Angular displacement is usually express in unitejny2dnjs)vh ; ii.r9j, 2*zzs of

  Angular velocity is e .ou;of0nk+f h9pr() z;maah qxpressed in units of

  Angular acceleration is expressed in unit9 d4f9cw4 -s1qsehhecs of

  A boy and a girl are riding on a merry-go i/zjy n/u+tt+o --xsr-round which is turning at a constant rate. The boy is tr-/sij to +-/y xznu+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-rounsk4drq /o8r rw +:(fytd which is turning at a constant rate. The boy is near the outer edge, ar(r:q /tywo8 df+rs 4knd the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a coyqmy invwu ;57 *h)x5onstant rate. The boy is near the ony5 7uq5oh*myxw vi);uter edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a col jnr/ -i z+zu,)w0eqjnstant rate. The boy is near the outer edge, while the girl is closer to the center. l0/qw nj-jz+e rui,z ) Who has the greater centripetal acceleration?

  A boy and a girl are riding a ;fp)tpa*lhi,e o+ ct3merry-go-round which is turning at a constant rate. The boy is near the outh t,3p)ipo tel;*+f acer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurate k 0+(ng l; 8unfuat5mistatemnimf0+ulg ua5t k( ;8nent?

  Rolling without slipping depe y6-yk2k+if aqnds on

  Two equal forces are apptmau+*pp0kefe/p- f1um l mkx,z5r-0 lied to 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 exertmku e 5/ 0 0*rupmzk--fxe,1afmlp+p ts the greater torque?

  Two equal forces are apmu+b.e9: j7lm8vg ztsef5h h5cbb ;+5 au.yj rplied to a door at the doorknob. The first force is applied perpendicular to the door; th7uc hymevz+9l. e;:hf5 .5m8 ubrajbtjs5 gb +e second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. 25pu vr5erdh 4 The first force ih25vd5p r4 eurs twice 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 an object's resistbav :ptr9g mwgum :350q1ba lf.;3vxkance to changes in rotatiafgkw9a 5 1pqx 3b0;g::t3 lvbur .vmmon?

  Consider two uniform so(i.y4 w2n kupolid spheres where both have the same diameter, but one has twice the mass of the ot 4k2(pu onwi.yher. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres havebin ain5 s-eo1kd;/xgb h(( x9 the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertbx eg nio/hna 1;(i5dx- bk(9sia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and try(vuj49vt3amv0w 5 el 1zj a+wice the diameter of the other. The ratio of the larger moment of inertia to that of the smallv uaam40r+5 v9l3 jw1yz(j vteer moment of inertia is

  A uniform solid spherejqrolh(r,e6sge*0 / s has mass M and radius R. If these are increased to 2M and 3R,srelh/q*o 0e 6g( rjs, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied 8m6bjzer:7 xp npa c87to an object, that object will

  The moment of inertia of a solid cylinder aboutfqa8mr*0suww dmy1 9u3;tlgi/ mf 9c - its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio ofr fq usywm3;8mt99algmwd/1- fi0cu* its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, *u ;jrbu3:j3z7 v:y wcnpxf p8one 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 tb 3jy::npvcfp78j;rwx u zu*3he bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolletwe(wpp0o7 kfe:/w* pr it: -s without slipping down an incl:ip/p-( te7 pkrwwowet 0fe:* ined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an ibixbi+ng i68d. ydy-s /z;,eh,qe;t u2tejy +nclined plane starting from rest. The angular velocity of the sphereybis2jy8i; -e+i,hzg d.y+tbude/,qen x;6t at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net exterb5+9yf6mrvj(i8 ;w y1wcvmt5kujg 8v nal forvk 9fc(vw myj1i5;8r+v 8ym5 6wugjtbce acts on the system." This statement is

  In what circumstances can the angular velocity o kt/9 :b-qjxhr8m s:rpf system of particles change without any change in the system'8qpxks:j :/m-b trr 9hs angular momentum?

  The Earth orbits the Sun in an ).ku 6 /hunwmuelliptical orbit. Ignore any friction which may be present. What happens/u) uu.wkn h6m over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ellipticrdk9lt7igg p* 0ng ppdr))xlm 8*ez,cgj/34bal orbit. As the Earth moves close to the Sun, then which olp7m)8gd z ) c*ldb3gx4*pjten /ri kg0 ,grp9f the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fas24 tgbmg+oq-tt spin) by pulling in his outstretched arms close to his body. What happens g-bm qo+t4t g2to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by p;6 bg byaih97r5;yvj0v8atvzulling in his outstretched arms close toj7i9t;b a8agz vyv; r0bv6hy 5 his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling ie* jhio9*r zs,xb h99yukl oim3m,;h-n his outstretched arms close to hh99lmkj -iyb9*;zmx es, iuh hr*oo,3is body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation/f.esp(k )b/ n*yxteg of angular momentum.

  What arc length does the Earth travel in a three 33 bjzq .1ehg;m86fz,ugagpn month period in its nearly circular orbit about the Suhpazf 3zbj8;gn6 g.,q e13gmu n with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a cgg y::w)wli /l,o0 t7nn gd3zulock has a length of 0.30 m. What distance does the tip of the s7nlg )0l,t ig:z wyg/do wun:3econd hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions pekl9o oa+9xe/ er minute equivalent to?

  A bicycle wheel rotates uniformly throu3: ud6ef/pg2y k 2wpe5hcz /sjgh 2.0 revolutions in 4.0 s. What is thesd5p6wegyu k3he :2j /2z/cfp frequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHzm8 7bzkzwr8 (gwga)9u . The period of its bkzmaw( gu 7889g r)zwrotation is

  A phonograph record rotates at 45 rpm. Throughq/or2skl;yt*:y+fhds epz ,m 3a/+hp what angle does it turn in 0.20 s?*y+pd/s:+p 3ayhs,o k/l mzhe2t fqr ;

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on th:cga:gf3drpf *2 ;nt se outer rim move in 2.1 sgsnf;radptg 2:*:c 3f?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0utks6s2deho 8sa3 p; ) s. What is the average angular)pu 8h2 6;3ksestsoad speed of the wheel?

  A bicycle wheel rotates uniformlywc:2burc5u1ha3zh8 ) jc gj-r through 2.0 revolutions in 4.0 s. What is the linear spe5b :13gh- 8 ajuhrjz2uc)wccred of a point 0.10 m from the center of the wheel?

  A cable car at a ski res(y e zwo6s)h-w;*lfc,isw rx+ort 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 the pulley rotate for the cx s;)h+er- f6,iwc o(y*z wwslable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotatingxhau, tsv b qwa-x,b 14muki1e6g1 u4* with a constant angular speed of 2.0 rad/s. What is the li u41b1iv q*xu web,h1m6xu,4tg aska-near speed of a point on the wheel's rim?

  The cutting cord on a gas-pow6kcbcdqbqh99 )yf5 k1ered weed cutter is 0.16 m in length. If the motor rotates at the rate 9k56k1 bhf)c y9db qcqof 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 a constant angular spe5b 6g:ivf.q8rhwgbt,ed of 2.0 rad/s. What is t 8vtb,5q b6.igwh:rfghe centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicouq2s 6ukv a:ih1k- 2qa7btw,ycle wheel of diameter 70.0 cm wh6u ba kq 1,o7q2:wiksuth2-aven the bike is moving 8.00 m/s?

  How many revolutions per minute (rpz3m2)qkhqxday sx ;j* 6d(p7)s jdfew1w kt3 .m) must a circular, rotating space station (r = 1000 m) rws)1 x2kdjj7 .yhe * z3( pdfta63sx;qwm)kdq otate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flg-umgmj5( n; p/i*sw1 qduy//wjzeo4at circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fr;4(/ -z/5 ydsguj1 um /iwgm*qnjwpeoiction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radmne3w ; 0z.icsius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by ;ecsn03z.m iwstatic 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, isec)9xc df-ib3;e stp swv. 2qdb/6 gvlx/tr 26 whirled around in a smooth level table. If the maxim6fq/g /2cdxt rx.9pe;s-2cl stedvvi6wb) 3b um 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 rolls without slippi 2iqhlbfoku69mr*c bdc85xg1vm2k ,4 ng 10 m down a lane at lkm8xcf 4k6ur,* bdq2591om vib2hgc4.3 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 accez6jo 9lgh4 v+qleration 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 x ux04*csfwp+0y:np k constant 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 0.30rsf4nsjkq x-q /: e49a0-m radius automobile tire rotate after starting from rest and accelerating at a cons4qs kexf -j4r/sanq:9tant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular a*:k4kqc/nsz q1)/(o oxh zt2ormk v 7jcceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelera us yu7 eymh:uy-i *(0f(zo7ottes with a constant angular acceleration of yz0h*fmu (uo iyot7s-(:7uey$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and r7 4ie:sen9wdneaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average anguesn ew:d 79i4nlar acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly fr 1n3(qudpc;fpom 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in comdp 1cf; uq(3pning to rest?

  A wheel of diameter of 68.0 cm slows down uniformly f)h1q)3hof 5pjg7hk non 1p ev3rom 8.40 m/s to rest over a distance of 115 gp5ep)k3 v nf jhhno13h)1o7 qm. What is the angular acceleration?

  A wheel of diameter of 68.0ohlxy-tth ,. , cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long doeso-tlh.xh,, ty it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotm40* i wjy+my x;a1fhpates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before comh; i amy4y* m0fjp+1wxing 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 wk5 w (iq 1yseyy;o3(l 5mikey9heel require tightening to a torque of 90 Nm. If a 30 cm long wrench sm9k yoyike1;ywe(5i ly35(q is used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nmon zt4,m 5c- y7bfik qtjo3j3(. If a 30 cm long wrench is used, what is the magnitude of the force required when the f(ykot3nb zq -,7o5 fjtcj 4m3iorce applied at $53^{\circ}$ to the wrench?

  A wheel with moment r7 0*ygs:ms.k 9xutt sof inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as fowu)xg b,h83lu8j ph b1llows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertiaj,1 wh bhul g8upx)83b about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis though8wkvw 1b62 lzat 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. (Sew z6 21wla8vbke Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivot.8tdum trf4 z 2:)f6 1hhqfyofed about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 mdmt8th yfuq 6f4:2f)h.1oz r f, 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 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is i7p z9s dqm:8rjnitially 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? (The8q pj7sdmz:9 r 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 1.5 kg. Neg ol*:cinf ik2,lect the mass of the axle and sprocket. If a force of 20 N is applied tangentiaoc*kf,l n2:iilly 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 disk pulley of maxl*9n,fvpnz158 l zr ess 7.07 kg and radius 66.0 cm. What is the angular acce5 vlnn9p8 zx1lr fz*,eleration of the pulley?

  A 1.53-kg mass hangs on y7l( 8bl mg2hsvbkp/(a rope wrapped around a frictionless disk pulley of mass 7.07 kg2v hlkbm/ps8b(y g7l( and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If e; 107sqy/ n.5iddd0xvpr ihmit 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 of j d(cijdk9f )sfu6-vy 9i2xy6$5.00 \; kgm^{2}$ 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 m start qk9hnl8+s+m it+u ef/s 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 emiuh8n k+fql+/+9tsinclined plane?

  A solid sphere of mass zv ap8:efm* 8l gq3r8h1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up apvl*z gmh88f3ea: q8 rn 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 all nj.m am,2*: hwov ))irufn1 .tf*pqkxowed to roll down an inclined plane. How fast is it moving after dr* *1uoa)f.rm):ihf.k,q2 tjpvnwn mxopping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slippink4hs-y1b(i1s c k1h/le 3d ) mh)zkl *bgz8nyeg down a 35e incline that is 7.0 m long. Assume it started from rest. /dhg1mc e1l4k3n s bk1y)zs8- iybz *kel)(hh 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 mouz4rzbh 0eb(3 mentum 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 of ixxwq.k uy2bgdfrrg +8zr(/9.nertia 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 rada9ly3 2v8 rzjv/s with arms extended has a moment of inertia o9382r l zavyjvf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?