units of

  A boy and a girl are riding on a merry-go-round wh;/wvt xb/v4 9cj wftm1ich is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular dj /c/mtbv 1v9ftx4w; wisplacement?

  A boy and a girl are riding on a meq 3d fo;si7u0rrry-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 greater angular sq 0r;3 sfo7uidpeed?

  A boy and a girl are riding on a merry-go-round which is turning at a const,tlsc +4.y-o qqq)zuv; ,gbowant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear speed?,uo-) ,y +ql.;qow4 vbqcszgt

  A boy and a girl are riding a merry-go-ro1 ..an(g (jjj2d/ hb,lql5k b+p acapqund which is turning at a constant rate. d.bkaj1p 2bj qpl5/ ,.hnajqca( (g +lThe boy is near the 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 i) /zt;iiy st4es turning at a constant rate. The boy isttyz/is;ie4) 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. Whicbfek/ qa36mi 3h of the following is an accurate statemenmbe63a3 ki f/qt?

  Rolling without slippx mfo+nfv7 5p*ing depends on

  Two equal forces are appliedkvdf : parm+d-1 e;o/wcq 4 -s 4mn:vxni,x*qk to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater to v p:xqq4e ;-*k oxnmri +:m4vk1w,n-d/fc sdarque?

  Two equal forces are applq 1 /axx1 9uxy5zbwan9 -yrvz7ied 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 force exerts the17 xyxu bwzyxa9v5 a1/n-9 zqr greater torque?

  Two forces are applied to a doorknob, per3n0cgt 3evq+rs +()dv +hu*qgy*yaue pendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the second isd)e c n*g+usegv3y(r +ha3 +y*0vqu qt

  What is the quantity used to measure v lyyt .*gt 7: hht87q4+zobgfan object's resistance to changes in rotation?8tyhl f 7vt +z4tqb:.go*gyh7

  Consider two uniform solid sphere2e+*(enkj3p z egrp8)rbyi+ 8,rs cfdtz y .6cs where both have the same diameter, but one has twice the mass of the other. The ratioj+z8ebn*yryrs d fec3. 8g,icp +6)et2 (krpz of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres dcay(8cmd n)/g-3 vyyaks33fhave the same mass, but one has twice the radius of thvdny/sa3)cyky ag3(38fdmc - e other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and 7r*j6pv4-b5z;s ;r6lctzaxm y6ndhptwice the diameter of the other. The ratio of the a564jsn6bvd* 7 zlr-r m;hz6py xtpc ;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 x b 4sul70b7xwn6bhs dxb230e are increased to 2M and 3R, what happens to the sphere's moment of iners0nwu7 blbbb43s27x6d0 x hxetia about a central axis?

  If a constant net torqu./m5sk;p6qxdpp y8gj;y fgt2e is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is kq4ia2pvx x:)/:tqj*o ogtb3 given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotation*o4/:tpo2tqxga q 3vkbji):x al kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg,21cfikvr8d+n dge v *- one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kidge28di*c1f -n +vrk vnetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphe 8 c(l5ok9( ioyashr:nre of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere as io 8l9( ahok5(c:yrnt the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an j1) wyz cb0qagj1l 2c7..vlme inclined plane starting jjc121)7yga l.e qm0.cvlz b wfrom rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a s0 pzty63uejr/ystem of particles changes when a net external force acts on the system.zp y3r/ej06u t" This statement is

  In what circumstances can the angular velocity2dwio9k )l:na k q/yy1mz,nhbk3;z* y of system of particles change without any change niw;,b9k /ldykah2m kz3:oq1y z )ny* in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction bo3oq8 n 0vitq,ybrj93vk, ; awhich may be present. What happens over time tok9yo vb ,boi,3jr0tqn; 3a8 vq the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in/b ogvoxul8 4c+dh 1)u an elliptical orbit. As the Earth moves close to thulhvdocb /og4+u )x81e Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast s6xbibxs 71n2 i283utt thyup3p5sc fcc;uz35 pin) by pulling in his outstretched arms close to his body. What happens to his angular momentum b35u21u i2s3 x67; 83i 5ysnztu bhtfcccptxpabout the axis of rotation?

  An ice skater performs x1y6 sxb+3la 5xn mbp7a pirouette (a fast spin) by pulling in his outstretched arms close to b p x7l3n1s bx5yx+6mahis body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouetq7,pf*zg1gk:9o+i i6v cm t+lyih+lfte (a fast spin) by pulling in his outstretched arms close to his body. Whatg7l:c+kt*9q+vyl i mf 1+if ,h6zpgo i happens to his moment of inertia about the axis of rotation?

State the law of conservation j;c. 92e4qui9nthq g xof angular momentum.

  What arc length does the Earth travel e3 , g3rfbunv*in a three month period in its nearly circular orbit about the Sun wiru ,*v 3febgn3th a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance doe u;i7czdb au(2s the tip of the second hand cz;du2 ib7u(asweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revord0tka0hzqn ,0 n5nj n:bq 96llutions per minute equivalent to?

  A bicycle wheel rotates uniformlyi q ;qznhij6 y926jfx/ through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's 2h6qy9jz 6xiiqn;f / jrotation?

  A pulsar (a rotating+14t q zql089b;pwni zm r 1*h.7)yieimjoxje neutron star) emits pulses at a frequency of 0.40 kHz. The period of its ro qmh 4jjepw. iz0ol bytn; zm*8iqx )r1i1+9e7tation is

  A phonograph record rotates at 45 rpm. Through what angle d du2lrh*j r(57s1qg m,og8bjgoes it turn in 0.20 db*m18ur hgr7 5qj2sgo, j(lgs?

  A wheel of diameter 26 cm turns at 1500 rpml6 jyd89,lp qm. How far will a point on the outer rim move in 9y8q6d lm,pj l2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutionsh(2(n+ybnhp 7pt60cxm0 sqb t in 4.0 s. What is the average angular s7t shptc(+xq 2p0byhm60(nb npeed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What:s jkurn g1r )1g9ws./ 5cyczp1en4 qr is the linear speed of a point 0.10 m from the c11 )rw.pns z usckgrj:gqr1y45n9/ecenter of the wheel?

  A cable car at a ski resort cac)( lzte oie:8rries 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 : 8te(zcleio)fast must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotatingn n0 )o,ip)sfg with a constant angular speed of 2.0 rad/s. What is the linear spee ,p0oi)nns) fgd of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length/f(r8:fvzey b,x v3o6/m l sqfah 7ay(. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the ea o:z 6/yv8lq (a,3hv7frmeffxs /b( ynd of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed , u9i7mq9lxm xof 2.0 rad/s. What is the centripetal accelq,9mux9x7 mi leration of a point on the wheel's rim?

  What is the centripetal acceleration of a ivh 9zxup(vmq zan 8,a/.7 1tzpoint on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.t vnzv( 1m za,u9h78q/ax.zpi00 m/s?

  How many revolutions per minute (rpm) must a circular yh: 3fky4u,pbv+7dvl8 zm6n t, rotating space station (r = 1000 m) rotated8fuym3+yv47 v:np,tkz h l6b 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 of *qr ,g34l;p8 te k7w/kyswnwo20 m/s. The maximum centripetal force (provided by static friction) i8g k*prtekwo y/l qs7ww4n;,3 s $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat cir;a6mgm80:8e ahq yxo*rdpe c(cular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (o(q;xpaeg 8me 8ra*hmd6c:y0 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,w qf 3ktj-01oj o8 rfsw4(pou4 is whirled around 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 so4ow uwfr-(8foqj013ks p4tj tring is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls on1l2kp.yzpg- 1koj*qw w54oyt4 n a2 without slipping 10 m down an*k1gpyl24 4z5w-pkt j2noy.ooawq1 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 angulag r./dm ehu.8pr 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 cnd*tv i qq26t0b;pl fsx:49 aeonstant 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 :0q x9zt3jjwsa 0.300-m radius automobile tire rotate after starting from rest and acceleratinxwtsjz90 3: qjg at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has 1ob, shbyo 5.sr65 ye4m6hvv0*hu jnhan 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 constant angular accd e2hqqh(f n0xpn ,e02eleratio ,q n2q2nx0phe0h fed(n of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from regtyqtpp5 -d-m: i;h .z3b2yjjst and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutionsgjjd--t . :b hm2zypipqt35;y. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows d44/usypmk5yka r*6h down uniformly from 8.40 m/s to rest over a distancuakd/ y5h m6rp k44y*se of 115 m. What is the 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/s tol7cc6;yfjd - i rest over a distance of 115 m. What i6yfij cd;lc 7-s the angular acceleration?

  A wheel of diameter of 68.0 cm slows down u8z/sutyb - +,yu1 y(tbvma4n ;suxye1niformly from 8.40 m/s to rest over a distance of 115 m. How long does i4z+-, txeu ba/nym(8 uybyy t1;sv1sut take for the wheel to come to the stop?

  A centrifuge in a medical laboratorp 0nu-(jqvlm:b zf7d*y rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming t*7j0 p-nl: (bvmdf uqzo 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 ts r3 * ww)em)xxoob+d0orque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to0rso 3 xo)d*be+w) wxm the wrench?

  The bolts on a car wheelqijxl./*6lb f require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the foxq.ljbif*6 l/ rce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertiawsm.g+iw f8h6/dk 2z)q lvgu/ $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled a6+.ri z*h.c vufychq3s follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about zu* hq+yi vc.crf3 h.6the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionleuo65+d8 zx8du- jxedjss axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N tu6xjd8e8dz 5-duo j+xo 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 pivoted about a -a+cjq z9 . mpb9 mooj1iw;p 724ikmspfrictionless 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 rs ;+jo7i9zqm9- ajp1p ibw.k2co4pm mope 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 endp cc2 xd f.k(qjs )e(ffa47nt*. 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 about2(a)jf.cqe*4 px f ksntf(c7d one end is ML2/3.)

  Consider a bicycle wheel to be a ring offwb u)j;r(;.ua 1zd 2g6 qjxnx radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N i( wgzru;qjjf d;xu6n )xab1.2s 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 a rope wrappednk 1mf5kufelaa 343)k around a frictionless disk pulley of mass 7.07 kg and rae3)f u3a5kkfa4kmn l1dius 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 pullw,wu7vj/xj p;ek-x.w7 j a;u dey of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the j -paeud7 w ;7u jwvwj.x/k;x,mass?

  A rotating flywheel can be u lq.x: y(i)j)mof0i) i7bvzmased to store 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 inero 9reup ::-2qlstcx 6wtia 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 an , 2srx.lehw:ng twzwey/ 7-jt9 ss/;ud radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plau9 slgt; xjzww2t hwe:,/7n-e s.r /syne. What 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 a speed of 10 mzqvwa,t jwe0z-mo hv36 b2p+ ;/s. How high up an inclined plane can it climb beforeqw vh+a tob,-wzzje0v3p m;62 coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg i,g/s6) lrrd*rsh pwa8s released from rest and allowed to roll down an inclined plane. How fast is it moving * d)p 6ghssl/ar8 rrw,after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a 3:d8njufhs7xh 22uyw*gbs(x/5e /dyx* sfj( 8u2nbh: gwx7hus2incline 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 momentu-e1yj x* jtx7jm 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 inertid9tdqngp: )knq*m/ a; a 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 i 0ru0awhu(1vgy(nsu- nertia ov(10ur(hg aw 0nyuu -sf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?