Angular displacement ibdfn-ct2m*vykeo * ydf fbyo;iet) (0);(,ris usually express in units of

  Angular velocity is expressed in unei/e q xv5e9q0its of

  Angular acceleration isakn91 c.3f7qxj 6 krwp expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a coogfh5 *o;;(m-*ozzvb 6g utkgnstant rate. The boy is z6- mfgz;o(g gh ;v5 k*bo*tounear 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 meri.,:c9axjl 9m 3ezudnry-go-round which is turning at a constant rate. The boy is near the ou x, 9umd:3zi9encja.lter edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding l l a8dys3:8p-hq)qgyon a merry-go-round which is turning at a constant rate. The boy is near the out:a )q8l qdp hlyy8-3sger 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 constant rg8ne vibyqtz*:)jkbacb y /,4qs 0**r ate. The boy is near the 4 qz0gbrs)a*yv :y*t,jb nbeq8 */ic kouter 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- ize4ewgu( 7dvhld3+. 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 tangential a7eel +h4 u3( gwzddiv.cceleration?

  Consider a rigid body tha m1e- p0w5kdf9uons4at is rotating. Which of the following is an accurate statek w 0dfn9po154 asuem-ment?

  Rolling without slippinup/s- ;+c+ayfgdm c4ug depends on

  Two equal forces are applied to a door. They* dm,5 q6/4olq trvww first force is applied at the midpoint of the door; the second force is a4ly ro 6q,*wdmq v/5twpplied 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 doorknob. The firmgza ((f 8nbd4st force is applied perpendicular to the door; the second force is applied at 30e to 48gb af(zd(mn the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpl vo ljz 2avl45c uj-uaq89q)tc(47dcendicular to the door. The first force is twice as large as the second force. The r ov t l7(2cql9zajcj- q8 dc54vu)l4auatio of the torque of the first to the torque of the second is

  What is the quantity usecs.b0,q k (n6nths*xh d to measure an object's resistance to changes in rotatit,s.bnhn6q0 *h ks( xcon?

  Consider two uniform solid spheres where both have the same diameter, but ogoj);8weya+:ql+f)aa*ny c u ne has twice the maa;ylca+e a): yjnwgof)+u*8qss 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, but one has twice the radizlz0)/sy6 r. 5cw;g ofz4ur (t1bivlr us of the other. The ratio of the larger sphere's moment of ine o 1ut vy.gr45izrwb(s;lcrz/f l6 z)0rtia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice 9zce43fz0brdu,0 km5xt l lo0the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of t oz09mf lrtx dlbue3 c5k0z0,4he smaller moment of inertia is

  A uniform solid sphere has mass M and rad;ho;*oo3j zz c8fg pc1ius R. If these are increased to 2M and 3R, what happens to j*zzgc o1c;p 3ohf8 ;othe sphere's moment of inertia about a central axis?

  If a constant net torque is applied 95v j*r rgh8vkwwebvcnh* 7ya):rm 97to an object, that object will

  The moment of inertia of a solid cylinder about ittx 7;fb)dp(cx62it ox s axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is)otidx;ptx( 7x6fb c2

  Consider a motorcycle of mass 15* csiopt:e mad20s2,v0 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 uniformsv* 2 it:dso0 epmca2, disks.

  Suppose a solid sphere of mass M and radius R rolls withoyl:l.e p do.yv-*rhv*ut slipping down an inclined plane staelv:.vp*y *lo-.rhyd rting 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 rcd12qq a k0e.gt.tk9 uolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the.e qakgtqk19cud t02. bottom of the incline depends on

  "The total angular momentuwn88mey3 8ajbs0 gnfk;r/rw xq 9dq3 *m of a system of particles changes when a net external force actwr /bqjnfr 0s*k9 a3w;q8e ydx38mng8s on the system." This statement is

  In what circumstances can the angular velocitmn qdz5-1nd tv w3,q0(+cdenj y of system of particles change without any change in the systc dj (d1vz5nqnnt0e-+m ,wd3q em's angular momentum?

  The Earth orbits the Sun in an ellipticac 6 *zc- +ovv/gr:frwal orbit. Ignore any friction which may be present. What happens over time to the Earth's angularr/cw-czo a:*+gv 6frv momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbii.,qu/:g,, r 4a ahdof+t ,z 5wype.sgc3i ibbt. As the Earth moves close to the Sun, then which of the following best describes the ,zqpea: 4d w .ii+,b3bihygctrg/foas,,5u . orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretcr(* q7nqz o.;on spwwlx/*n 1zhed arms close to his body. What happens(* *nw .zw;o/lp s7noqnqx1rz to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) byhg7:vtr2v ds6 1m(yti pulling in his outstretched arms close to his body. What happens to his rota1(m: 6vgidr7vt 2hs yttional kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outs-s h4mch2zb z)1e lsb1tretched arms close to his body. What happens to his moment of inertia about the axis of rotatih-s14s zc) bbml12ze hon?

State the law of conservation of angular momentumy x*69f,lsvtr:j j7ou6q e4ub .

  What arc length does the Earth travel in g-b,nx yvp n*hue+39xr5wo3 ya three month period in its nearly circular orbit about the Su5v 9+ xoy gnh,b-enp*x3ury 3wn with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a l 45,mo zvdou*sength of 0.30 m. What distance does the tip of the second hand sweep throug 5u*vosz4,mod h in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equis0av*xhddt6(h7g m/dvalent to?

  A bicycle wheel rotates uniformly 13 w0ig hne:ijf:o1az through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rz:wi011:agi 3j nfoheotation?

  A pulsar (a rotating neuwwwjp h)c;a6g vatwp0k 6g. s bc01z4;tron star) emits pulses at a frequency of 0.40 kHz. The p;jwcpa;ww s)zgw0pab k6gc6 t 1 h.0v4eriod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it t0 ex 14xymygrhybm2 ,8imys:. urn in 0.20 8y,b0yxxrsime4y.my :gh 1 m2s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point onqc ; k/)y9fkfj the outer rim m9yqf ckj/f;) kove in 2.1 s?

  A bicycle wheel rotates uniformly through x ,/otoq 0n,fc5bs) ejahi i*xx;39kk2.0 revolutions in 4.0 s. What is the average angular exh 9sxoiojnc 5*tx0,/;k a,f3bk)qi speed of the wheel?

  A bicycle wheel rotates uniformly through 2 n vs,ik/z 7as9 ysjhj15c8/ skqzvf* .jem5m;.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of thec1v msjiq5a/sf/me95jsjyh , k . 8z;*znkvs7 wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The me2*e 38ytt s s fu4(v1l2lptacable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the f8m* l2s21ueeypt( av4t s tl3pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a copt6qlh3,jm n)db wd. 5nstant angular speed of 2.0 rad/s. What is the linear spdbdwltm,56)j 3.n hqpeed of a point on the wheel's rim?

  The cutting cord on a ga5t:4;1ky4rigs t xegas-powered weed cutter is 0.16 m in length. If the motor rotates at thesrxe4g1 ttak; i:y5g4 rate of 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 constal8xdifl80 ;s ant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point o ;8axi8lfl sd0n the wheel's rim?

  What is the centripetal acceler 1uzj u/xn 2ylfqp+m 8zf41ko8ation of a point on the perimeter of a bicycle wheel of diameter 70.0 cm whuloj/4 z2fzfk u8+nmy 8x11qpen the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must d0(st59/; lgmb4ee6mwz rm yfa circular, rotating space station (r = 1000 m) rotate to mr/ l;gd4m6ywbets m50e9f(zproduce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular nr:vtc qk-icbkejmk)(;0l9 fd 6o6e;curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) iskrb -omk)6 f9qec6 (;t;dnijc l:ve0 k $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat xh.h8 )r bvveq(50cg8g afm3icircular curve of radius 50 m with a speed of 20 m/sb)3qcv.h0x8e hrigv 85 ga(f m. The maximum centripetal 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 end of a 0.750-m stringvsu )3g*-dh fm, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 Nuvm g f*-3hds), 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 t ,m.bzmb)wr 5dw) 2gsslipping 10 m downgm) d) r,t5m sb2.bzww a 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 accelerati/zth7t9, ohir *ifc(gon 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 angulazezy3rf5 )1xcb ),msir 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 automobile tire rotate after startincnzysg n *kkk.20p3 4vg from rest pk3 0yzgvs* .c24nknkand accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, an *k /ai.q bnpuemauef1(,i18id 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 const6mimv x/l azl7xa f626 ,9zghutozn(9 ant angular acceleration ofzgli no,h v(fm 6xazt6/x97z6mau92l $-5.0 \; rad/s^2$. 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 turnvzz)g1lhz jj/-p+ 6zm ing through 2.0 revolutions. What is the averagepzz 6lzhvmj +gj1-)/z angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 1 kom5m70phuam/s to rest over a distance of 115 m. What is the total number70 1ao 5mpkhum 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 rest over 8t)ov h u2qr12f yo0dyc-z9pda distance of 115 mv)yho ty dc-oqf2 1rp208dzu 9. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down unifox6c eoq 2.-lyhrmly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to theh26 -qx.clye o stop?

  A centrifuge in a medical laboratory rotates at a rotational sp ;-we4tyx4 qg3kxtzw2 7zl9edeed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acc lxqt94w7zk2 gxd-zwy 34 tee;eleration 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 wheglxz6:0 qr : lwjfcyja b98 9z)l)js7sel require tightening to a torque of 90 Nm. If a 30 cm longa67j sjl9cfl9 gx zl wb:)zsry :)08qj wrench 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. If a 30 cm xsjcb )2 qw7v*x01wmkbpmi90long wrench is used, what is the magnitude of the force requirexs7qkw vw0bp mcjx92 *mi1)0 bd when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inej+e9)vxzv: * l-dcwon 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 follows: mass m is at the origin, mmff62z ei ,bg7k*df8 vass 2m is at x = a,kfb ifve7f*2g6m8z, d and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted bi.a qvv )r;g) o0jnt8about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a )0) q;tnvv gr8ijoa. bforce 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 frict ym. ocd 139xsemso,h5ionless axis thought the center O. A rope ced3ysmmo os 1,9x5. hwrapped 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 rod is initialo c5.2kic(kjlly held in the horizontal position, and then released as the free end is akcl5jc. (i2ko llowed 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 1.5 kg. Neglecipxr1(oqx , 1a3uw ua4vfy-x(5;jbp/tnc u) a t the mass of the axl ytpo x-pu uaxr(141iqxj3,u5c;nfwaa v() b/e 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 a4x(wq 5v2fyqz frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accq 2(wq4zvf y5xeleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk x.-lbwm)567o8xfnqpkp5gir pulley of mass 7.07r )x g865 x mpp-.o5qklfnbi7w kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to storedm)qf jhp7(+.7 csl wk 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 inertia jr rm s:k0yyf qc)i, q0t9:i/tof $5.00 \; kgm^{2}$ 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 starts f 6oh+cj*q;maqz0q wj 0rom 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 inclined planm0q ;qqah*w j0czoj+6e?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s qhisjc14p empvaop1x i7u:l- e:z0 q1 c8)yu:. How high up an inclined plane can it climb before co1pj po mx1ecqh :0u1iva i7cy)usl: 8:4q p-ezming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released ie ycd;a 1;pv ( ztn;+jgb:p-ifrom rest and allowed to roll down an inclined plane. How fast is it moving+d:pzc;jyv1nb ep;(iti ;- ag after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm r-abgmq9-dkn etta(,ie7t k,q4a -(q folls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. nt(q7tfe-qa4b-(ma ed ak,gq9, kti- 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 +)yld e9uy ly6momentum 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 8n, pnh8h+ltc 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 5.00 rad/s with arms extenzq)b.)vn9t0z53hg8 pa jmc ssded has a moment of inertia ofs5qs)a)z8t 0hj9gmc v.z3bp n
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?