Angular displacement is usually express in unk./ /;dulztf4s mhif -9yupy 5 zqz8irdnx .6:its of

  Angular velocity is expressed in units 4 p(esm*izg1 clm:gx 4of

  Angular acceleration is expressed in units j+;dfv2 yn* 3-bn kc(qck:juf of

  A boy and a girl are riding on a m +mlje fu6w7 uliw84 zr)dve:-erry-go-round which is turning at a constant ratev48 )lrdwm-7+jwlfi e6ue zu:. 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 on a merry-go-round which is turning at a concskqnoz+ 6v,+ p2.mp3rljft -stant rate. The boy is near the outer edge, and the girl is closer tol +nr.j6-c2 z ,+ppok msq3tvf the center. Who has the greater angular speed?

  A boy and a girl are riding ,hz /2vfs hetf*8rro. on a merry-go-round which is turning at a constant rate. The boy is near the outer edgsr2/f,*rezfvh t.o 8 he, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a m bpzwk2xk6 q07erry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal accelerak 2b0zp6k7wqxtion?

  A boy and a girl are riding a merry-c f51tm9ln/7 :nxc rlsgo-round which is turning at a constant rate. The boy is near the outer en 7 1nft95l/ :mrlscxcdge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the followingxiyt37f. . pgh is an accurate statem. i 73hp.tfxgyent?

  Rolling without slipping depe)ism16 hyq liucg pcex;3k21+nds on

  Two equal forces are applied to a doc4qv zq:6uk, rz-/ns hor. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both hvkqq4z /n6uzrc,s -:forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first h;vzj mn+0tl0q*h5wogr h6. v force is applied perpendicular to the door; the second force is applied at 30e to the planevh.j6 0 5w;lht+hrmv0z*gnoq of the door. Which force exerts the greater torque?

  Two forces are applieark :)4l vs3cmv cwl17d to a doorknob, perpendicular to the door. The first force is twicemc 4ak):3l1ws7rv clv 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 measure8f9;j*cv mi, 1uyek8ycgy1tgywm u37wim5 n ( an object's resistance to changes in rotati, 7;g j8vec*t 3ymumkn(wcw1myi5g 1 i8y9fyuon?

  Consider two uniform solid spheres where both have theryj0:/ +m t5zf4rj:sszq*g bqba v g26 same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertizy0 bb* z/jg2+4jqa : t s:rq5svmrf6ga is

  Two uniform solid spheres have the same mass; w)cqs ncsb(tmh8qj i(yd1my/n32 y +i-qat,, but one has twice the radius of the other. The ratio of the bdc )ty( 8/y;j-qtyimsnic s,2h +aq( 3nw1qmlarger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres 7qqb1 +(d8aqlcs8 2woxvo 3oowhere one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smdbo81v23s q q(wc olxoa7qo8+ aller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2M a-s0gru3y gc5d0 m,iwjnd 3R, what happens to the sphere's moment of inert0muyg r 50jgd-s,wci3ia about a central axis?

  If a constant net torque is appix;no4 /f63 dld/nti-rf8pjx lied to an object, that object will

  The moment of inertia of a5y n+z8ubsx- 1:meppbu/ u dj0 solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rob1 0 bpmnxus/ue+-:y 8jd5pzutational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass(kvkxf tj 4d9+ 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 to the total translational kinetic energy of the bike? Assume the wheels are uniformk kdjt4f+ (9xv disks.

  Suppose a solid sphere of mass M and radius R rolls without slippinge9 hsj)bf-q54i i1fku xxu/ x+ down an inclined plane startinqxxkxi bf)- ues/fj9u hi1+54g from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and3z (/- bpzc/bbqewjz* radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the p/ e/ -b3 wczzzj*bbq(sphere at the bottom of the incline depends on

  "The total angular momenqb::lh2 0w7w3a 5.bu glt,i)iiaie ds tum of a system of particles changes when a net external force acts on the system." l ,.atdqaw iwb0h sgil23b) iiu:7:5eThis statement is

  In what circumstances can the angular velocity of system of particles c; aevc4h p+ (/gw boh+8addb.qhange without any change in the sy ga;w4eb.cv+a d/o(dbhpq 8+hstem's angular momentum?

  The Earth orbits the S 8t+ 9eg6h.g0 xbiwnfjun in an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular mome wgx . 69+0tbigefjh8nntum about the Sun?

  The Earth moves about the Sun in an elliptiwqkyuj (oh 4-l(zn,)s cal orbit. As the Earth moves close to the Sun, then which of the followinguk4) oj q(whnz-l, ys( best describes the orbiting speed of the Earth about the Sun?

  An ice skater performf l 1pjlj;m7wpu;xo9(ite, *0 6fylb qs a pirouette (a fast spin) by pulling in his outstretched arms close to his bj*l97;um1f; l pe(6ixw y,pqlbjot0 fody. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his mf yab-m494hwu992zfmm x1p c outstretched arms close to his body. What happens to his rotational kinehwy49p z-m4 99 aumff1 bcxm2mtic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling ina,w rs8n0-; oeiahcve vk:-9h his outstretched arms close to his body. What happens to his moment of in, 0ahwicn8ovehvrae-s-;k9:ertia about the axis of rotation?

State the law of conservation of angu9wrqn 3;* sky /ln y2ly1aewp6lar momentum.

  What arc length does the Ea .kz1xm- 0v+v6ejifpe rth travel in a three month period in its nearly circular orbit a1v 6fv+pei-jm.0 ze kxbout the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. Wuaba w3(+u5uchat distance does the tip of the second hand sweep through in 3 minutes and 45 seuuwb5uc (+ 3aaconds?

  How many rad/s is 25 revolutions per minute equivalent to?slk2+ 7 l,z4azaob1oz3i 9c cog0dji*

  A bicycle wheel rotates uniformly through 2.0 revolutions , 67y6k191hwd:xhuycb p9 3sepo-d( llbnxq zin 4.0 s. What is the frequ-l (xhsynkbh9e61 l pwzd 7,pd:y6b xq9c 13ouency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 y4.eth4krx*my(c 2 w okHz. The period of its rotation *2toxhmrc(44 y.ekw yis

  A phonograph record rotates at 45 rpm. Thrizl * z.h/9gklough what angle does it turn in 0.20 igzhkl .z9l/ *s?

  A wheel of diameter 26 c2cr0a ho1t*)h t *b:,s eiugax6-gvqem turns at 1500 rpm. How far will a point on the outer rim move in 2cr1e a ,0ath iu6bt*g )xes*oqg-h:2v.1 s?

  A bicycle wheel rotates unif:hy)e ,yjh4dq/bm*7slq(jx)p +vn c p ormly through 2.0 revolutions in 4.0 s. What is the average angular speed ) *jjpym x 7(b+ysv4,/phdn:hlecqq) of the wheel?

  A bicycle wheel rotates uniformly through 2.0 r/)p7fgym/p 2 fz/ztrcevolutions in 4.0 s. What is the ft)72// gf/zcmrpypz linear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort car;8+tn( en+jae uos*u4fl v h5nries 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 fast4lo+eau;vu*sn +neh ftnj85( 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/sqqdrgtn *6n gxs6vv5jyf/,)ub. kts-s( (8sq. What is the linear spee*s5un)dj(s- .8qqs(g,vfrqnb66g kvt/ tyx sd of a point on the wheel's rim?

  The cutting cord on a gas-hih ; r lt3jxnho)o7y( m(zv+-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate m7hth3z i(xvhr- +n)lo oyj;(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 radt,d sj u5w5xpv-ra v.t* i.ql)/s. What is the centrtjr, 5-sv vwl..5)pq ud*xat iipetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle wh-re/ 627mb1dfjnwuas p268 k fe9gvhpeel of diameter 70.0 cm when t1-j wvrpf gh6mb2kfa78n96e e p/ dus2he bike is moving 8.00 m/s?

  How many revolutions per minuc2py 8n1l i*x7 x;tqkjte (rpm) must a circular, rotating space station (r = 1000 m) rq;kjp*y1tn2lxi7 c8x otate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with aks z* k+7-btwc speed of 20 m/s. The maximum centripetal force (provided bywksk +7tz*-cb static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circulj-nex0- )u1 :fqium(eueaos3ar curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by st e au01jusemun -x)3 fo(i:qe-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 whiy oh(j2 rzw7e2k 4p.warled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mass h.7erh(oz 2jy kawp42wave if the string is not to break?

  A bowling ball of mass 7.5 kg and g -d32ytkebxo 4f:1stwh5db/ radius 9.0 cm rolls without slipping 10 m down a lane at 4.t:t5e ks/do1hg f-4yb2 xbwd33 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 constana8;ew4 hp o-vct 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 cgd) (,cngq6ai h2;ggnf :ln0wonstant 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. hwbh /,vw:ee a 0.300-m radius automobile tire rotate after starting from rest and accelerating at a constant angular acceleration oewvbe ,w/.h:h f $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceler g dxuss*7wifp9ff- f.8oj2m9ation 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 vyl*m*dskw* d-; zxah1zp, e,accelera;yp* k *h1,-e sx,vwddzamz*l tion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches anc thy i0qrezzsoi) 8 wzn-9;.k7vtm,; angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acctzi;7ns cvtm0oy.rhq,ezk)8 i 9 -w; zeleration of the wheel?

  A wheel of diameter of 68.0 cm slows down unifh *wwts.;d ,bs*f4rk. ospi 2gormly from 8.40 m/s to rest over a distance of 115 m. What is the tsb sk h.2g.d**ps ;rw,t4wifo otal 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 resu m zp-eo,g /+ 4br6rc5lntpg0t over a distance of 115 m. What is th4 ,r/tlo cnm5z06pgg pue-+r be angular acceleration?

  A wheel of diameter of 68.0 cm6(yb yg.lyg.1fuu -1x meh b x;fmup)6 slows down uniformly from 8.40 m/s to rest over a distance of xuy)f yxg.mumy- gl1 1;u be.b6(6pfh115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotati,sof:0,gldd7mexhn ,onal speed of 3600 rev/min. When switched off, it rotate hdf sm, ,enlogx,d7:0s 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 w2qa6 r w.of*olong wrench is used, what is the magnitude of the force required when the force is perpendicular to ta*r2oq f.o w6whe wrench?

  The bolts on a car wheel require tightening to a torque of 90 ;d 3h ge if./wro8yk7 jd+f)vlh+,bpsNm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force df;ykvw+37eh8/j. h )+l id f,p rsbogapplied at $53^{\circ}$ to the wrench?

  A wheel with moment of ine nqc9vbu9:biyjj q azag36j0sv,4y )/rtia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as followl /ic0g 3naz3er bhn9e:zu*2os: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the m9 na ncul03ie3*ezg zohb/2r :oment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictiok+g2zs *nuh;/w wd*xn nless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, e*wg/+z *su n2khdxwn;xerts 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 the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a friy+*kzco :w6s )q.f( l9*kr4zk bewwnpctionless 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 maw* wknf4sl6: czzeobk.p w9y*r +)k(qny 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. w,r-ni 9 yrz2pThe rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular accelyri2-rp,9 wz neration 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 rx z y5gl x5.9dida1w6wadius 30 cm and mass 1.5 kg. Neglect the mass of thyxxdw5a iwdg.961 l5ze 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, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionle2: hwsbmbj 5,y4a0e jqss disk pulley of mass 7.07 kg and radius 66:sj 0 b5j,2mweqyb 4ah.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a ro*cac,h3n ff o:pe wrapped around a frictionless disk pulley of mass 7.07 kg a3coh na,fc* f:nd radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be qjo r 2/-h hkd2;drmh7ln2tl2 used to store energy. 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 inehjo govk5u(j o m:h631rtia 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 an wxct/*p6f(t vmix,i6d radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the xx6mw* /fi i,c(t6vpt inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed an bch+34 jnfj)x(,/igt1m irof 10 m/s. How high up an inclined plane can it cxjhm af4 3+i1i, /nbrc)(gn tjlimb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest an ha,h :jb: (:sridgn-+z jnw5zdn98ynd allowed to roll down an inclzayn : h8w(jnsh,9n n-jr: digbd:z+5ined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass er)oa83tf m;d1.5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia o rted; o38fma)f 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 b;w;g-t+ bzztf 1cg. i-8 udunpy $20 \; kgm^{2}/s$ 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 iner u6mpjrs (7)1ay)auzntia 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 rotati-h-, k-y2 ./ylifgopalhw n*k9mmq*zm n*le) ng at 5.00 rad/s with arms extended has a moment of inertia lz* lan- lhn-qm/.y9, wyhgom*fi*km-p2)ke 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?