Angular displacement is(a ld7l-+1kv,rki f 6ne*kaf i usually express in units of

  Angular velocity is expressed in unor4go6rn n)umi *a ;2jits of

  Angular acceleration is expressed i+n y(u3t ad 3iuba/g v94olk6hn units of

  A boy and a girl are riding on a mero8vp7dz9 hbj vbbr0b+j b74i 1ry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girjojpr i84v bz b0+hbbd97 bv71l is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding fh ;. p-zoppnzq33t*c 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. Whoh*n.c f33-po;zqpp tz has the greater angular speed?

  A boy and a girl are riding on a merry-go-round whi -jxi-biop 2mf9h d6;pch is turning at a constant rate. The boy is near the outer edge, and the girl is close b2o;ip-d f-j6xhpm 9ir to the center. Who has the greater linear speed?

  A boy and a girl are8as9o5 xo6wa ,ktu/lh riding a merry-go-round which is turning at a constant rate. The boy is o8, tlxkao5/u9hws a6 near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant rate3/4 r eyosqoz::9pvg o ps8z1u. The boy is near the outer edge, while the girl qp/ v3:os9p4r o: yzguesoz81 is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is annv7s; w66g7w albi;gs4c vl-t accurate statement;6 wc4ab s-wl tg7 lvvs;ng6i7?

  Rolling without slipping dependsy6og.)sg.u(sce 2nays a kz. * on

  Two equal forces are applied to,b 2;dq. w3/orui1nm5feb ci4*wquy j a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater t if/3.y4 mbqu1;cnj2bwu wrd*5 oqei, orque?

  Two equal forces are applied to a door at the doorknob. The first force is appsu0; r crs((f m)u/tm9fv no (y)y8zvblied perpendicular to the door; the second force is applied at 30e to the plane of the door. Whic nm u v(rts)r;mov/su(y9(f yzf)0b8ch force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the -uoh,nj oj:+fe:(o 0 aew(oll door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of thewoej(oajn: ,e- loo( 0uf :+hl second is

  What is the quantity used to measure an object's rer1 m 7ou eex;m6u86+qor7pk gwsistance to changes in rotationr8uwq7ok 1u6remx 7 eg+mo;p6?

  Consider two uniform solid :f )5jj6av+uo x)s+jhi7pm el spheres where both have the same diameter, but one has twice the mass of the other. Thehol)vjs +6xj m: je 5)a+ipuf7 ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius of t 1 .np73d9tqg3bch ubwhe other. The ratio of the larger sphere's moment of inertia to that of the smaller 7ug91h c db.wqtn3pb3sphere is

  Consider two uniform solid spv8o(rt(y l 4js j,am1fheres where one has twice the mass and twice the diameter of the other. The ratio of the larger myl8(s,t v o1(mfa4jjroment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and/ce2ffxlgb6w ; r0,k j radius R. If these are increased to 2M and 3R,k rw,fgb/lf j 20ce6x; what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is apr*(va7xp h: owplied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2. 0ezvk/za a-)n If this cylinder rolls without slippingzn)ave 0 kza/-, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of massaeml* vj y-q,8unx 9 b ug(ba201.gdnt 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 kineti2y,menv qb8gu1 a g0(t uxd.a9n-l b*jc 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 andpw-eal;5l-6bh oerod44jxv ( radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the botlre( ho4bejlo5dx-4ap; w 6v -tom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slippi:y; trsw (r+j ymu89nong down an inclined plane starting from rest. The angular velocity of the sphere at the bottom or:rus; yo tm89(y jnw+f the incline depends on

  "The total angular momentum of a system of particles changes when a npmlns,uusbgp3;z-* kh61d d2et external force acts on the system." This stat*udnp-uk ;26b 1sp sz ,3ldghmement is

  In what circumstances caf/ c/ ;9msxh6qp1 bos3f cgdyjj972fmn the angular velocity of system of particles change without any change in the system's angs ;g79fpc oxy /cqdmh1 j2jb9/mf6s f3ular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frwu7e 1ke;zu 0ziction which may be present. What happens over time to the Earth's angu1 k;e07uezzuwlar momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the E bwzyqec,j.l,bc+ 0g8arth moves closeecgb80,.j bwc zq,+yl to the Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a trcq09 :q p41pp/kj ulpirouette (a fast spin) by pulling in his outstretched arms close cqpu90p:lq4pj ktr 1/ to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spint 7e1je;2; a/f8bf cdfeldsf,0l8w jl) by pulling in his outstretched arms close to his bodecfl 0 t,fj7f d;je1 f82e/ls;8awbld y. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performsst ww9wm-c -h q/se tmt8u)r0+ a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his mom/h )w+ tqsw8uwcs et0- tm-mr9ent of inertia about the axis of rotation?

State the law of conservation of angular momentum(::x2 b. 3b.tmht9wm wf 3mpa*mht zvw.

  What arc length does the Earth travel in a three month perdzg73e*p 3 3cc hp(eisso (zz/iod in its nearly circular orbit about the Sun wit/ zis7pz 33c*s( ce(3zepgodhh a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock haso 6g2h ex+bqysu7) 8av a length of 0.30 m. What distance does the tip of the second han he286 qo7b svgyx+)aud sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolumb+;r/ o 0jfsutions per minute equivalent to?

  A bicycle wheel rotates uniformly throughg+q :a *hbvdcx3f7fz+ 2.0 revolutions in 4.0 s. What is the fcfx: avgh+73 fq+zdb *requency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. a4q4cce/ 5lo+ ghi;miThe period of i/oml4 cg4eq+ 5ia;ichts rotation is

  A phonograph record rotates at 45 rpm. Throug3cso fs34j/ jhcfi6c)kk g6 0uh what angle does it turn in 0.20 js34gjcf/u3i s6ck 6o fc)0hks?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a poi7h-h + laruy /sdd;,snm4r kurp+o4t+ nt on the outer ri y-pdoak,h+rr u;s rh /4umst+7l4+ndm move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revola j/vrv6isr(l pj w5x: : qvk*xa3g*5lutions in 4.0 s. What is the average angular speed of the wvq/pi l3walr 6**(: 5kxjax:g jvr5sv heel?

  A bicycle wheel rotates uniformly thri;1fg )a.h ubxm,my h4ough 2.0 revolutions in 4.0 s. What is the linear speed of, .4hmgxu;ah) 1f yibm a point 0.10 m from the center of the wheel?

  A cable car at a ski rehh5+; j14gum s utffw/sort 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 t/g5f tw;4fmu u+j 1shhhe pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a const wrfwn6 q0 j-,.gezy2iant angular speed of 2.0 rad/s. What is the linear speed of a pow.nr - iz0, qwf2jg6eyint on the wheel's rim?

  The cutting cord on a gas-powered weed cutter o *7k i2h)kclois 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 the cordckki2 7looh*)?

  A wheel of radius 1.0 m is rotating with a constant an*m gw;4)ujkr cgular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wc 4mk);*rujgwheel's rim?

  What is the centripetal acceleration of a point on the perimeter of 30t1 ore ntq-y7q ph*ja bicycle wheel o n7eht jy3o 01r*qt-pqf diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minutamj3ctbs/jl *3y g 9v.z: rkn2e (rpm) must a circular, rotating space station (r = 1000 cl/.grn my:23ajvj3*9tkzsb 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 of 20 mz)x.y a *waj8n/s. The maximum centripetal force (provz) 8x.a*jnyw aided 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 radiu t5,;*pezo wius 50 m with a speed of 20 m/s. The maximum centripez;uet w o*,ip5tal 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 )j:j71gah23 ls;l y5sctul rp end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the strinpyl 2;3 sj 1 7gu:h)5tlsrajclg 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.vg1on+1 f8:him tg14wy/lq ni0 cm rolls without slipping 10 m down ag1y 1: 8hwvogiit4nn1+ /mlqf 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 angular accel o+aj-o tex4q7eration 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 cons j0k4g9a t u.xl*mly:(sa;vdrtant 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 autqxs o -98vvec+-+3oxvusr;rb : 0vbflomobile tire rotate after starting from rest and acceleb sv qxc x v+e+v0ro-39ro8-;flsb:vurating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has ank4mujci8z 0h 2ts09ak 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 constantz (eup( w(qyq(udi 6lm rpm:6: angular accelerawmr (qq:zi66(pu: dlemy(pu (tion 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/s while t3 jg/2u,jzg2z/x p pkturning through 2.0 revolutions. What is the avep32/ jpj,/tgk2zxu gz rage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows on+.ftz l5aa/hw/ zt 2; qez(jdown uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotateso.ht5ta(jzlzqnz;f+a /2 e/w in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/8.pszh :r zcc7s to rest over a distance of 115 m. What is the angular.h r:7zs czpc8 acceleration?

  A wheel of diameter of 68.0 cm slows down :fd )5 9afksclw*w*itoe+h idm+( 1 xluniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to coasf5iwl d(9k+x* :m towe1lhicd f+) *me to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rels*bur q18xzd ) ;sx9lv/min. When switcrx1l;s8z)xb dl us q*9hed 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 su2axerq chro3*wmt 2 *h ws+3o(y( f+90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required whaw2xhy * u*q(r twmf oc+3o+s(e2 r3shen the force is perpendicular to the wrench?

  The bolts on a car wheel requirre1 -4bthyg 4xe tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when 4heg1-ry4 t xbthe force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerti t.ulnzf u:p96a $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule idnw+/5; skkk mk9f0ilx d :+yis modeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertkdk/ykw5nd;x0 lik:+m9 ifs+ia about the origin?

  A solid cylinder of mass 10 kg 4ibwmc*n9 6 c ok; diq:f*ms(,tjvvjvi-1/j bis 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 t1m vn/j j f* :iimvwbvb;-9(qj d4,k6ct*ics ohe cylinder?

  A solid cylinder of mass 10 kg is pivoted about m0ifklpf+ bmv*x +r30 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 *l0 mpr3 mvi0fbx+f k+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. T( 59id2n rq6frynrd (bhe rod is initially held in the horizontal position, and 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 endr fqb(n96rdyri2 5n(d is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg+2h)jt6/jzrnp h0 4hpkep; oa. 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 h rhpn;j zkph a)ojt+ep624 /0speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of q, cb0ydfi kl.49m9jkmass 7.07 kg and radius 66.0 cm. ib,0f k4dq9 j.9lkc ymWhat is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a , qbkjk2 36meunq fb26frictionless disk pulley of mass 7.07 kg and radiq mf62q,k6ebn k2 bj3uus 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is requq b. lxhjl*:hdnu7,lic l+ q(zi8g+*oired 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 bzxvl zs8bna 5y)(my/*5s l b;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 0.010 bj ;h:,po ha-bp q7fu:m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is thu:- q b;poj,ah fb:ph7e 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 of 10 me fxy, a* +;v0bwarpq-0y wnp5/s. How high up an inclined plane can it climb before coming to aw yw+pxqya e5r*nb,vp ;f- 00rest?

  A hoop of radius 0.50 m and a mass of 0.20 9y l5)vrtr1xi kg is released from rest and allowed to roll down an inclined plane. How9vy5xrrti)1 l 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 slipo.ehd7rpi cl;x+8g q;yz )le-ping down a 35e incline that is 7.0 m long. Assume it started from l7 ce)yproeq ;d-+xl 8i.;zhg 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 changes by +m+ /y+xt/1flhqsx lf $20 \; kgm^{2}/s$ 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 lxbb 0m85dj3zmoment 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 5.00c)(8ks) ldlkz rad/s with arms extended has a moment of inertia l8dk))(l sckzof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?