Angular displacement is usually exprkb.u1php-.,c t w5a zyess in units of

  Angular velocity is expressed g*f4 c) qw.o67pvyjdrin units of

  Angular acceleration is expressed in unit bj,ozz kr xffk;9 6qqn629dz;s of

  A boy and a girl are riding on a merry-go-round which is turnie418q3kzec :jk uz1kh ng at a constant rate. The 3j:qku41kz1z8e eckh 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 turni2i 8i09n touj6v ;bq ri+fpe5xng at a constant rate. The boy is near +;boq8p 0r nt vi 9j26ifuxe5ithe outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round7zp0 tu-pg ci) which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to tuc p0-gzipt7) he center. Who has the greater linear speed?

  A boy and a girl are riding a merry-ggi qhw47 mlzg 2ib+3nj3r9- too-round which is turning at a constant rate. The boy is near the outer edg9wr l 3- mnhi3ij 7z2o4g+bqtge, 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 y*xc9fm9e znel)snaeps 2aj5d5.-;c a constant rate. 2csnmef;9)sc*-.a9pe ln5 ed5yxzaj The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which wntl8 x*bdpai d :7 pje3zmt(5.,c4swof the following is an accurate sta5 mtj dad*zw,i( .bsl pe73:wcnt8xp4 tement?

  Rolling without slipping depe(v1px8tso kydt ,uq 9.nds on

  Two equal forces are applied to a door. The fw2ft (jz q:f(jirst 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(qj wzjf :2(ft exerts the greater torque?

  Two equal forces are appalg+f 0 .,-b v +nfhya/ okgqvw36e1pglied to a door at the doorknob. The first force is applied perpendicfw qnl v3g+o g0-, /yv.egp16 ak+afhbular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doork,7og:xn 0(4o 4t wxzsb-qoufpnob, perpendicular to the door. The first force is ( 0t ,z-:7on44bxqfgs uopxowtwice 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 uzuqw0+r j-fd5m p .d uf,9n(umsed to measure an object's resistance to changes in rotatiu+n0m5qum .w d(,f-9pjzudr fon?

  Consider two uniform solid spheres where both have the same diameterje2.x sin 3cwhya6c*px 6e( e7, but one has twice the mass of the other. The ratio of the larger momex7p 6 che32w ( x.e6*jcsniyaent of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the sb;e tlz4n iu(,f1m:cz mvm*-hame mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smae-l4 (c vzmtn; bm1m:hu ,if*zller sphere is

  Consider two uniform solid spheres where one has xye6bcy2q7:o4o8 nc* ,gaq tl twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller momeyb,*xcyat q :g276q48oo cnelnt of inertia is

  A uniform solid sphet7esy2an6vh)8eq8fe e69 w rore has mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central axisqon8 tys w26e76f 8rahe e)v9e?

  If a constant net torque is appih j6z g//+f4cp6vrr vlied to an object, that object will

  The moment of inertia of a solid cylinder ismci) 4j jj.2 jn;q9qabout its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rji.)4c9iq nqj2;jm js otational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of whg orpigb0xqg07u.x4 / ich 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 unboi7r gg u 4xq0gx0p/.iform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping down and1vwh s a/:2hb inclined plane starting from rest. The linear velocity of the sphere at the bow1b2s a :dh/hvttom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an in.gzo ui,r x.vj )+;fswclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depe .fxuw z vr),soj+.i;gnds on

  "The total angular momentum of a system4ys 8cb rm90h1oe9aony1n yu6 of particles changes when a net external force acts on the system." This statement sehr9yn8o6uoba1 y mc4y n910is

  In what circumstances can the angular velocity 2s 0 :k9*jh gfd)spdb -qivv-cof system of particles change without any change in the system's*v:i scj0s d f9dp2--kbhvg)q angular momentum?

  The Earth orbits the Sun n,fzx ey (h2pf 8h;.q6 1ttcsehtr )/din an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about tc./ q,1(te)r;efxd t pfzhnth8s2y6 hhe Sun?

  The Earth moves about the Sun in an elliptical orbit.(vbg z15lpqzt3osb -*0xe g /g As the Earth moves close to the Sun, then which of the following best describes the orbiting speed p* tq/ xlgozs- 013ggebzb(5vof the Earth about the Sun?

  An ice skater performs ase;rb bv(hvavt,8allx ) (5m. pirouette (a fast spin) by pulling in his outstretched arms close to his body..v)s8l( vbmvabhx 5le (r;at, What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrdu 6fgskb*8z3 o4b6 htetched arms close to his body. What hap8f tok3* b 4gsuzh6db6pens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hi,(f(chfuz3hz 88 v nkqs outstretched arms close to his body. What happens to his momq fk(uzz 3 fn8hc,8vh(ent of inertia about the axis of rotation?

State the law of conservation of angular momentu8 yuinq rsy;p+*g;e0rm.

  What arc length does the Earth travel in a n4;qdcig5 q ,.eaus y;yhs4b1three month period in its nearly circular orbit about the Sun with a gds;.an ibq4cuys4 h,q5 ;ey1radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0kcp dm 74w5i z3pn/9mn.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 sec pp dmnz49m5c7 w3k/nionds?

  How many rad/s is 25 rerh 36dekk6zt) volutions per minute equivalent to?

  A bicycle wheel rotates uh2od-z4pum(+f v( j tuniformly through 2.0 revolutions in 4.0 s. What is the fredfz2 ((m ujt+h4opvu- quency of the wheel's rotation?

  A pulsar (a rotating neutron star)jz0g (, 24yq:pbhcy na emits pulses at a frequency of 0.40 kHz. The period of its rota02n,q(pjz y cgy4ah :btion is

  A phonograph record rotates at 45 rpm. Through what angle doqko.h 3*lh .-rgmm b un9eiq,8es it turn in 0.20 s?-.h l* eu. nr3kmiq8 m9g,hqob

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point onk2,5nfy e+vem7t ghk* the outer rim move in mh+egvy72ek *5fn ,kt 2.1 s?

  A bicycle wheel rotates uniformly throughhepm te ,pi 2;s(t:lpf 9nc;-9f f8jgv 2.0 revolutions in 4.0 s. What is the average aneg 8nc;9j iett(pl s2 pvpf;9hff-:m,gular speed of the wheel?

  A bicycle wheel rotates uniformlyu.hn 4 oknr+ 6 uaf5-itry91ku through 2.0 revolutions in 4.0 s. What is the linear speed of a.5na+f r16 uuky- trno94khiu point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km q4g-5w4whu wuh,su1g. 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 cable car to make the trip sg hh q5u1u4w,w4 gwu-in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular spm zgukw5pjaz)*9w)p5 eed of 2.0 rad/s. What is the linkz59zj* pw gpa5))mwuear speed of a point on the wheel's rim?

  The cutting cord on a u : mqzcc:pb/d3.ed7f gas-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 fd e:.md7qcz:3u cb/p 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 speed of 2.051gb9 yl(8d7opljh sr mg-ds7 rad/s. What ihp o(lm85lr1 7dggsbdyj s97 -s the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration ofhko 3(gy+ g.ez i7qek6 a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is ke67o g(e+zih gyq 3.kmoving 8.00 m/s?

  How many revolutions per minuzyu2h 8h1plg /z 7q-jute (rpm) must a circular, rotating space station (r = 1000 m) r8hluy- 27z /gju hqpz1otate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m g*,+/x1p(xq oedfpu d with a speed of 20 m/s. (,guqpxdx do*1ep/+ f The maximum centripetal force (provided 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 radius 50.j 1u) +e,xo6pttmser m with a speed of 20 m/s. The maximum centripetal force (provided by 6t+ ,exo mptseur.1)jstatic friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the ends tj/p(/;wpkwzr/yp , 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 mt(pykpp;/ /w ,zjrsw/ass have if the string is not to break?

  A bowling ball of mass 7.5 kgq j3f9+un3en; r v3cjcg)ktp+ and radius 9.0 cm rolls without slipping 10 m down a lane acq9ne)k+f+n3; g3r 3cuvjtpjt 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 t pjc+ri :5z p*ch029yl .jwaxacceleration 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 accelerati:c9lkr*z 6 eafow7:q 5igv .opon 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 aug c gws,n(muffo)3*l /tomobile tire rotate after starting from rest and accelerating at a constant angular(m3)fs w no*/uc,gfgl acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acc 4(t6ja ngj +ylwfwu z02g yt),fexyy0:w-2vxeleration 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 co4 8zrymedah- t;+ks2h9:ccu onstant angular acceleration a+ d zc29o- ey 8cu;thmh:4ksrof $-5.0 \; rad/s^2$. 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 tu-8t ps t7rz ;t6hp-pgmrning through 2.0 revolutions. What is tpr67s- z- gtp8;tp mthhe average angular acceleration of the wheel?

  A wheel of diameter z)fev hh 7xjwm8xwhus(6 0u. ;of 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total nu.; vsxuwh( 8 uhx0mf67zw j)ehmber of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 6lhok*nbeyzg fq;6c e414 ge/nm8i e578.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. Wh6 ;hl4 f8eeioy1n7kg* me/enbz 45gqc at is the angular acceleration?

  A wheel of diameter of 68.0 cm slows df( a efo51uvsixy) -ys )84riwown uniformly from 8.40 m/s to rest over a distance of 115 m. H)si- 4wxsuv5 f( yior) ey18faow long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a 6a01 bqi4,okudh:j yc1lgl8 wrotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accel84 j6qc0 ,do wlliga:yk1bu1 heration 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 wh pc.-+nz,ipvsgzyln ;5 w01sgj to.,beel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to the wrev1.s tgz.izocg-p,+nb y5 n;jlw,0sp nch?

  The bolts on a car wheel require ti3gf;f lj1wh 6oghtening to a torque of 90 Nm. If a 30 cm long wrench i6h ;3lw1jffog s used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia r atp w 0a7gvl)dig(7q6t,3ln$3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: ma rkescju, m7y3(dq;l(ss m is at the origin, mass 2m is at x = a, and qe7;(sc jduy3 (m,rkl, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionle ,vw.vbd*s5v css 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 *svvd, cv.bw5= 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 frictionlesupv6r tomyg95 7 ;8i,t m8igtrs 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 many radians does the cylinder rotate through in the first 5.0 seconds, if it starti 8ytt 8mpg6 7u;it9rvg,r5 mos from rest?

  A 4.00-m long rod is hinged :1cipd +9fozwoe5 (bgat one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to falldfcei9z( 51: oogpw+b. 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 beeh5x*dbhoo99-eo.. / 2 xgcxo5ovsw j a ring of radius 30 cm and mass 1.5 kg. Neglect the *j5 e5 vhshw9o/2boc- d9.o.oxxxoe gmass 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 speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on 5iey,d ls 8nb1ntwm+.a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acc5w.e 1+8 btndniml,ys eleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a fr(ibx6xok +l 8wr r/5zlictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the +irl xw rbk(zo68/ l5xacceleration of the mass?

  A rotating flywheel can be used to store enzmej,vvq8-az 5;w ky:ergy. 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 oho(bmqpe 9 fyh- dl+xe +2.he)f $5.00 \; kgm^{2}$ 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 uu (mui+ qlz-+kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is theuim l+z -q(+uu speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kgi qhp0 :bj95xj and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before cj hq i95xp0j:boming to rest?

  A hoop of radius 0.50 m and a mass of 0.bif , 8u-c(5xxwqz( ll20 kg is released from rest and allowed to roll down an,i-(xwq f58 lu(xblzc 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 pnb98*zxu:u e.uauom4 u1i vh4u o.,kradius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. Thkneop:b4 4i h .8 xu,mu91ou*au.zuuve 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 changessp* 71hzpxqtyc-s7y* 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 16 mvu:)o0lsf9vlj afinertia 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 5o)av d+jb,)a f2kymz22ko wy/.00 rad/s with arms extended has a moment of inertia o fazm2)/oa yow+2d)jyb,kk2v 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?