Angular displacement is usually eh,-4mb/.kf9j vop 1ml;n y prtxpress in units of

  Angular velocity is exe bppvpv: (cvwz31+ s4ho- km6pressed in units of

  Angular acceleration issz (d;x,y6 ukr; qvx0 ia,s :o1tyk(vr expressed in units of

  A boy and a girl are riding on a merry- g(3 btoz(s-ilrn(v m9go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to tg9 (b (t(-vsm nzol3rihe center. Who has the greater angular displacement?

  A boy and a girl are ridingt7,) :vobv2z9ldd chz on a merry-go-round which is turning at a constant rate. The boy is near the outer ed,2vvd7lod:b9 )c hzzt ge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding ons z e,e.muc +y9v7spf, a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to tys+7,m. ,espuev9f zche center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant ratmta7xs 87dgt, w) rm)se. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centria7)x)t ,sgt8wr dmms 7petal acceleration?

  A boy and a girl are riding a mep.;lr5j yly4j+g; *iw m kyrakex6 55arry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is w5kr ;5 g.yy 6 *5kimae+4ajyjl plrx;closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of thj ssug, wsfuy4ny4 (4(v;rjl8e following is an accurate statemes( s4y,gwln8;4u yrs jv (fu4jnt?

  Rolling without slipping d9,lz iz +dkskhd/)m ual: b2a)epends on

  Two equal forces are applied to a door. The first force is applied ,bx,9bglu m ;3pf kdn)at the midpoint of the door; the second force in;3fumdx b9)pbg kl,,s 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 doodyv :o3b 2i s4iu.5gd j*ncuu7rknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force u5u cns3 v.u*2yi4ddg o7ji b:exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular tq5 ssagz1-jv +o the door. The first force is twice zs-q1aj 5s+vg as large as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure a/ yygu39n9zz hn object's resistance to changes in rotationyh/3 9gzun yz9?

  Consider two uniform solid sphere/: zg(vejtcc9sm pyz rz9g8 +.s where both have the same diameter, but one has twit9.zvc 9ge 8gszy(rmjzcp:/ +ce the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, vfhf3m9ifcc9o7(xs( v/yhy , but one has twice the radius of the other. The ratio 97( fc, ycvy3fif (vhsm9xho/of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one4g lj -+bo*(uasug;9txs. qoe has twice the mass and twice the diameter of the other. The ratio of the -(lgeqtjuo og4s b9 ;.xa*+uslarger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere* rn0dn z5lqd3-dao8e has mass M and radius R. If these are increased to 2M and 3R, what happe n8 zldqa r-50d3*nodens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an oba3 zpn.:wrt1mi f1.s xject, that object will

  The moment of inertia of a solid cylinder about its axis is ghvl q;,-8taxi iven by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotatixh;li v -a8q,tonal kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a 7ssed-7ck1vp r ,i*qymass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy 7 kyrqd-ssiv,1 e *cp7of 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 R rolls without slipping down aqpzzh9+en )*cn inclined plane starting from rest. The linear velocity of the sphere at the bottom of t* +z qhep9cn)zhe incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slippibb-i 0hu j/tt 9xc,g6nkoh5*tvei-) u ng down an inclined plane startinvk,0*g9t )ie 6cittb -bn hojhu-/x5ug from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a vf9je ph.i ,vk698 4hew1lba l.. j2wdlsifc2net external forcd.ip82.aif j.ll9b4 e hw96h,kf vlse2cw 1vje acts on the system." This statement is

  In what circumstances can the angular velocity of system of particles changea.) q1e.cr9jzkx7 on x without any change in the system's angular momentr)zajx xckn.9 o1.e7q um?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frx6 hq8k/5pedje olf /(iction which may be present. What happens over time to t65e/loeh jd/(8pf qx khe Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ellipti/1htf pdv8ee3 a 2ln-ical orbit. As the Earth moves close to the Sun, then whiche8fv 2/ep3a1h -tdli n of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) ;x6.f x6/mra u.wb dxdby pulling in his outstretched arms close to his bod ur6wxm.x.b faxd6;/dy. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a piroi1n )zdzh8 8ck 7; kvq8/ik0dpyfq xl6uette (a fast spin) by pulling in his outstretched arms close to his body. What happe)vfx07 i6kq/dzdkz ky 1clqip;8hn 88ns to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hig r qaqp.,wsde /( (/kd+ct np f.r06vsu;yuq7s outstretched arm6ge+qc fprpu wtv;q y k,.d.d0s/auq(7(r n/ss close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of an mtvu; h2 fxk*kzmd.(ev*f-(f gular momentum.

  What arc length does the Earth tf:vjm kyy*yi z l8hen:s6 m46/ravel in a three month period in its nearly circular orbit about the Sunm *6n liez hyvsmy 6y::8k4/fj with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has im uq1zv ( j+zsq5l1).nkvog vrz k.-(a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 s ovs+.v5.ln)zk ( jzzukq(qv-1g rim1 econds?

  How many rad/s is 25 revolutions per minute equivalenfag/w 5qntdf; pb.sakg 8 *p,2t to?

  A bicycle wheel rotates uniformly throu p q*j9 q)+j(mb/ugvtqgh 2.0 revolutions in 4.0 s. What is the frequency of ()qvgqt */ m9p+qb jujthe wheel's rotation?

  A pulsar (a rotating neutron star) j/ d: /an,bs:(jgbh dnemits pulses at a frequency of 0.40 kHz. The period of its rotati: nd(,jhbbsj :/gan /don is

  A phonograph record rotatesh-v kmb904st a86)sb8t gqhnp at 45 rpm. Through what angle does it turn in 0.20 s9tgmp8hbq0 48ab t snv)sk6 h-?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point o ;zohgu+s7ybi- ;opv ;n the outer rim move in ;shy ip-bvo ;g+u 7;oz2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is tk, sjdv7fs b4lah9tg z3l 3qe;wt 6z;;he average angular speed 4eq3g6;twbsjd ,t shl v79k z3; ;aflzof the wheel?

  A bicycle wheel rotates uniformly through 2ayz:;fm,gvw 1s;o k n;.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center ;,1;o mwa:ns;gzy fk vof the wheel?

  A cable car at a ski resor-,04a lamg b0s6z0vzq mwaa5:kaft1at carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley 01vlzq w-zab0f ma g:,0a5makaas t 64with 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 2.0 rad/s.ka703tyt :of r What is th k a0:oy73tftre linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered w;.8ow ctyib066nl vm5cr 9 gbneed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of th8bwvt;myir nc o9b5 . 6gl0c6ne cord?

  A wheel of radius 1.0 m is rotat1 58l .yjhdeyging with a constant angular speed of 2.0 rad/s. What is the g51.jhe l yy8dcentripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle )83c(8gsa((ei ue4yfrchq jhwheel of diameter 70.0 cm when the bike is moving 8.0q8eface )(ry 8is((4ughcj3h 0 m/s?

  How many revolutions per minute (rpm) must a circular, rotating spacezk*ipkiu w8 -+ station (r = 1000 m) rotate-8 pk+wki *ziu to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curvu1k: clk3 w5.sjvgr -fe of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) 5rvkf:g cl k w3.j1u-sis $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radius 50 m with ((eywjzv v;c0jo fgl,f4 6:qn a speed of 20 m/s. The maximum centripetal force (provided by static friction) is nz q;lveo (,6(j y0g 4wc:fjvf$1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attacm-wz ol k0n,6g4n,wq6kj/r 9- syjipehed to the end of a 0.750-m string, is whirled around in a smooth level tablp,z m4 9rjnlweykik -/6wqj,0g -ns o6e. If the maximum tension 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 mqd)(mn2/qkn a28p k 2t q+qnurolls without slipping 10 m down 2n2ak/+n k2 umqmt)q8 pn (qqda 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 a 6.ba heiefj.)ngular 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 acceleration of --.chjkrxn, b y y9g,bik1et-$4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angular velocity at t = 2.0 s?

  How many radians does aojauo3f*-m ag,p m gbk,,whej (q/j,, 0.300-m radius automobile tire rotate after starting from rest and acceleratingk/ag*o,m,fh( , ,e qojgmpj-3ja,wbu at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest,1c5l;bb( rperuw es.33 i)wqf 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 angular accele 8zaru mnnm2igk*5v 7/0gzrm4raur 24zmzigmm7 rkv0 gn*n5a/8tion 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 sp)(3(yi x btqru/-vhag eed of 6.0 rad/s while turning through 2.0 revolutions. What is the a ar ix/h v3-q)(uy(gbtverage angular acceleration of the wheel?

  A wheel of diameter of 68.0 c4,zcv 0plxg 8vm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the w 40vp 8cz,vxlgheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniforml:aj,ed s7au9hlcl(3e h2kgg ;y from 8.40 m/s to rest over a distance of 115 m. What is the angular acc a:;usda7cgl2hgk h 3el(j,e 9eleration?

  A wheel of diameter of 68.06s8zsa). 4iu8jh w3rp zlk ,il cm slows down uniformly from 8.40 m/s to rest over a distance of 115 mks ri,usapjlzl88 ) .i4wz3 6h. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotaa+e q( kf5*ugctional speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coqek( gu5 f+ca*ming 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 wheo4 -ldrv:e/18u ik4 5ek;aahrisn (nlel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular tore1n-/lvia 4r d li4(;keasun:5 okh8 the wrench?

  The bolts on a car wheel require tighte9ey )a *7v4(avcuvzda u9k*jyning to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the fora9d4vc*uuy9av y* zvaj(e7 )kce applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ine 21x 6y m*czr0dkb)mmrrtia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is mom0 69cpp:lqpb deled as follows: mass m is at the origin, mass 2m is at x = 9p0:m6clqp bp a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mas4d xlgs. 9ew-qs 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.gw 4x-9elq. ds 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 h 2erwraes)0ljl2*1ckg 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 in0s l *e2ch1l raw)e2jr 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 sq-ub ,xca12n g;kqa6 horizontal position, qgc-kus,q;x ab1a 6n2and then 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 30 cm and mass ihx2 s:y3- drl1.5 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 wheelxsd 3 2-yirh:l achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley ofc5* u .isddc paqlvo7+k61(mi mass 7.07 kg and radiupq*6+.ccl (ds1k7a5u div imos 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapab*gd,p3b: b gped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. b:3g dg,p*ab bWhat is the acceleration of the mass?

  A rotating flywheel can be used to store enu y/ rj6(8csxaergy. 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 inertia jrcl +o8ld7 n(ohl5f/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 radiuscy t:yx7 gca ;j,3+*v0f1gmsyuv/yb f 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is th1f;y3/tvg7gsj + fm* yv0a,ux ccbyy:e 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 * ln0d csru a*wfq5:0arolls with a speed of 10 m/s. Ho0dac*frs 5l: 0*aunqww high up an 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 allowedjl -y;2n wugsck7 ,wit.cs+u. to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3..u;+ wn.7lws,ct2 juk s-g yci0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down jkd * uprq z0a1hnrll6rh79 8/a 35e incline that is 7.0 m 8arh 96 k 1u07lnrh*dqlj/zprlong. 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 c/6 277 pj2n:e efzjkblin2af1(xmbvh hanges 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 inert2irs6p lqze6dpo (4,y ia 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 p)vhn2 bt38hv xssctz36s6+g of inertia of) 3n zg26tsph863st cbvhv+sx
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?