Angular displacement is usucx0: kfa.h.1w0wq(zvgs- r) fh)z a0dg juwv6ally express in units of

  Angular velocity is expressed in un cclt;b+v*o1;ukoz, gzxu1 2a its of

  Angular acceleration is expr5 cqh/;3vw3ox( 8gr9 zxditxqessed in units of

  A boy and a girl are riding on a merry-(o0 o )bj(dcr ripx5z3ds/j/ngo-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer tc/)/ j(iordz(dj3spbonxr 50 o the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-rounv 58sddp /fr2yd which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the centes rf/8d2d5 pyvr. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-roun74n l4 24g9bwp lvikgutiuq7;d 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 greati4g 77 lup2g4itk ;nblw 4vq9uer linear speed?

  A boy and a girl are riding a merrytza;zai b kj- i33u,u.-go-round which is turning at a constant rate. The boy is near the outeruia u bj-3.z3az, ikt; edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-ko)w lz *4yr6m:k8mlt go-round which is turning at a constant rate. The boy is near the outer edge, whilem)rlk: yz*6kml4wto 8 the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of )vq ia);9e,quipfbc )u ,xv; bthe following is an accurate sta; ,p)e)v,ixacbvu; )qq9 fbu itement?

  Rolling without slipping depends onr pr 7g5j,elv (u*bjxmir4w h5m..*hx

  Two equal forces are applied )p d1s8 srn,u2x :gweh-q;z1kd/ufd yto a door. The first force is applied at the midpoint of the door; the seconddx phdu1 1s: 2zqedr/ )n-y;uks8f,wg force is applied 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 doorkno8l tcun0xunke 6w 266hb. 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 the gru6nh 6n2 ke tlw8cx6u0eater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The first fxfp+x0z2p c5* y1iejw orce is twice as large as the second force. The ratio of the torque of the first to the torque2+ xypcp 5ef10xjwiz* of the second is

  What is the quantity used to meas kk;tatgot7q,na4j ., ure an object's resistance to changes in rotati4 kj7qnaoat g ,,.t;kton?

  Consider two uniform solid sphereg4xe djafut4(-h 96qhj*8ia i s 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 of the smaller momea a-ghi 4u9tx 8q(6jijhdf4e*nt of inertia is

  Two uniform solid spheres have the same mass, but one has g 8g0ltqm:il**it.zg+sxf4d twice the radius of the other. The ratio of thefz*m40+dqggillgts . :*8 xti larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres wherhe: l2b)6 ztqfe one has twice the mass and twice the diameter of the other. The ratiqelz hftb)2:6 o 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 these are increased l4n p4b(n 5t3lo1ad e5 fqrq/ao,.md yto 2M and 3R, what happens to the sphere's moment of ine p t monfaqy3,b5(1d adrq4/ l4.5nelortia about a central axis?

  If a constant net torque is applied to an y/l pmcnpqhz k1 1.h1/object, that object will

  The moment of inertia of a solid cylinder abs,j +,r8oyrlb k(he 9 (hv;,zfb0 urdrout its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translationalreyhr;vu(r f,9b8,0r sloj z+k(h, bd kinetic energy is

  Consider a motorcycle of mass 150 kg, one 3bmuw jmw w(di8.u*/f wheel of which has a mass of 10 kg and a radius of 30 cm. What is the rfb.j m(mu/w wu38w *diatio of the rotational kinetic energy 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 radius Ryobm*.s6 *ut5jy z uz7 rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the uo j5*7mubtsyy6.z* zincline depends on

  Suppose a solid sphere of mass ;qm:vosnjz/ -M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottoosv mj;nz- q/:m of the incline depends on

  "The total angular momentum of a s t)wurw.ecwc63;m37s(xdp 3cndx- zfystem of particles changes when a net external force acts on the system." Thisntuce3d.dc3c(w) ;pwx 7s mwxf 6r-z3 statement is

  In what circumstance2b tx ja o(lmpf/,:pb8s can the angular velocity of system of particles change without any change in the syx:al8/o2bbfppt( ,j m stem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictlpz/8ds9s )vy07qnrg 5q5hkh ion which may be present. What happen kh5q)yl7/0p5g89qvns d h zrss over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun icf3uxr z /:ph(n an elliptical orbit. As the Earth moves close to t: r/ hf3z(pcuxhe 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 spin) by pulling in trg(rt3 :xq( :lb o92 i4jjedvz0dvwn5ya. v5his outstretched at 4xjiwr rdqoza :vtgnvy0b5:2(l.dje 39v (5rms close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fasrlw x4 f javzh5.on;0,t spin) by pulling in his outstretched arms close to his body. W,h wv45xa0of. j nzrl;hat happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his ougucee3, agv :0tstretched arms close to his body. What happens to his moment of inertia about the axis of rog ucae03,vg:e tation?

State the law of conservation of angul+8 /:plwmj jmcar momentum.

  What arc length does the Earth travel in a three mon;aa mq0txj r1b bj8h6/th period in its nearly circular orbit about the Sun with a r0bjr8m1abx6j q h/a;t adius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length ow dhnvb.u j9c zm):nd9(qo.0p f 0.30 m. What distance does the tip of the sec:9n9(.)jozddch0.qv pmw bunond hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 reklz*2 , fw8xxl:5o 9m (0wh+ntuaku cevolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.0g09 fg9q6n 0rg sjbhf1rs(xc What is the frefrc1f0gx0 g0sn9 g( rh6 b9qsjquency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. The scy95v:oty1b period of its rotation ivtyocy:s 15b9 s

  A phonograph record rotates at 45 rpm. Throg 4(,gyr./+ jv eg+womgyuzj7ugh what angle does it turn in 0.20 v r/gzeu.g7+m +yo,gy j4wgj(s?

  A wheel of diameter 26 cm turns at 1500 rpm. H9s,: ;byoe+0fjb bep(o 4fbebow far will a point on the outer rim move +sp: j;b o4(e,beb9febfb0yoin 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 w tnvke3;ih-eom0xwn d 63n8, s. What is the averamwit68n;303vo-nwed xhk, en ge angular speed of the wheel?

  A bicycle wheel rotatesmx(*i4 3y-(cws s0caq7qxpl l c3c0yj uniformly through 2.0 revolutions in 4.0 s. What is the linear j axcqpic4w-0lsmy0(qsl7(*c yx 3c 3speed 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 whic(r+ j og 5uox86fom,+vjufnr2 bi6jq6 h moves the 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 ib2u8n6ivjuo6f6 mo5xrg(j r+q jo+f, n 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angpb6em)bjebnc0 f7x5-n q1st +st-cc6 ular speed of 2.0 rad/s. What is the linear speed o6cc-+enns0-7jqp1ef)x b6 5b mtbt scf a point on the wheel's rim?

  The cutting cord on dy 2 r+it0prha w32jb*a gas-powered weed cutter is 0.16 m in length. If the motor rotates at r 0dtw32b 2 hpra+jy*ithe 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 7ed.y*b tnhhd a8,ib.a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheelhh,8.7. addyb te*bn i's rim?

  What is the centripetal acceleration of a point on the perimeternt2a6g(2nxw k,t2 p.1 v ypoej of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 m/snv(t2.k jw2xp ya6 o2tpg1,ne?

  How many revolutions per minute (rpm) must a circular, rotating space station (.kj-cu 5 *d 4 xxa4i2i /cnrfzeyc vd7i5,5cnlr = 1.rc-f ynx4cliv n /5xe52c kz*uac 7 i5j4did,000 m) 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 ofo0v9pllwt: es,vzfah (2b, b ; 20 m/s. The maximum celb0( tv, fpe:92;whoas ,zlvbntripetal 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 w fqqvc;xg+r8 :.yr.yiith a speed of 20 m/s. r8i.f.ygq cy:;rq+x vThe maximum centripetal force (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, is whirlo*j wj0,z;)y:u6 byz0ey wosoed around in a smooth level table. If the maximum tension that the string can wizw0 ;by * s6zyeyoj)ow0:,oj uthstand 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 slipping k *( sbc lj-w30d*hphh9li+c6 fb/jxb 10 m down +6 lhslki0*wp( bcxdfh9bbj /-h*j3c a 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 vl)o va0 h*y-7+u8iymi 1 dtyfa 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 with a constan elxa0z52 cyhu5u6 l2tt 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 rotate aft2gweuiv 0hiuj4;e . x)er starting from hge02ui )xw u ;.4ijverest and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at re yhwyxw3p (dq ) a:;q1ygnl+c+st, and has an 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 anguly :8c1r q5 c;c xenyyqj)jjl9ic4+yy/ar acceleratioy/nqq9 e c45+18cly;cicx)y:jyjy j rn 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/rw6 f2/ v)e8w0xrojvis while turning through 2.0 revolutions. What is the average angulww 2r 0fje )ivxrv68o/ar acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down +9y d:q4 sjdfq(mnzet8;4x bbyg 7 3xtuniformly from 8.40 m/s to rest over a distance of 115 m. What if; 4n(s8 9yb4 eyq7:j xbgm +xzdtdtq3s the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down unif4jv -pphsec 0h3ge:w.ormly from 8.40 m/s to rest over a distance of 115 m. What is -pv3hege w04hjps. c :the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s toc37s 7va5hdtcnwk*-nk s91d u rest over a distance of 115 m. How long does it take for*7dv 53cs sn u9kah17dt-wnc k the wheel to come to the stop?

  A centrifuge in a medical labora. hnh yc*56iafg2 d4hmtory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0mhf2 acnih*6dgy45 h. 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 tightz(8 i-jl1 giibening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitug8j-l1 ii(zb ide of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel rqlj. dm(r6jb 7equire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required .jqm67l(jd brwhen the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertiafgl3n n1)y;m xlfmj +; $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follo1k bnt *s)ldf,ws: 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*tdn)l b1k fs, the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionleb3a6 kl:uj: p:rx6 rw;ua2nmnss 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 :k6lxwna:j rnm :;3arp2b6uu 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 frictionless axis tcv qn4/zw3l u) kqp 9)h8ry.g-zxez4 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 second4v lqrwztu cpk xyq4).nhg9e8/ - 3z)zs, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rrg mzt7-q1k0qod is initially held in the horizontal position, and then releag-71 q0qrt mzksed 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 30 cm9cnzz gh,9oc, dvy: o2 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 ozgonyv9,z:d 2,c 9ch 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 wrappesugkud ( )x- n4hbm7;pd around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angularhs g n;-x7(budpu4m) k acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk j452m pftu0l cjxmp29;vv(6 e.5ue hwryyb: vpulley of mass 7.07 kg a2v;5c hjx0 2ue4l(t u 5pyj6yrpvvfmm.9:bw e nd radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required ts)iu:5c w9k ::h jawast+kh e)o 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 of9wpv vzb,q,i kr8vg+f7s ;+wj inertia 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.i- j aq qhy..4xq:r+qyu(pg z,010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. (q -:y4,x .ipyzhq+g.jaq ru qWhat 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 o:8 fx9 sqc kb.6 eu m1j lullgzi*1j/fq2kp+7af 10 m/s. How high up an inclined plane cjug9f7:+u im6ql/bj1 .xqcp281 aek k sfz*l lan it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20/g vv:+dxvltp23(n4 ty 3(rk 6n fqcox kg is released from rest and allowed to roll yp4gft c+v n2xqxv/3todl(v n36 (k:r down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping6iqromx:c0(jgp b eaozszz:pc3-j:3i ) 4k.u down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a s 34:uc q6mbcjpk(gjo3. ) sx:-ria oez0:p zziphere 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 ;z -vvn(7te 7h9km,dnnm4rkbq6 kz5 d $20 \; kgm^{2}/s$ 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 inert af-198yg7yyr apvj:kf8,uu pia 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 inem /4rwt6uw.lqcc cspt gn08cj6d9r*1 rtia oum966 4g8d1 *q.p0cnrjtw/wccrlt scf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?