Angular displacement is usually expr0 jajnjaxmwq q+5158pess in units of

  Angular velocity is expressedo;m6z tr*kp j5 in units of

  Angular acceleration is expressed in units 6pmh-e ) 9ssk5fwtopw3r (d1cof

  A boy and a girl are riding on 7ypw7t/: x pbya merry-go-round which is turning at a constant rate. The boy is n7w/tp7y : xypbear the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding -th7ep / bxgs +c,/sfoon a 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 has + cs7xeo,/bf p sh/g-tthe greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at am+ kks936 vii9gnxx) ke7,wbv constant rate. The boy is near the outer edge, and the girl is closer to the center. b k7e,s3ixv9g kx6nv+mi)9w kWho has the greater linear speed?

  A boy and a girl are riding a merry-gmxxh5kjzn69g k6q 3rs. tvodn/.k a :1o-round which is turning at a constant rate. The boy is near the outer edge, while the girl is clo1g.k6 kv6/.a3mx5rjszot qnhd kn:x9ser to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round whichy8 4pkyv/benyr6m18g is turning at a constant rate. The boy is near the 1 pg yr68 b4vk/yny8meouter edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is ay0r u6 -ecyk-pn accurate st-u6p0-rkc ye yatement?

  Rolling without slipping depenbrqkg8 mu 2jk60pry37*/j meids on

  Two equal forces are applied to a door. The first force i 5b /kh7)jgt, 5h)ynf7bhg un8rp)mpys applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to tfmk7)5jg8,rbgb) uhh )7pn ypt/hn5yhe door. Which force exerts the greater torque?

  Two equal forces are applierh*r- g9sm,x pd 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. Wpgr-m,hrx* 9s hich force exerts the greater torque?

  Two forces are applied to a doorkz tu/c -)zo8spni9, uqnob, perpendicular to the door. The first force is twice as large as the second force. The ratio of 9itu)nscz 8opz/qu ,-the torque of the first to the torque of the second is

  What is the quantity useh83 ptgk. vx1-pita.md to measure an object's resistance to changes in rotationv atipxp-m3 8h1.gtk .?

  Consider two uniform solid spheres where both have the same diamco s).y7h3zn seter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment o3h c)sy zno.s7f inertia is

  Two uniform solid spheres have the sb8ql,/9i2oi l8 9r - goepbzly cp3af6ame mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of qplr y8a6i2i8gb9,e9bl /-oop3 lfczinertia to that of the smaller sphere is

  Consider two uniform solid spheres whe9/5b lh dasqf1re one has twice the mass and twice the difq/l9d 51ha bsameter of the 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 a(4q s7x; bzpi3 va jwmkwaf;/y9-(mlthese are increased to 2M and 3R, what happens to the sphere's moment of inertia aj/lfqaa a-4;i3b m;(m7 9(pkwsz w vxybout a central axis?

  If a constant net torque is applied to an object, that object w /jvj) 3 xca6btfl3h7dill

  The moment of inertia of a solid cylinder about its axis ie)fc;e8 kr bki65u+jos given by 0.5 MR2. If this cylind)ijb5 koc+8e;re fuk6er rolls without 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 ,-vgs2wtrtd c8iz544 ,mmjs e of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of -2 s g,jvt4zwst,c84rm5e midthe bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R roiwvzcxb.4q5 5pu p.2z* -c.oqvd9jti lls without slipping down an inclined plane vu54vpo.tx5bd.wi p2cz. qiqz*-jc 9 starting from rest. 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 h 2btz 9(*y qlozj,az9without slipping down an inclined plane starting from rest. The angular velocity of the sphere at bj(2, ahtzo qzyz 9*9lthe bottom of the incline depends on

  "The total angular momentum of a system of particmzelp:83 t4ym q ;tpp9les changes when a net external force acts on the system." Th8t ppte:p4 ;q3zym ml9is statement is

  In what circumstances can the angular velocblv ,6qcpa5f0ity of system of particles change without any change in6fq0bpl5v, ca the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit.9qbz7 7 q4no zdfqyn) ,n2dee: Ignore any friction which may be present. What happens oqez,e :ondy 9 )n27bn qzf7q4dver time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. z6cye tivz)(6 As the Earth moves close to the Sun, then which of the following best describes the orbiting speed ofc v( yetzz)6i6 the Earth about the Sun?

  An ice skater performs a piroqbhg/ 6a:fh: 9j dqom0uette (a fast spin) by pulling in his outstretched arms close to his body. Wha: :fabq/q 60hoj 9hgmdt happens to his angular momentum about the axis of rotation?

  An ice skater perform f9:2,h9zxhn8-met h:bb dywws a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to he9f2w hy-wm: ndhb,t zh8 :9xbis rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast sp7k)ne c2- jgbudc 0 lvmp,h/l4in) by pulling in his outstretched arms close to his body. What happens to heud40 ,g/k- b)chncm2vjp ll7is moment of inertia about the axis of rotation?

State the law of conservafy b y,*9+jcvg q*0khotion of angular momentum.

  What arc length does the-f3br kb( mr6x9fjd5i Earth travel in a three month period in its nearly circular orbit abo fb(3mkrj r659 fixd-but the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a len n31cb*.zys ymgth of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes bzy n*s.3ym1c and 45 seconds?

  How many rad/s is 25 revolutions pers5* zv5t5gue9z s7s ze minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolup3vjw 07 6s3jl cg8xhitions in 4.0 s. What is the frequenvh76is0plx 3j cw3g8 jcy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. T 1 xfyi n.,tfrf*o9rc;he period off r;9icfnr,fo .ty*1x its rotation is

  A phonograph record rotates at 45 rpm. Through qs,ls bbcpol025w k.s1), oduo0tw: twhat angle does it turn in 0.20 s?oolldc0:)25 .,sows,t us pt0qb bw1k

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on xxo s3rh50lv+ the outer riolx 3r+0vxh s5m move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. hb.7/ mvx, fml1f9x)kgz4 yp f l;gkc9What is the average angular sp , 9xcf)kg.mmf7 1kvxlb/y9pz lf;hg 4eed of the wheel?

  A bicycle wheel rotates uni900uxe2tv i8kiuku0j0 +; ljfric5 n nformly through 2.0 revolutions in 4.0 s. What is the linear speedi0uejrkvu;95x0l nuinc2 + fk0 j8 i0t of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort q/2 ifw u tol6dk-dbs0bk4*/r carries 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 fast must th0d-k2 ub/ li td6*r4qkwso b/fe pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a cw5/*h83e ac5(b hgozzcey ngo)nq x. 1onstant angular speed of 2.0 rad/s. What is the linearyanx8ech (og1o 5e bw 5z.n )gq3hz*/c speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If t(vvb*eyhe, 52lz1u lmhe motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the en,2le1uz5vybl e(m*v hd of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed o0)kvdlxvx1f9 )h zu6af 2.0 rad/s. What is the centripetal acceleration of a point on the whk xv1z6 h)dv0)a 9lufxeel's rim?

  What is the centripetal acceleration of a point on the periesx+kha n*-5tmeter of a bicycle wheela-hk+tn x*s 5e of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space station (rl45yo n+tx b4wt:pht 4 = 1000 m) rotate to produce an artificial gravity o oxp+ n4bt5hl4twty:4f $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speemyng nufc 673uar f/y:f:qx2/d of 20 m/s. The maxim/f/xqy y af n:fm2n r6uug:7c3um 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 radius 50 m with a speed of 2+ 9wqrhmpz6h2hs )so70 m/s. The maximum centripetal force (provided bm+h26 )ho7 sswp r9qhzy 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 stv ne,5*+a f+cn rq9qptring, is whirled around in a smooth level table. If the maximum tension that the string can withst,q59+ ceaqnvr n p+ft*and 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 without sl nm fu jx(0hum+opz)(,;vhdp0ipping 10 m down ao0f ,z pv 0hjmud hn(+)mu;(xp 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 anguvlot ksa(:*x-o7m zig)lt/ .olar 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 constant angulae9evv t1+, kf sj-y0twr 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 radiusjo 4c dy6poofz9.cywb jrx/f;g- 1, :p automobile tire rotate after starting from rest and accelerating at a consbg4opjryw1 fdo-o;6x/cpf y ,j9zc.: tant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angutf o/*fzxm7s( 1b/mgilar acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s l2l v3xvt ji(+decelerates with a constant angular accelerationij l+v( 2txvl3 of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angularx:nkp3l,.eot-j v+im1n mj 07f8lm mx speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular accelerati3tmm0j87en+1:nfkm m xil ,xvj .lpo- on of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s tfeikgob; )dv(63a)k; s o05vqqunz) no rest over a distance of 115 m. What is the total number of rfqg ) o)q uk;avnv5ki( ed)s6b3zn;0oevolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0gnq)7w:. btpg cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular abpgw7 .gq: tn)cceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s tokz.4+(ot/g yzrkun la .e1kx+ rest over a distance of 115 m. How long does it take for the wheel t k/.+o uxryazl.4z (eg1tn+kk o come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed ogxm 3f.hso g.+f 3600 rev/min. When f. oh.+3gsmgxswitched off, 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 melh u0.:fkd d90 ly em 5om/j.c/dh0ptorque of 90 Nm. If a 30 cm long wrench is u.uel :o j00mypfmdl9./k d 5 dcmheh/0sed, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel rs0v. ;-m 8shpiiz+/ rf:jjzip equire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when th:/.pi +; -ih0pzrfvj 8 mzisjse force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of innqacze t.*)4 e c87syod -:hufertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as syw: 5xb*m5* fa mze+wfollows: mass m is at the origin, mass 2m is a mwb55 m* ze*wsyx+:fat x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of gxy f 9.k4igej0 u:)de u/. obodbox71mass 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 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 cyl0e 4o.xe/y9go: i7) u.gukbbd1jox fdinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thoufr5,hwjcr 5 )ql 11tl,rqh, nvrhnx1v6oyz 60ght the center O. vyntnrr 0hrr oxc 5h,6)j16h51q qf,,wzv l l1 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 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The un3o9(6 qf7*5j n0zfivxnky ayv* in*rod is initially held in the horizontal position, and then released as the free enju6x*fnvz(7nf3y0yn ai k**q no 5vi 9d 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 rinwcs (l y*brz5:ks9zjue sy9;*g 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 radius 4.0 cm for 4.1wuz(;*9lsz5ey s*sj ryk9 c:b 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 dih x,2;g,upuf)2 rzar p8jp*od sk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of tu p)x8rz2o ,2pr, ufjdag* ;phhe pulley?

  A 1.53-kg mass hangs on a rope wr: 2jm fi dad;pj 5nx250fsfnj*apped around a frictionless disk pulley of mass 7d0pndn 5fm fijx2 2sj:afj ;*5.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to1*0eo.m+vhrmwm7i m w 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 iner+ aprg c9+7hwwvmp+k )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 masgg;;z1aqx 3gd s 1.0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of theg;1;z3 ggxaqd sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 ka,upov 1qqyqszv sm0w+617 ki5v2w .wg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it clim 1iqvswzwk ys+6,1q75 mvop a0.2 quwvb before coming to rest?

  A hoop of radius 0.50 m am9mqf(myzn sk3/c 2x 6nd a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it mym z6m cm39 2f(x/knsqoving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and rg mazpw 2l- w; uzjyc*v: 3:e(kz+hd+xc3e-spadius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia +3p-j:; *:hczgd zv uwpsek23l-+z(mc axwyeof 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 momentum changes by 0+7f wito3- 1m(v- eaymb zoqs$20 \; kgm^{2}/s$ 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 momentx tump 0on5s b3vps(qun1w *e.j 22z1e 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 hi0g(qy c0q: kbas a moment of inerti:0iy b(qq0gkc a 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?