Angular displacement is usually express in units n4 vzmlm/y *)n36 t7xwee .2nvtw4but of

  Angular velocity is exhssa72il1h u4pressed in units of

  Angular acceleration e4h*r g gy)j v8:n,espis expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a consta b fgm02w *bfm;m31ttxjcu9t8nt rate. The boy is near the outec2j ttxm0*bwff1 ubt8; m3g9mr edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are rw*i.uz-( p /t.pkvk5u( fcbpy iding on 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 the greater angular speed/*k5ub wfpu- ikz.pp.(v(t cy?

  A boy and a girl are riding on a merry-go-round wt v-ma)*dr 6on 5mm9quhich is turning at a constant rateq)mut6a m -r5*9dmov n. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are qopz1 by 1ie 5/.iauz;riding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the gi1ip/ya1b e 5i ;zouz.qrl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a.jqjlmz3k /(w ; :wttv merry-go-round which is turning at a constant rate. The boy iw qz:t/v;(.lktw mj j3s near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotatinmv cvzn0v:q 7r 8hq-8vg. Which of the following is an accurate statement?vvqvnh:7z88 v0r q -mc

  Rolling without slippilkj dp(wn9 b0waju97j h1, y1kng depends on

  Two equal forces are applied to a door. The first force is appljvv9wb5 :u) xlied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exertsujv vwx 5:bl)9 the greater torque?

  Two equal forces are applied to a door at the doj; bf9r7kyjv 6orknob. The first force is applied perpendicular to the door; the second force is applied abjr6kv9j ; f7yt 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpen.*q) ad+ kq;wv9b kfnjdicular to the door. The first force is twice as large as thebqk avn.f jd; +w9*k)q second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used t3./0x97. ae zektkz xhe(v1tbk4lszho measure an object's resistance to changes in rotatiozek9vxs 3al7ek1 4z./(zk.e thbx 0t hn?

  Consider two uniform solid spheres where both have lz3+sv)xmn14x5om m1do j+ jxthe same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to thatms +vdjj+1xo 15 zmx) xno34lm of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius gy6o 04, r0juozgsja6 of the other. The ratio of the larger sphere's moment of inja ggr0 ,06ozj s46youertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass andvp-po8uc wrr)x0/c i1 twice the diameter of the othcwrvc)i r1px-po08/ uer. 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 these a. 84svc agqrxpf -broz0u* h3( 2o-rtlre increased to 2M and 3R, what happens to the sphere's moment of inertia about a central axis?08ovr.-tc4gpfx l3-z2a (b*hsr quro

  If a constant net torquewb(5k/ ovgk4 u-,twm+8ao;l wa : tvfz is applied to an object, that object will

  The moment of inertia of a socs yco:hp n559 ttdv97lid cylinder 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 m, mipqp;(qnalq 7i4bm-di:.sass 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 of the wheels d pnm,(-7.slmbq 4;qp:qiaii 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 ro/ 3 ,sz d2dyn4iygqms1lls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline isgy/ y,ndms34q12d zdepends on

  Suppose a solid sphere of mass M and radqxrgn)ck 7-/pd.j,5n4cm hgk ius R rolls without slipping down an inclined plane starting from rest. The ang,n-/ .c)c4 hjgnrpd75k gkxqmular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum f(zqv f-4p3loof a system of particles changes when a net external force acts on ozp fvfq3l(4-the system." This statement is

  In what circumstances can 3 gzo7qy,9r6g+c ybc )krqty- the angular velocity of system of particles change without any change in the system's angular mo-ry+gybr7ko zct, 9c)y6 3gqqmentum?

  The Earth orbits the Sun in an ellipticr3kq/)veo/0rsk v ht )al orbit. Ignore any friction which may be present. What h)r3kor0e )/ svt/kvqh appens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth /jgghhc0h4b 2 moves close to the Sun, then which of the following best describes the orbg g/bc0h h2h4jiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pullisd ripu19k) cn08 pp6y7kn;n yng in his outstretched arms close to his bo ck6u0nsn nyk9)p1d8p7rp; yidy. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchhh53*8 s ytt-v1b csched arms close to his body. What t5s*yh 1-s8v b3chtch happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fo3kw rfp 07+tuast spin) by pulling in his outstretched arms close to his body. What happens to his moment of 3 0fw7 topku+rinertia about the axis of rotation?

State the law of con lvlr1;75b).pqmdk;n2j) mkz n d ll1sservation of angular momentum.

  What arc length does the Earth travelvv1 7sc8l2apo j 6+nnf in a three month period in its nearly circular orbit af pv1nla 6 no72svj8c+bout the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.39if4f.zwx u+t2yi re1 0 m. What distance does the tip of 4eru+ .if fyx9tw1z2i the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions 0xnjwmzv 8kc w7v9w3-per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What ivit 5gn4oe1ag(q3lf (zwn7 zsi;*0oys the frequency of the wh*tyo ;z13a5 (f4(gl07gnozi ws vqeineel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of lkiw t02: /dndy6cmwt-mae /( ; zu:fn0.40 kHz. The perio az l-ui/( wf0 ywenc/dm2:n:dt;6 kmtd of its rotation is

  A phonograph record rotates at 45 rpm. Through wmmn +hg *n1ug+hat angle does it turn in 0.20 s?m+ 1hm+* nungg

  A wheel of diameter 26 cm turns at 15/ ozg0 7cs:t ofrsuhj )(h/i qtd4j1x*00 rpm. How far will a point on the outer rim move in 2.1 sos*)jd fc ti4/1hgo:trsh0 7 q(/ xujz?

  A bicycle wheel rotates uniformly through 2.0 3+tbqv r..tp8yk el6nrevolutions in 4.0 s. What is the average anguyne kltp. v+bq86 r.3tlar speed of the wheel?

  A bicycle wheel rotates unijt9c au5ndt0 oq/ppax9q5j4a;j t44 oformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of q 9qj;44p5 ootja dau90 n/t 54tapjxcthe wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable whicd2cm6w8wv(hjmfs ;+vh moves the car is driven by a pulley with diametsjm h8c6v;wvwd2 +f (mer 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 cons a8y/.asnqh)-; tl,9g79epb h xiozyr tant angular speed of 2.0 rad/s. What is the linear sn-bpiyte/)sgl.h9, ax ;7z h8r9aoyqpeed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the md*u0;ud m/ xwgotor rotates at the rate of 2 0wu*gx m;udd/0 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 consne ydcgf0j-0o6 vo 4)stant angular speed of 2.0 rad/s. Whatoys) fv0-e n40cjdgo6 is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perim/1em6xylm* 3mf g/svceter of a bicycle wheel of diameter 70.0 cm when the bike is movcm *mfxs//e 3y g6vm1ling 8.00 m/s?

  How many revolutions per minute (rpmo:s r mic:+n48o5dt:py e(ckh) must a circular, rotating space station (r = 1000 m) rotate to produce an askeio:: c5dnm 8t4yr(p o+h:c rtificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m wit wzps7wkj)4;/w rh vkbe(j5+vh a speed of 20 m/s. The maximum centripk5 k)z;jsrjw4( evww7/b+ h vpetal 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 2mc* nj 1iw4l;vjvu s o41z9up00 m/s. The maximum centripetal force (provided by static friction) is 1v lp;cj4491 vn*wj zm0soiu u$1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.75xtokps9 1iu3-0-m string, is whirled around in a smooth level table. If the maximum tension that the string can wx-k31o s it9puithstand 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 sqt2j*n ex q2tbtd(.rn+ t* /nqlipping 10 m down a lane at 4.nt2*btt j+ 2 /dqt.qex qnn*r(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 angular acceleration of we:/ok fx5e :c$4.5 rad/s^2$. 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 anm7+*vc*ng 7)u lkzs uxgular 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 ti7v6fetbg w:uck;he q .oa03 g3re rotate after starting from rest and accelerating at a co:. 73 eh g3taoefbq0 w6ckgu;vnstant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and haj um-43vqxc *is an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotatihl)wh/bm5 e3b.s og y,ng at 20 rad/s decelerates with a constant angular acceleration of wgs 5/)h,m e3 hbyolb.$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angulany-q kvcqo54+ r speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration q4-qov+cnk y 5of the wheel?

  A wheel of diameter of 68.l78j* * cuhc6hfqyzk,0 cm slows down uniformly from 8.40 m/s to rest over a distan8c7fj ,hcz6qu*hk ly* ce of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest21c.r + +nbg tmxi7xcd over a distance of 115 m. What is c2rxc.+g+xi mt17ndbthe angular acceleration?

  A wheel of diameter of 68.0 cm slows down urf gnu7quhzb13sr3y t2 o2w7.2hgh. fniformly from 8.40 m/s to rest over a distahnf2g 2 .yqu1g2zf.sb7otr3 rhh3 7uwnce of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotatq:wxrqqneq cp; 07 19g*c il9fes at a rotational speed of 3600 rev/min. Wh9lncc9;q*i0e pgf7xr:w1q q q en switched 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 torque of 90 Nm. If a 30 cm lt6-kpha2yq2nk,7u m b ong wrench is used, what is the magnitude of the force required when the force is perpendicular to the w,6qt2kpk-7uy2bm hna rench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If dxtb)0 gow)e0() reaja 30 cm long wrench is used, what is the magnitude of the force required when the force applied (ertxeabo d)0j )w)g0at $53^{\circ}$ to the wrench?

  A wheel with moment of inertal g5zm.4 i:uhia $3.00 \; kgm^{2}$ 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 origin, mass 2m isp swm9umhs5.wg,r0-s at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the mgwwm,r p.ss0 9uh-5s origin?

  A solid cylinder of mass 10 kg is pivoted about a(3px,a qktdiv cpk(8( frictionless axis thought the c(pkt8p (vkad (iq3,cxenter O. 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 frictionless axis thou,9r dwa 7l5 )skp+ekmeght the center O. A rope wrapped around the outer r9dkm, +s)e 5ar e7wlkpadius $R_1$ = 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 one end. The rod is initially held in the hor6aw3 3kge xho -9suj.wizontal position, and then released as the free end is allo u-o jghw3s6awe 9kx.3wed 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 ce 6;u61kmtz 3b bkdosg g8+n-cm and mass 1.5 kg. Neglect the mass of the ax ;gu6stg8c e+bbmk16kzo-n3 d le 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 frictionless dn3i 7k;e nf1mcisk pulley of mass 7.07 kg and radius 66.0 cm. What is the angulnm1nc ;f 3i7kear acceleration of the pulley?

  A 1.53-kg mass hangs on 9 w qh1rru** db5mq)c wj.u*jdsz)n1n a rope wrapped around a frictionless disk pulley of mass 7.07 kg and rau)j urw 1wz)* n*jnr .1dqqm*h9sbc5ddius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. +rkz +9 rwk cj,iudiz1r5 s,i6If 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 in;oo 8 l6fe,vkk xoytnz-u:h9 6ertia 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 rtyoz-f . q4r/fi+b(hradius 0.010 m starts from rest and rolls without slipping down a 1.0-m high incybz.+4/rhitffq(o -r lined 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 radius 0.010a4o5f fhka(wj s fsop3(a;k6. u2i ,wo m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to oh6fkawu2k jiawo;s4 pff.s(oa,3 (5 rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from mauq z5l)94vp rest and allowed to roll down an inclined plaa 4lmuzq9p5)v ne. 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 slipping dyz x8y5vzuv(mz k0 l :yn2 xbo.874crsown a 35e incline that is 7.0 m long. 7s8kxvz (x:2.lmyo vn 5yrzz uyc48b0 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 kf9 ercz 9x7-imomentum 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 ofbz fk+e 7dgw0*+w b4*i kam4l9r ybhq: 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 has a m3ia)y8 h ch(mz rf9u9i)qo dg/oment of inertia h9cah z 3d(9fq /)yi8umo)rig 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?