Angular displacement is usually expresir aq7k(,wbguu, 8;b+ c7asjss in units of

  Angular velocity is expressed in units owd / vp0z9vn(uf

  Angular acceleration is express 6 7rv yxqbs,/ub,kegwr3eb4-ed in units of

  A boy and a girl are ridwzg7lk6x4 m 4jing on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is ckwg4mjx674lz loser to the center. Who has the greater angular displacement?

  A boy and a girl are :hx+o8 feohpt (vlxorp): 5a1 riding on a merry-go-round which is turning at a constant rate.p )fth+a5oh 1ovo px:ex(r 8l: The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning zaf ab5k72q8lat a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linearbl5z 28kq7aa f speed?

  A boy and a girl are riding a merry-go-round which is turni+8 3z bc.i8h6zgn cmdhng at a constant rate. The boy is near the outez+ bc6. hc 88zn3dgihmr edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are ri abl*a6,h5ckn-h xux -qpr ,w:y fd6i9ding a merry-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 has the greater tangential accelerauk66xrl -y : c*9xqiaap nb,wfh5h,-dtion?

  Consider a rigid body that is rotating. Which of the followi) vpjoq 7u*u-bng is an accurate statem)uu j*vbq7 -opent?

  Rolling without slipping d0a8uqtjx3: giepends on

  Two equal forces are applied ttiojz9kmct m k /h r7-ecng))x;(3*p bo a door. The first force is applied at the midpoint of the door; the second force is applied at the o*tm/m 7(e;hj3- xkt)c9bz icp) nkrgdoorknob. 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. The first fon5 rkz; uy +jvka/*u oh(zz20irce is applied perpendicula 0n5a+ iuu/h(zvjy;2kr z k*ozr 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 do;/ g nj;i8x:rvf a5*cjerz mc0t,r .bdorknob, perpendicular to the door. The first force is twice as large as the second force. Thzrgr;8tb/mfedj xcc:i * 5an.jv,;r 0 e ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to chahf nm4+ ,r6 dnyykdit .;w;cuwx9 56wwnges in rotatiodyi+yuf6x d65,wntrm k . w;;h9cn4wwn?

  Consider two uniform pqh pp y+y6ipn 9a1*ld+c 7tk8solid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of i1ypitlq *yd97k +86c+npapphnertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the sam3v uu;t1m8sy *g/ db-uz73jqe.e kcniz8)lgr e mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of th -kzu t3d)un3erc7u.z1 giq8e*gy b8;jlv/sme smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the g1 4+ vtff*5hh tp4apsdiameter of the other. The ratio of the larger moment of inertia to that of th54vsfa*p 41g+tpfhth e smaller moment of inertia is

  A uniform solid sphere has mass M and radieys6.,byl/ 8mfr 3i jrus R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central, ir 8/.3rym bf6lsjye axis?

  If a constant net torque is applied to aq f .wv- ;3v3px5rmxghn-c +gnrx7p+jn object, that object will

  The moment of inertia of a xwh)zg0r5 3 : ed4l8o02odvsl.ewfva solid 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 kine 30h: .z2 s4oagdo5xl )e0wvlv8efwdrtic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 10 kg o 4e ua/emohx)k:s8 6band a radius of 30 cm. What is the ratio of the rotational kinetic energy )haxms u4/be6o8e k:oof 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 radius R rolls without slipping down an in;/pbplcxsd2 0i h5: cy6aux0eclined plane starting from rest. The linear velocbadl0i5ph; x6xues 20/pyc c:ity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere oyora) 7jzm nrf nuxy6a:)d)6: f mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottomjmrnny 6)ay)r7)d x: : 6oazfu of the incline depends on

  "The total angular momentum of a system of particles cha;bz6*p p;0zfvms rr0 unges when a net external force acts ons*r0z6pfb;m; r0uzvp the system." This statement is

  In what circumstances can the angular velocit7 a(w/zb*l)vh*+vy eu psp4 vrw3uiz;y of system of particles change without any change in the system's angular momenhy*be+vpz 3;4 u(w rz )7l/uav*spi wvtum?

  The Earth orbits the Sun in an ellip3nngq4srfepl) 3u1ww.q /xyao ,1hc)tical orbit. Ignore any friction which may be present.gx 3 uncse/3)q)wl1npoy afq 4,w.r1h What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves c , ghdoz(gf,as8,d jyr )334qotjzyg9 lose to the Sun, then which of the followin9, d og3hdg(,t4, zaosfyj3 gzj) yr8qg best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin)4y xsbt3xn 9h.u4oee8 by pulling in his outstretched arms clusyne 4et4xhox3. 8b9ose to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pi8 fpc:jgm+t6p0x 7 rtj,xb jmq.dx72 erouette (a fast spin) by pulling in his outstretched arms close to his body. What happe,80dxxpx2c tej6bmjtf7 7 +q mjgr.p:ns to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pi.yx r a6bb.m/rhn3b/prouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his m/3xr b 6bbam.hyp/rn .oment of inertia about the axis of rotation?

State the law of conservation of angul mj2 xx1ghg n3yo 3urjb5/s0g8ar momentum.

  What arc length does the Earth trave08a mt3bl 8tzkl in a three month period in its nearly circular otb083zmkl 8 tarbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. 0u jqu0o7ix)dWhat distance does the tip of the second hand sweep through in 3 minutes and 45 secoux70uqdi) j 0onds?

  How many rad/s is 25 rev56.- d9lz,yox/fww 7or j hn;rv+ sgjzolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions ix8 *sss1z 3psmn 4.0 s. What is the frequencps8*ss3xsm 1 zy of the wheel's rotation?

  A pulsar (a rotating neutron stalm xre)i(d hpyhi+uc(p3q ,31r) emits pulses at a frequency of 0.40 kHz. The period of its rotation31lr pp i+(y3md(h cue, ihx)q is

  A phonograph record rotates at 45 rpm. Through *vr pxr7 *2ss,7xzecuwhat angle does it turn in 0.20 s 7e 7cxx,ss rvpu*2*rz?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the ouwxy82v57yrg. iwz 8 6wpe,zfgter rim move in 2y exwiy7.8w ,8pf z5zgrgvw62.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions inp 5eh rh+0g*c+3zhwzs 4.0 s. What is the average ah5he z* rcwg0 p+hz3+sngular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 xk 3yh+v.:4el j hea+zs. What is the linear spezev3 hxl j:++a h4ky.eed 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. The cable rfi4vs/ej)/+ n y f:u98a aftpwhich moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for thej pn +ey/a): 94st fufi8/rvfa cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a c k7ybq /8bn:bvonstant angular speed of 2.0 rad/s. What is the linear s v:y/7 bqbkb8npeed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m h 63:5 icvtc,k1ezcxcin length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of t,k3e:6vi t 5xhc1 czcche cord?

  A wheel of radius 1.0 m is rotating with a constant angu jqd5 8,o gn.o-q+d,qbo)wzdflar speed of 2.0 rad/s. Whajqq,o5g-fndoo +,)b .zqdwd 8t is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicyclgc226//hf*e s coyugtal ;3jr e wheel of diameter 70.0 cm when the bike is moving 8.00 m/s?lg/c *s t3 eay2f/ ;c2oh6jurg

  How many revolutionsyn9l xf 1+9vpa per minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravit9lp+ xyvn19 afy of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of rv.yg7ll10pcv .e,k3 1jgvson adius 50 m with a speed of 20 m/s. The maximum centriplyc.s7egv0 p. vv1g 3 l,k1jonetal force (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 ciai44 3e2e,tp hzjiee 6rcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction)e6eijtizh3p4a4e2 ,e 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 aroudzs)6-jrriu)qz ggj9hm i/ 30 nd in a smooth level table. If the maximum tension0-z 9h /r)u6gs i3r)jjdqgi mz 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 withoutniab - j0)a*fi slipping 10 m down a lane at 4.3 m/s)0fin - *aabij.
(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 wits5xal;9 jxrq m;lr5b1h a constant 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 wi gx +bfm 6j.rji)90tjith a constant 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 automobile tire rotatw)9bkxmp orl /7k 2k0ae after starting from resxoa/rkbmk)lk0 2 w p79t and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleratrenz60 pyy53 rion of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20( a2o+i 4k kdanii8ao3 rad/s decelerates with a constant angular accelerati(4nk i a 2+dk3oia8oaion of $-5.0 \; rad/s^2$. 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 ino*+ rh29sfv while turning through 2.0 rev*ifhvr92s o n+olutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm uh/9;p*:5it uzmfi9wy ujn 1o slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is ttz9/ umnuw:yu 51ijh fp9oi;*he total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows doh8q8q9r ol cwo2ay0 r3wn uniformly from 8.40 m/s to rest over a distance of 115 m. What is thor9ao02h 3 lqq8 8ywcre angular acceleration?

  A wheel of diameter of 68.0 cm slow tsd6vh).,hw,7 r caeus down uniformly from 8.40 m/s to rest over a distance of 115 m,h6.)7u t,v racdwhse. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory r y xd2, ymyuqu.i375gnotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before cux532 g, . yidumy7nqyoming 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 whzi(;o:z47gdq6 nj qib eel require 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 fog(d;z j qq7b:iinz6 4orce is perpendicular to the wrench?

  The bolts on a car wheel requir *l:l e;ld59oz9vrgpfakt c5 2e tightening to a torque of 90 Nm. If a 30 cm long wf5 g 9:*2zc9o5latr ;e vdkllprench 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 i0ht. v a,yre+f)htyi2a;ibf, nertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as fo3zc b1l/9geto,cl+bt llows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2co3 c b9e,/l ttl+1gzba. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted auzg p-wbo1++a 9aq8 afbout 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 forceo+fga+pb18ua z aq- 9w 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 ajtufkv) qs 0t).8q(2.uy cvke 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 myk)q0tue 2 sfv)kvj cu.(q.8tany 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 is initially held i9pj qdta 6i:k 6/jeg+op l.jsr4-cv /bn 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 iner+g4jpdckt9bjeq ail /j.:vp6/s r- o6tia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5fe0jb px0o.o4 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentia0o4 ob0.fejxp lly 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 wrapped arounp,uqfg:e2n 4nd a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the p qf gn:,4neup2ulley?

  A 1.53-kg mass hangs on a rope wrappj/sejn6 zoc(/ * q,jz* btepl:ed around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the accelj6zp eo*/tl*szn(bc q, jej/:eration of the mass?

  A rotating flywheel can be used to store energy. If it is requ;f p199y6vhu,lsvozlired 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 in8)poj x-bd7ax ertia 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 rbtp4jk8gv a+8adius 0.010 m starts from rest and rolls without slipping down a 1.0-m +a gpt bj88v4khigh inclined plane. 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 r -.s0ufyfx)94ypu j*wg7puaa adius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to0fu -p* aaf gp9sxy ).jwu4y7u rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg /(bz huy,cd/q :hhh 7zis released from rest and allowed to roll down an inclined plane. How fast is it moving after dropph/zqz7hbh y/,hdc( u:ing a vertical distance of 3.0 m?

A solid sphere of mass 1k*i yicy6m/x* lk-8l1 owdr;s .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 inerti6/cs ;1ldiw-y*rkl ixo*ym8k a 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 momentu01- wcmu .6n3dagco8 vdje6 f(vu mps2m 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 inertvyu ai (sycl:k(l+e -2cq)5rn ia 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 hx jvvfe*,pjhm 287,t at 5.00 rad/s with arms extended has a moment of inertiav*vhp j,82h7mx,j tf e 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?