Angular displacement is usually express in units m :kt6k0l;zu m+mg,vm of

  Angular velocity is expressed in units of0,f)rq76cdb)b t ezzig9n 1fq

  Angular acceleration is exp5e hql.6,g5jm0n) d lnpj)v5glrp;biressed in units of

  A boy and a girl are riding on a merry-go-round which isg40m: gt/5wyte k5 pnw turning at a constant ratmw4gw/t5ny :t0 5pekge. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding (fotfyd a .*f*keg+i( on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and t.k*(g f+ftio(y*a dfe he girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-rounwr60lm5-mk17yymlpwtjo:x h 1 muf4+ d which is turning at a constant rate. The boy is near the outer edge,u+ -mpm6omtwyfj450kmy1 x7 wh1: rll and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round whi-cxaxd8 m5fibk *69 wkch is turning at a constant rate. The boy is near the outer edge, while the gird69cw-f*im8 xkbx a5 kl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-rzy1c*m 1ie0ji9rlxmr )h wx p 6la),a)ound which is turning at a constant rate. The boy is near the outer i1 l l6h)0a, wrjxx91 )m)raypi*mezcedge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which /,kqjv9vs 4v2:ee *z/bql; gw am2kfqof the following is an accurate statv,:v2qlkve 9 zfqqbj 2* /am ;sw/egk4ement?

  Rolling without slippiaxoa3 ckejt 8)3b 8o-q/t, o4l9k xzxrng depends on

  Two equal forces are applied to a door. The first force is applil fz2bfjz+/ :- uyfyh1 / mvdm+-3dhiied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpey fv/ 1+zzfu-bjd:m3lim hy-hd+f2 i/ndicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first forctj.p rl1,tyk6o(mb7e e is applied perpendicular to the door; the second force is applied ,b 7ptrjt k(. ml6yo1eat 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendiul0q1lthb-f 7 u :0o 0)tv4hdcl7 wccacular to the door. The first force is twice as large as the secondtduvcu hb0:co faqt0h l-l)c0 4l1w77 force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure anv l5h:1g -j)rudxmx,p object's resistance to changes in rotation?d-rxmj l 51p:uhx,g )v

  Consider two uniform mu(yb1z d g(5gsolid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that ouz(m(b 1g dg5yf the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius xyhska(j6s:4 7ay,s7hvv i ) cz8r6ol of the ot6ss vckz, yh ao7:j) h6(s8 raxv47lyiher. 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 twice the ry:qxip.g w 00diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of g qy ip:00.rwxinertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2M uqun /j)mcv-8 of7w exhy1s8,and 3R, what happens to the sphere's moment of inertia am/ uwvxqhe,j )fy8u18c o sn7-bout a central axis?

  If a constant net torque is applied to an object, that object wmhp(cp8a *:1iburo) r,ygep) ill

  The moment of inertia of a solid 3zxpaa0y)c cjkh6s: 0cylinder about its axis is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass ;krhy -wr-n9z 150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy ny9;r-w-kzhr 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 6 samv6re1ud. vwm(q0 radius R rolls without slipping down an inclined plane starting from rest. v6u 6q(10rm vamews.d The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius b f16hfl1 i76tz0 xkbxR rolls without slipping down an inclined plane startiflf 6 hbxkb7 x11t6zi0ng from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a sys+m u:iqiz wg44 u1t/qhg/u 8xqtem of particles changes when a net external force actsi1t:u4mqwhi gg4 q/ /uzqux+8 on the system." This statement is

  In what circumstances can the angular velocity of system o*vq .1wios**8tm y suhf particles change without any change in the system's angular sv1*h m*su. *iywq8tomomentum?

  The Earth orbits the Suz/*rgo1 xpd9 ice p5v/n in an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about the Su95reivc zd/pg1 xo*p /n?

  The Earth moves about the Sun in an ez0gu84 k/ jlh2cwjvp (lliptical orbit. As the Earth moves close to the S/z8 402kwvhlc g(jj upun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fa 808(rugu md d :.bq0:bzh3igrh0zsrlst spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the g00 drl: (zb8hsum rq.:dzi 0rh8gbu3axis of rotation?

  An ice skater performs a pirouette (a fast spin,p i k-)15aght;uwjs t) by pulling in his outstretched arms close to his body. What happens to his rotational ki)5 ;u,jw shpktgt1i-anetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretz1d7v5km4owo2 wzr y d 8*hwn;+ymg am328oyvched arms close to his body. What happens to his moment of inertia about the a3o2wo o2adz;m 8vy1*yrgdw w mn+5kh8y74mvzxis of rotation?

State the law of conservation of angular momentume sbt;9+atm 8d.

  What arc length does the Earth travel in a three month period in its nea.3 cw1k9y1;s,swflhp,sd qii rly circular orbit about the Sun with a radiu 1 9kl s;i ,1wf,ydpiwqs.3schs of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a l4w4:i7wgo ocmength of 0.30 m. What distance does the tip of the second hand sweei:m cgo4w47wo p through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per z0+1 a -yhj0 mki1fpmeminute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.+u ax0(jp;hbrnn + g1i0 s. What is the frequency of th1uxingj;prnh +a (0+be wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 zz 8 zauv3)v s4qzuc80h ).txq)faepccv::+skHz. The period of its rotation 8h))avqstvc.: 0z3a:z+vfc e)zp4 sx uz8ucqis

  A phonograph record rotates at 45 rpm. Through what angle does ib-3.z/jdil 9gpo o(ijln k.0it turn in 0.20 sgoo l0(in 3jii.d9p- zkl.bj/?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a qpz tbok6a(cf,1/ lf4point on the outer rco,a l k1/f6(b4 fpqztim move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 rev9dn* bc/qjvc/xoso 52olutions in 4.0 s. What is the average angul oj5s bvx2c*//odn c9qar speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revoluti1w l0( l44rh((zhakts )r sqdmons in 4.0 s. What is the linear speed of a point aswm( t(lrz)4l4ks hr 1d (q0h0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. 2, wy xy3t*mkc The cable which moves thc my3*tyk2x, we 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 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.08mvg dh-)e8viu b-u4p rad/s. What is the linear speed of --u v8h v84pbd )geuima point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. I:vm pwfy5 -o+bf the motor rbmv-5p+wf yo :otates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad dy8k -t k39jngb6fofnx6(c /v/s. What is the centripetal acceleration of a pd9fj6fv8bnk-x(/ 6 tc3gk yon oint on the wheel's rim?

  What is the centripetaed w fij kn/npd12.wxi0 1.ky)l acceleration of a point on the perimeter of a bicycle wheel of diameter 70.ed.1i)2jdpy1x n .kf0k nwwi/0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular,,lg b ky:w6c2c0e7cc f rotating space station (r = 1000 mg fl :cc7c6kcey2b 0,w) rotate 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 2j o0(ripvk+5p 0 m/s. The maximum centpk r0+io5j (pvripetal 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 20 m:e*dtdo5ai56 cdt 62 yats0ke/s. The maximum centripetal force (provided by st kcde tddt*o52t0 6asyei6a5: atic 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, is whirl hvd*0oc 7qdv5ed around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed dv 5*c0hqo7vdcan 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 slippin0w 5rcovc.( f;6fq2o ygrvm ral k8j.7g 10 m down a lane at 4.3 7 ;.(yk0rwj6v. gra8lrv2co qfmco5f 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 d7pb9oz y1;(*n4j ny:9akad9r urh uaangular 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 angular accel;qfef,ptfxt3j z f,+5- nkcnuc.*q o/eration 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 rotate after startingjpqu+h 7+zl0lepis4vvlw -;v+j,ed) from rest and accelerating at a constant angular acpl4; ulzs+ji jd,7vq+vhw0l vpe-)e+celeration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accele3)p a:go 5ztydration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s declw8, dzb,p-cghg-3r ,;tbu leelerates with a constant angular accelera z;38grbp,-c btu,gld ,h-lew tion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest an, vvk 7wet91r*2qxlird reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular accelerati1v q*x lvr2rtei 7k9,won of the wheel?

  A wheel of diameter of k2lp*ovrmd;qu24q8 p4 je(gs 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to rpl 2 rusd;84v( 4oqpemkgj q*2est?

  A wheel of diameter of 68.0 cm slows down uniformly f0 fgxn(:hx)y/l6ldud- ,0guk qzf8qfrom 8.40 m/s to rest over a distance of 115 m. What is the angular acceleration?fqy:0zgluf f(-,) /6 u0 dxkh d8xqlgn

  A wheel of diameter off4 ygi4, bqe44meuke3 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to t,eu y4 geb 3i4ef44qmkhe stop?

  A centrifuge in a medical 5.3u czw tmxz3.h+wg mlaboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration bef5wwxtmm+.c.3 h3uzzg ore 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 r9-yzai8p+ zuocon 5 l3xea8n- equire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what isc8p n-+xaz3iooy5u al -9n ez8 the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightd z88mmz0mvtf2n y-(-h)nh a8vrh- qaening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requiryv2 )-m(rhm0 -fztdvqzhnn h 888a -maed when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of i :vyjwpz6ws48ucn 2 ,fnertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is mutz 69e ,zpg:zodeled as follows: mass m is at the origin, mass 2m is at xt9ez:zg,u p6z = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axiu6 tnni ;c9j/bs thought the center O6juibc n;t/ n9. A rope wrapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a fric 2pky 72sm3zu4jopylcom c)ity g)k1n1o(4x,tionless axis thought the center O. A rope wrapped around the outezs go3un4,pimol xc cp 1ko2y7)my ()k2 1yt4jr radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 oz.kxn4/c,/ pb9xfm-st c, f w2znc gj5ne end. The rod is initially held in the horizontal position, and then released as the f-5z wxc,ptn.j/xckz, sf94b cg/2n mfree 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 30 ok8 v1es1g-ttq7o/lccm 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 4.1 s, what linear speed does the wheel achieve, assum/ 7 -tvq1scgk ol8toe1ing it rolls without slipping?

  A 1.53-kg mass hangs on a ropzpaaa w9-i*psth + ).be wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pu +bhpa-) tszai .p*wa9lley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley 68 g+kuqfg cg8 j3j msaieg3add :2b0.of mass 7.07 kgc jbg2306a: f kgja.3di+8dgsg m8u qe and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it ilnq9- qc9bq9bb6v2* lw ty5ias 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 mp- 95:opwg8(qn/bo z msw m4rinertia 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 0.00c urd+hd/rv 010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What ih 0v+0urr/cdds 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 ab8m*uxlwjd8)li4 i*l y 9c+hm rolls with a speed of 10 m/s. How high up acjly *l i im8x+l98bw 4u)a*hdn inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allow byk+w lfa7+qzvfy;fjzq; 24 2ed to roll down an inclined plane. How fast is it mozj; +;kq4+z a2 wyfv fbqyl72fving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down4 vc,(rats na+(oj6cr+e.hzc a 35e incline that is 7 e h+a4 ca(s+6.roj v,ctrnc(z.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 momentum )6q(eg crhj q79szm8mchanges 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 momentp1v+ xvu1ml+ q 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 a6 c f8(arc/brarms extended has a moment of inertia /rraa cfb6( 8cof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?