Angular displacement is usually exp7d,sa3 zjtw mv5k+ ,zaress in units of

  Angular velocity is expha 308uya2 x)8vpzgk./omewnressed in units of

  Angular acceleration is expressed in u34*uyag. q kl(k6dobe nits of

  A boy and a girl are riding on a merry-go-round which is turning at a constant ru8 cpioq+y6wc 4+cye 5ate. The boy is near the outer edge, and the girl is c5c 8 4ccwup6oi+y+eqyloser to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round whicq -x1u9k61vryhk: *pmdoym o3h is turning at a constant rate. The boy is near the outer edge, ak y-qm 3:*y 1dr69kompo h1vuxnd 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 zx5.lr vc6q/ bturning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the gbxrz 5.lc6/vq reater linear speed?

  A boy and a girl are riding a me b7 47*6ngmi-srue qvhrry-go-round which is turning at a constant rate. The boy is near thsn qe rhbi6m*77u4g- ve 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-gqk4a2i,1vvqe3qb ;c do-round which is turning at a constant rate. The boy is near the outer edge, whil2idkvb;q v3 eaq1q, 4ce the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body thatero ew,3b9 yy dq4obc0/f9jfyx*d;t , is rotating. Which of the following is an accurate statbj9dbd w oeoxyryf*,eq t,0;94fyc / 3ement?

  Rolling without slipping q4a/7mi n29l6u9c1 ie 2fxyp+x whuca depends on

  Two equal forces are applied to a door. Thcm95ea;v 6q :j cwv)6aubz9 qfe first force is applied at the midpoint of the door; the second force is ava:ej q u; 966zfa9cw cbv5mq)pplied 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. The first nolp30+-urrg force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which fo grru-+ 0l3noprce exerts the greater torque?

  Two forces are applied k+5zpbw d,q hw nd83v,to a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of thewd3 ,85wzqb+ hkvnd, p torque of the first to the torque of the second is

  What is the quantity used to measur2 /j 5g+xf.t6fpg+z/8l dm d4pwyn kqrl9m3rte an object's resistance to changes in rotationky3 8dm/qgz6tw 5mfr/ 9ptfl rjn+p2xl+ gd. 4?

  Consider two uniform solid spheres where both have the same diameter, but oneql*0jcqgs y; 7 has twice the mass of the other. The ratio of the larger moq;j* 0l 7gsqcyment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one3zect)yok nr2807pvz . v 9jka has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the 7 p9. yvok2 3a)vtkej c8rzn0zsmaller sphere is

  Consider two uniform solid spheres wd;88e .l+i zk ohra5txhere one has twice the mass and twice the diameter of thez x5;ahdkt irol+88. e other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If 8 *zdxk f,njec,ttd fjzv68,5these are increased to 2M andc,ke5 8 t*,xz,6fdftj8d zjnv 3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, thatlr+aqufpu*.g1gvi45 n*n h/ y object will

  The moment of inertia of a solid cylp a-(*bf:q lku+:vh blinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to it(*ua f+kvq pl:lh:b -bs translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one whee h,r4 xjn,dm97yrdd:ol of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels toydxnr4 h, d9jr 7m,d:o the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M sy+n a-m 9fis0and radius R rolls without slipping down an inclined plane startingsm 0fya-9+ ins from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M an937 u.nvxwu momf3xk/s+ lg 2nd radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incliml .7o2f3wu gxsnx9k+ umn/3vne depends on

  "The total angular mw f0nofh).tc/omentum of a system of particles changes when a net external force acts on. )f/ft och0nw the system." This statement is

  In what circumstances can the angular velocity of system of p: cynvtnfsh .9/j o3n.articles change withovntfh9.so./ :yjc3nn ut any change in the system's angular momentum?

  The Earth orbits the Sun in an ellipti 1s*uflsncgc *:g)nz v)l2hx :cal orbit. Ignore any friction which may be present. What : *h2s)nlfl1:ugvnc*cs) g zx happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As thel6d6r18u mlfuh n,q +w Earth moves close to the Sun, then which of the followim +ull 16whqu rfnd86,ng best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstren8 9z:bs+5mwmw xowg3tched arms close to his body. What happens to his5xbo s9z8wn g:mw3w m+ angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretmap,rigr+k gtm j p;6.wphc1bx+7fqbw8p6 7*ched arms close to his body. What happens to his rotational kinetic energy aboub6;r t.7c ,j ppx+* 7pmg fwqmb6gi8r pkaw+1ht the axis of rotation?

  An ice skater performs a pirouette (a fast spin)c g4/(neg)pplahk/ 4a by pulling in his outstretched arms close to his body. What haplgp/hc a4a/) n 4egp(kpens to his moment of inertia about the axis of rotation?

State the law of conservation of angular mofu bj(5p4)l5rd:2zg pz fl2(s;lf y iymentum.

  What arc length does the Earth travel in a three month period i-z37im:h i :whe1t sxnn its nearly circular-x hiz1htin: sm7we3 : orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock hasv/zzsmx3ym43r3pe .z a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes an/m xy3.4e3mz vzz3 rpsd 45 seconds?

  How many rad/s is 25 revolutions per minute equxyflk; 14icq 3ivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 ldo d )/huv.s)zjck*8pn. m8fs. What is the frequencf.z )ndv)l*.pjc8 d/ moh us8ky of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Tiqdv i ;w3w338x ky/pxhe period of its rotation ixq;w3x v3k/3d p i8iyws

  A phonograph record rotates at 45 rpm. Through what angle doe4c8bspr 7l/rvmqq(ccsg t:98r 8 b v)ss it turn in 0.20 7c:mcv98 s4 pq8rtqlbsr/c8(srv)g bs?

  A wheel of diameter 26 cm t6*y ijunv5.t lurns at 1500 rpm. How far will a point on the outer r*nuvy.6ji5 tlim move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 sfshx sprh*g/at d uv w-9l+ 1m(y36j9rg9t 7bj. What is the a*hs7marl w3 9j(byudx h +r/9p6vjs19 -gttfgverage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 7dz 9kvino. 9prevolutions in 4.0 s. What is the linear speed of k idno9vp. 97za point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distancex8tw l3 er7:ee 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 mu etwerx:3le87 st 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 spepi l(n(e w4qi*ed of 2.0 rad/s. p iwl*(qein4( What is the linear speed of a point on the wheel's rim?

  The cutting cord on a ga0wy4u-gfu q(xs-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, 0g xfu4- uqy(wwhat is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating wg; 3zyalu,5rf(a 9)ui3zn crjs *y kk9ith a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's ri y)azgc f ,*ka;3lr(kjs5rzu nuy399im?

  What is the centripetal acceleration of a point on the perimeter of awgca7 c. o9u;f bicycle wheel of diameter 70.0 cm when the bike is moving 79ac;wo guc.f8.00 m/s?

  How many revolutions per minute (rpm) must a cirt7 04r,f)(+nq-djv mpnhfjl 5tq-y kp cular, rotating space station (r = 1000 m) rotat(5f7rd n, hy-jvl+4p)pmnf qjkq t0t-e to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a fujc jl;f3( snrb3x:7plat circular curve of radius 50 m with a speed of 20 m/s. The maximum jsnfcup 3b3l r 7;xj(:centripetal 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 circular curve of r/n *2hawv*c qi bqx9d9adius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fric*9qxn/ v*bq2c9d i wahtion) 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 around rkmux/(ezw+)lzr 9 p2cec; )b in a smooth level table. If the maximum crbu9m2(+z)e/ wcxz r ;e)kp ltension 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 z)bi fnf g1o/55)jodux8 ,llkafy /y,without slipping 10 m down a lane at 4.3 m/s.ba/g)k d lz,fyulof, 5xn)f1y oi/58j
(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 acceleratn:hdq -d4j.fyvgx 3v2ion 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 conyhp36bk s/ob xe-qhh c.*jo06 stant 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 auvn0jm94qa f2skp:zc :tomobile tire rotate after starting from rest and accelerating at a constant a249qsjmnvp0f k::a zcngular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acy1r6 4(evu f5atzs,cl ye:fn1 celeration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at + ufg4:7b;rimq p6kua 20 rad/s decelerates with a constant angular accelerat4 : u7r;+b qakiumf6pgion 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 whi/o)uy d-uja.ble turning through 2.0 revolutu/daj.) -oy buions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows d*3yx9sgt2p8ov58d ax ara t (lown uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel ro5 xat( v3l9ada8orpxy8 s g2t*tates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ov+/rpx 4 g4sxok,2qfaaer a distance of 115 m. gr a+xf q4akxso/4p ,2 What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformlyi: 52 ,fansgg 6/fyj f:r+qxxe from 8.40 m/s to rest over a distance of 115 m. How long does 2f,ixge sr: +fjy5/6aqn:gxf it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates ao:7ncgis* t*f d 92yvtt a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to rest.g:vd f* y*7ot9stn2ic
(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. j-drhk1pt1*8hvno x6 l di8:o rg df,3 If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicuthxkfop- rdjhg83 ,n*vd 1:8ol d r1i6lar to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cm lorr 2/chvf(/u /y l rfvga32 lm2x:0qpqng wrench is used, what is the magnitude of the force required when the force appl2v/r2:q x /cp2m/3l( 0lyvrar fuhfqg ied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertmkb4d fud 9t:*ia $3.00 \; kgm^{2}$ 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 orig9qz)g ubpy 53vin, mass 2m is at x = a, and, mass 3m is at x =3uvg9yp) zbq 5 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictiq+inn 1*tnw m h49ypyi, jl)e3onless axis thought the center O. A r+ *1e 4y) 9np,l n3qinwtjmyhiope 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 angular acceleration of the cylinder?

  A solid cylinder of mass 1(.muf3:-k:t u yqd;qj1buuft 0 kg is pivoted 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 the first 5.0 se-yuuk:m ffq q. jt1:ut(db;3uconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is inj 0w 8r;ulp9 eym 5chf8gy-sw(itially held in the horizontal position, and t 59wsmw(-ycghu; j8 ep 0ylr8fhen 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 about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius v./n +wue6 dce30 cm and mass 1.5 kg. Neglect the mass of the axv 6d+/n.cuw eele 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 it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frirh ze o)0l- p*)b2auu wnyp 9e p*rz:q2(tkge5ctionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleratiopeq( t2 p ge*y9uoabr2lwz)0 p :h) r5*-nzuekn of the pulley?

  A 1.53-kg mass hangs on a ropeuxdik 9qpl4+ 9 wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 q+pd l 994xukicm. What is the acceleration of the mass?

  A rotating flywheel can be used tly:7+v1gd lfuium 0y9o 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 inerkstpy/tv /p* /tia 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 starts from res/pnlf9 nbjg 92t and rolls without slipping down a 1.0-m high inclined plane. What is the speed of2 /9bnlnjg pf9 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 spe kg82a x )hzthqtt5a0x736e oued of 10 m/s. How high up an inclined plane can it cli7tzah8g3h xt2q5k)ox6e at u 0mb before coming to rest?

  A hoop of radius 0.50 m je ena( , fg;6y:+kgzum 7gg8vand a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fa g: z, 7nuagvkfm ejge;8y(g6+st is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm r3 jujrh.uw f18mi 9qy:iladw)g n5;7 oolls without slipping down a 35e incline that is 7. 7dm8o5uau9)jw1;ljifiqw3 nhg r y:.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 mos.m7erq3yg0 s x 4e5pnmentum 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 inertiar:kfl1m .8qsy1h t7va 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 zv 1rg brsgu.p0c;qwn0e r/ o)8:e8qdwith arms extended has a moment of inertia .s:gq/ )r 0 b8puen;1ed8wg0vc orqrzof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?