Angular displacement is usually ee(ybig+k6 ;nx0 fxm0,kle /hwxpress in units of

  Angular velocity is expressed in uno(h.jb5 uuq-sb yr8+ eits of

  Angular acceleration 2bz* ; q xrduy;xjt7m p4o/6wk5mg.kcis expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a2 g hti7m- ;-g l2eo 0hay:cyzl:y4aia constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular d g2c:yh0ai- 4h7-l ymt2ai: ;oyzgeal isplacement?

  A boy and a girl are riding on a merry-go-round which is turning zz yd0ujg6rq3* i.e s3at a constant rate. The boy is near the outer edge, and the girl is closer to si0 6zu3j.ezgd*q 3ry the center. Who has the greater angular speed?

  A boy and a girl are ri e o+3spv)/gc pl8opg(ding 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. We(pg3+/8v loposg) cpho has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at aihl 85bo5sz z+ constant rate. The bh 5 5o+bszizl8oy is 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 turningj f dbv6 cncv8lut+(vevy*(863s+ub o at a constant rate. The boy is near u3 ujvfd6 yt cc(ve bblv8osv+6*+8n( the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body nhc 6z9nqm4 2athat is rotating. Which of the following is an accurate statementq4 aznmc69n h2?

  Rolling without slip 0m+j- lwmpgw*r7mm6rping depends on

  Two equal forces are applied to a door. The first f8muiq4xy 8j5g orce is applied at the midpoint of the door; the second force is applied at theq mgx8i54 yu8j 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 doorknob. Th.0 jg5u2)uhgo 1njvvp e first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. 0noh2vpv. 1)ujg5guj Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular tyv 51o2b6kbk po the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the second isobkky 5bv6p12

  What is the quantity used to measure an ob;qrh* sp uocb9 np8l:9ject's resistance to changes in rotation* lupsqo;rh 89nb9:p c?

  Consider two uniform solid spheres where both have the same diameter, but oneid)ub8l,tn y jon rd/xnejp 2/whxjq*1.55 5 o has twice the masure8j2/ t*xp,1 bij yq nn.w n5ldd55o/xj)ohs 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)p+ny h ,pdn4 nv qs/r.6on:io the same mass, but one has twice the radius of the other. The ratio of the ,4qnynn rppo6 sdivh /n):.+olarger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice0r0rsryk hi02 the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smallyh00 i2 srr0rker moment of inertia is

  A uniform solid sphere has mass M and radius R. Ifpt1hx)j wt9w9mc p9op 3 cyo,- these are increased to 2M and 3R, what hap,co 9yw-c) 9xwt9pphpojtm3 1pens to the sphere's moment of inertia about a central axis?

  If a constant net torque is ap8bk -mj3 g;ct :x-uuclplied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 Mt tg erj6u/gzq0s3o iclw;0.+R2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translationas lzt6uegqr/o 0i.w0cj+;3gtl kinetic energy is

  Consider a motorcycle of ; .x.r 5tttnbbmass 150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ttb.5n .rb;xt ratio of the rotational kinetic 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 and radiu(srd-so( wr.ks R rolls without slipping down an inclined plane starting from or .dks-w(s(rrest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M as5,0j fthw7hr nd radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottosjt 0wf,5hhr7 m of the incline depends on

  "The total angular momentum of a sys+y:n /vmpb0;uhh7jdb 5;fwn stem of particles changes when a net external force acts on the system." Thishnj b ;fm+5 ;sn/hw:ubd 7py0v statement is

  In what circumstances can the angular velocity of system of particles chandes)8l: 3 0gguwcpk.jb;j kz 4ge withsb 3j)8:0gkegp d;k.czluw4 jout any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which malsb;2, fd 0is3kz2jd)yeqp+qnqj 15cy be present. What happens over time to the Earth's anbyqj,k1p+nd0q)zsdc ; 25 es 23fljiqgular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. yleku-1y qv75As the Earth moves close to the Sun1l5k q ey-uvy7, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (ap xh r j36o0,nm.hc30ato-pq-crd4yu fast spin) by pulling in his outstretched arms close to his body. What happens to his angul tnhuxrp0-r3y aoq, - joc h3c46p0md.ar momentum about the axis of rotation?

  An ice skater performs a piroq l;znwmsf, .7u4pac4uette (a fast spin) by pulling in his outstretched arms close to his bodaz4s 7f4 p,. lucqmwn;y. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullia6f5;6hgz tii ,0(vpye tp -sdng in his outstretched arms clpzveat;i (i6 pf0h ,d56yts- gose to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentumn2zl 5 e9xq l-xpu5re2.

  What arc length does the Earth travel in a three monthv,.07 ase jijn period in its nearly circuevj7n,a0i.s j lar orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a cld n5d *8,vnk 9kqmrse2ock has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and sn d2*8v9 ke,nd5qkrm45 seconds?

  How many rad/s is 25 revolutions per minute equiv xtfh;9i,i-v ialent to?

  A bicycle wheel rotates uniformv d)z0d n7kgs;5 efl4nu, xo9eg y2w6lly through 2.0 revolutions in 4.0 s. What is the frequency of04gez)9n 7 lkedx,fndvg5uols 26 ;yw the wheel's rotation?

  A pulsar (a rotating neutruof:fcya2n+ d,va(a 8on star) emits pulses at a frequency of 0.40 kHz. The period oya ndva:8, f ufac+(2of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn ineu6yfutf(z;3m7 2l nw 0.20 s?7w(;le62 nyuzt 3ffum

  A wheel of diameter 26 cm turns a; bi sgavwuzrnj5.(xh74hns4 m (py:9t 1500 rpm. How far will a point on the outer rim (5bsj.( r zx4mn:74 hspvuigaw 9ny;hmove in 2.1 s?

  A bicycle wheel rota3*d4q dozd;s;o p) x6vvc6hvktes uniformly through 2.0 revolutions in 4.0 s. What is the average angular v;dd4o6; ) zkhdoqxvvs c3p6* speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 ipo )nf t pjsxb+e)bt)u5)pcz 1.0.kyrevolutions in 4.0 s. What is the linear speed of a point 0.10 m fnybfz) +pkcue0i) )ps1) jop tb.t.5x rom the center of the wheel?

  A cable car at a ski resort carries skiers a 9quw 9j 1qa :z3rtsx 9,i (cvsg:xh9skdistance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fa9w1xst(93 q9xg9rk qa :vzjc:uh si ,sst 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 angularz(lv (pc)g)o*2mcq xi speed of 2.0 rad/s. z)cv *m x l(gicqo()p2What is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. -(p mu,xd k*rq If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord *kxdmuq(, -pr?

  A wheel of radius 1.0 m is rotating with a consta54eod( ot,fu - (dwsoont angular speed of 2.0 rad/s. What fo54( do -odsotuw,(eis the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bc1lgv y6 (:mybicycle wheel of diameter 70.0 cm1y bcg:(ymv6l when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space 3l:n )fc(hk xw a;y(5ys:u+qop,yqec station (r = 1000 m) rotatecn5) :3( eyh; a ,pw:xk(fyc+sqqouyl to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circularj a7xl wwp;+365 mazk0a;xrhf46uq *xrqr x w9 curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (proviax 9pw ja7 mwhklx0u6 w3r+*ax6fxr;q4;zrq 5ded by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circufyl u8 5jmt9lylt.;n m w3jh14lar curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) isl8n hml5wlymu3t9 t1f4 j;.j y $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to tqq8in,+ w+evwhe end of a 0.750-m string, is whirled 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 hvqww8qe+ i+,nave if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls witzi b-m(1,yz nuhout slipping 10 m down a ( mb1zyni,uz-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 con -l/b2jz6 iz; :tpfklb:ck(5uxx k+yi,k iu ;mstant 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 constant angular acceleration of:dkl;hz(p(onhegh:5 r 0r /p e $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angular velocity at t = 2.0 s?

  How many radians does 10 -hjdxg+eak r;xnd3a 0.300-m radius automobile tire rotate after starting from restx+d3n gh ad01-rxej;k and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an a16elldn)oc+vrn 2e5 n ngular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelr t:th+3ya 0vfvhg-l2erates with a constant angular accelerationtfh yhgav3+2 tvl0r-: of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches anfx,lg2epk+ l)7y 6z fq)i55-zp jqljn angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average z5ig-e,6 q2l l5jlfy fkz pj+p))nqx 7angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest overbtc)n)vp 7j0 9sd*)lusi18nr pr/rq s a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to cl*bs7psjd0)v1n srr/)qu89ipt n r) rest?

  A wheel of diameter of 68.0 cm slow4j q+a 2nzpft:s down uniformly from 8.40 m/s to rest over a distanct2p+j f qz:4nae of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slnox:0eajt vkv7y .4x9yqz*( qows down uniformly from 8.40 m/s to rest over a o74ye 9(x .nt*:jxqvk0y vzqa distance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotyemqwl 4p:-wtdhp +2:ational speed of 3600 rev/min. When switched off, it rotates 50.0 times at :h2pplytmew:+ -q 4dwa 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 tor3/mto jqkw67cy7c2d d c8/c-ys (ll zoque of 90 Nm. If a 30 cm long tyqs/o- 7c l o32cc8dzy/7wcd6 mj l(kwrench 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 Nm. am+hu 1m*s-7a- g5nnt81gtibt;g ius If a 30 cm lon*t; -5hu+a1i bs8g 1n tggtiamm7u-s ng wrench is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertt-e ox, grmh+4na/ s)dia $3.00 \; kgm^{2}$ 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, m:wpx,m7b4(.py( ortma fu436iu n ei nass 2m is at x =etbm4( npm w(7ia.rp6u,n4u :yfxi o3 a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg isoa1k9rol :; um34if aq 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. (Seumio:9;qfl ar34ka1 o e Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivogpwt ; ek; (zujr:7nsz a:w7c7ted about a frictionless axis thought the center O. :zc u p7rtwa7k(e;nzg:sj ;7w 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 in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The 1kaf;ph9f 6ucrod is initially held in the horizontal pouf9 ;kf1hca 6psition, 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 end is ML2/3.)

  Consider a bicycle whh13 i ;aky.t51fauykyeel to be a ring of radius 30 cm and mass 1.5 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, whatyau;.aft1 5y1hik3 ky linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless ghf1r,xnqyfff8 w73l)sh ) tx6cle3. disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accelera3,)nsf3.lgtqhe 8 h6fylc7f)1 wxxrf tion of the pulley?

  A 1.53-kg mass hangs on a rh30 szhau;vv(ope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the z(hhsu; v30avmass?

  A rotating flywheel can be used to store energy. If it is req)f5 g6m5 mglt)r4nzy 8twcua-uired 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-52gd clye8 dx $5.00 \; kgm^{2}$ 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 startss - j/xdfm1mv ek) xq8en00m)w 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 bott-nve) fmx8 e1m/q j0swkm)0 dxom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rollo(z r4+ , ylvn6m,dqals with a speed of 10 m/s. How high up an inclined plane can ita, yr n+dl(qoz4 vl,6m climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is relea9zq 8 *q,mcy en,e: c19xpbycased from rest and allowed to roll down an:y 9 xpyb*z,e9ceq8c1mn, a qc inclined plane. 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 w b2a,: iloftw6yo 06 g)mje/jdown a 35e incj:) gw 2amow6j/0f b,t6 eolyiline that is 7.0 m long. 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 changess:nbz-b o3j.1 hfr a)p 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 in:wrigbcfpc k 7jkz1u//97wr. ertia 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 of inerf/jrl v3knx ;w8(c )kfi2l; sqtia o k8xf/lli();sj;nvcf3q wkr2 f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?