Circular Motion. Subtopics. Introduction. Angular displacement. acceleration. Relation between linear velocity and angular velocity

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1 Chapte 0 : Cicula Motion 0 Cicula Motion Subtopics.0 Intoduction. Angula displacement. Angula elocity acceleation.3 Relation between linea elocity and angula elocity.4 Unifom cicula motion.5 Acceleation in U.C.M (Radial acceleation).6 Centipetal and centifugal foces.7 Banking of oads.8 Conical pendulum.9 Vetical cicula motion and angula Riding on a etical cicula ac, this olle coaste fans expeience a net foce and acceleation that point towads the cente of the cicle.0 Kinematical equation fo cicula motion in analogy with linea motion

2 Std. XII : iumph Physics Fomulae. Unifom Cicula Motion (U.C.M.): i. Instantaneous angula elocity, θ ω lim t 0 t πn π ii. Aeage angula elocity, θ θ ω a t t θ t whee, θ angula position of the body at time t θ angula position of the body at time t iii. ω ω a fo U.C.M. i. If a paticle makes n otations in t second, then ω a πn t. Angula acceleation α 0 i. Instantaneous angula acceleation, ω α inst lim t 0 dω d θ t dt dt ii. Aeage angula acceleation, ω ω α ae. t t ω t whee, ω instantaneous angula speed at time t ω instantaneous angula speed at time t. iii. Linea acceleation centipetal acceleation ω 4π a ω ω 4π f ix. ime peiod fequency (f ) π ω x. Relation between linea and angula elocity: ω ω as θ 90. Non-unifom cicula motion: i. Radial component of acceleation, a ω ii. angential component of acceleation, a t d dt iii. i. Net (linea) acceleation, a a + a.(magnitude only) t d + dt Relation between tangential and angula acceleation, a α θ 0 α 3. Centipetal foce: m i. Centipetal foce, F cp mω mω m (πf) ii. iii. π m 4π m Magnitude of Centifugal foce Magnitude of Centipetal foce m i.e F cf (in magnitude) When an electon moes ound the nucleus of an atom along a cicula path, we hae Ze m mω 4πε 0 m 4π n 4π m whee, Z atomic numbe of the nucleus. 4. Motion of a ehicle on a cue oad: he maximum elocity, with which a ehicle can take a safe tun so that thee is no skidding, is µ g whee, µ coefficient of limiting fiction between the wheels and the oad. 5. Banking of oads: he pope elocity o optimum on a oad banked by an angle θ with the hoizontal is gien by, µ s + tan θ g µ s tan θ whee adius of cuatue of oad g acceleation due to gaity µ s coefficient of fiction between oad and tyes when µ s 0, g tanθ

3 Chapte 0 : Cicula Motion 6. Vetical Cicula Motion: i. Velocity at highest point H g ii. Velocity at the lowest point L 5g iii. Velocity at a point along hoizontal (midway position) M 3g i. Acceleation at the highest point a H g. Acceleation at the bottom point a L 5g i. Acceleation along hoizontal a M 3g ii. ension at top most point, m B H mg 0 iii. ension at the lowest point, ix. m A L + mg 6 mg ension at a point whee the sting makes an angle θ with the lowe etical line m θ + mg cos θ x. ension at midway position whee θ 90 (i.e. along hoizontal) xi. xii. m M [Qcos 90 0] otal enegy at diffeent points at the top, bottom and hoizontal, E H E L E M 5 mg otal enegy at any point, E m + mg( cos θ) 7. Conical Pendulum: i. Angula elocity, ii. iii. a. ω b. ω g l cosθ g tanθ π Peiodic time ω π π Radius of hoizontal cicle, l sin θ l cosθ g l sinθ g tanθ 8. Kinematical equations in cicula motion in analog with linea motion: i. ω ω 0 + αt ii. iii. Notes θ ω 0 t + αt ω ω 0 + αθ. Radian measue must be used in equations that contain linea and angula quantities.. Finite angula displacement is a scala quantity because it does not obey the laws of ecto addition. 3. In U.C.M., angula elocity ω constant ecto but angula acceleation and angula displacement ectos. θ is only α ae aiable 4. All the points on a otating body in U.C.M. hae same ω except cente as it is not otating. 5. Instantaneous angula displacement is a ecto quantity. 6. Angula speed is a scala quantity but angula elocity is a ecto quantity but both hae same units i.e ad/s. 7. he diection of θ, ω, α is gien by the ight hand thumb ule. 8. he alue of ω of eath about its axis is ad/s o 360 pe day. 9. When a paticle moes in a cicle with constant speed, its elocity is aiable because of changing diection. 0. Cicula motion is a two-dimensional motion in which the linea elocity and linea acceleation ectos lie in the plane of the cicle but the angula elocity and angula acceleation ectos ae pependicula to the plane of the cicle.. Centifugal foce is a fictitious foce and holds good in a otating fame of efeence. 3

4 Std. XII : iumph Physics. An obsee on the moing paticle expeiences only the centifugal foce, but an obsee stationay with espect to the cente can expeience o measue only the centipetal foce. 3. Whenee a paticle is in a U.C.M. o non U.C.M., centipetal and centifugal foces act simultaneously. hey ae both equal and opposite but do not cancel each othe. 4. Centipetal foce and Centifugal foce ae not action-eaction foces as action-eaction foces act on diffeent bodies. 5. he diection of centipetal foce is same whethe the otation of the cicula path is clockwise o anticlockwise. 6. Centipetal foce is not esponsible fo otational motion of a body because only toque can poduce otational motion. 7. Since the centipetal foce acting on a paticle in cicula motion acts pependicula to its displacement (and also its elocity), the wok done by it is always zeo. 8. Centifuge is an appaatus used to sepaate heaie paticles fom the lighte paticles in a liquid. 9. Range of acceleation in cicula motion 90 < θ he adius of the cued path is the distance fom the cente of cued path to the cente of gaity of the body. It is to be consideed when the cente of gaity of body is at a height fom the suface of oad o suface of spheical body.. Whenee a ca is taking a hoizontal tun, the nomal eaction is at the inne wheel.. While taking a tun, when ca oetuns, its inne wheels leae the gound fist. 3. Fo a ehicle negotiating a tun along a cicula path, if its speed is ey high, then the ehicle stats skidding outwads. his causes the adius of the cicle to incease esulting in the decease in the centipetal foce. [Q F cp ] 4. If a body moes in a cylindical well (well of death) the elocity equied will be minimum safest elocity and in this case the weight of the body will be balanced by component of nomal eaction and the minimum safest elocity is gien by the fomula µ g. 5. Cyclist leans his cycle to make an angle to aoid topling; not to poide centipetal foce. 6. If a body is kept at est at the highest point of conex oad and pushed along the suface to pefom cicula motion, the body will fall afte taelling a etical distance of 3 fom the highest point whee is the adius of the cicula path. 7. When a body moes in a cicula path with constant speed, its linea momentum changes at eey point, but its kinetic enegy emains constant. 8. In hoizontal unifom cicula motion, kinetic enegy and magnitude of linea momentum emains constant, but the diection of linea momentum keeps on changing. 9. Since the centipetal foce is not zeo fo a paticle in cicula motion, the toque acting is zeo i.e., τ 0 (as the foce is cental) Hence the angula momentum is constant i.e. L constant. 30. Whenee the body moes, the foce esponsible fo motion is the ecto sum of all the foces acting at that point. Fo example, Lift going up and down with acceleation a. 3. If a paticle pefoming cicula motion comes to est momentaily, i.e. 0, then it will moe along the adius towads the cente and if its adial acceleation is zeo, i.e. a 0, then the body will moe along the tangent dawn at that point. 3. Fo non unifom cicula motion a α + ω 4

5 Chapte 0 : Cicula Motion 33. When a bucket full of wate is otated in a etical cicle, wate will not spill only if elocity of bucket at the highest point is g. 34. If elocity impated to body at the lowest position is equal to in a semicicle. Mindbendes g, then it will oscillate. he maximum elocity with which a ehicle can go without toppling, is gien by d g h g tanθ d whee, tan θ h d distance between the wheels h height of cente of gaity fom the oad g acceleation due to gaity. Skidding of an object placed on a otating platfom: he maximum angula elocity of otation of the platfom so that object will not skid on it is ω max ( µ g / ) 3. he angle made by the esultant acceleation with the adius, α tan a a Shotcuts t. he basic fomula fo acceleation is a ω.. In U.C.M., if cental angle o angula displacement is gien, then simply apply d sin θ to detemine change in elocity. 3. hee ae two types of acceleation; a (adial) and a t (tangential) acceleation. Fomula fo a ω d and a t o α dt 4. o calculate angula displacement, apply the fomula, θ ωt + αt 5. o find out numbe of eolutions, always apply the fomula, θ Numbe of eolutions ωt πnt nt π π π 6. Since F c, theefoe, no wok is done by the centipetal foce. [π ad 360 e.] 7. Angle which, a cyclist should make with the etical is the angle of banking along a cued oad. 8. On fictional suface, fo a body pefoming cicula motion, the centipetal foce is poided by the foce of fiction. f S µn but on hoizontal suface N mg 9. he minimum safe elocity fo not oetuning is gd h 0. While ounding a cue on a leel oad, centipetal foce equied by the ehicle is poided by foce of fiction between the tyes and the oad. m F µr µmg. o aoid dependence on fiction fo the supply of necessay centipetal foce, cued oads ae usually banked by aising oute edge of the oad aboe the inne edge.. he angle of banking (θ) is gien by, h tan θ g l h whee h is height of the oute edge aboe the inne edge and l is length of the oad. 3. On the same basis, a cyclist has to bend though an angle θ fom his etical position while ounding a cue of adius with elocity such that tan θ g If θ is ey ey small, then tan θ sin θ g g h l whee h is height of the oute edge fom the inne edge and l is the distance between the tacks o width of the oad. 5

6 Std. XII : iumph Physics 4. Always emembe the fomulae fo elocity of the body at the top, bottom and at the middle of a cicle with two distinct cases: i. path is conex ii. path is concae Remembe in both the cases, fomula will be diffeent. i. m mg N whee N is nomal eaction. m ii. N mg Remembe if in the question, it is gien that body falls fom a cetain point then at that point N Effect of otation of eath about its axis: he appaent loss in weight of a body on its suface mω R cos φ whee m mass of body ω angula elocity of eath R adius of eath φ latitude 6. In hoizontal cicle, tension will be equal to m centipetal foce i.e. i. he minimum elocity of pojection at the lowest point of etical cicle so that the sting slacken at the highest point, is gien by L 5 g ii. elocity at the highest point is H g 7. If L is the tension at the lowest point and H is the tension at the highest point then 8. When L H 6 mg i. L g, the body moes in a etical semicicle about the lowest point L, ii. L < g, then the body oscillates in a iii. cicula ac smalle than the semicicle. Fo a moto cyclist to loop a etical loop, L > 5g and H > g 9. he total enegy of any body eoling in a etical cicle is (5/) mg. 0. he distance taelled by the paticle pefoming unifom cicula motion in t seconds is gien by the fomula, d π t.. o find out any unknown quantity, if body moes in etical cicle, esole mg and if the body moes in hoizontal cicle, esole tension o nomal eaction.. Centipetal Foce in Diffeent Situations: Situation i. A paticle tied to a sting and whiled in a hoizontal cicle ii. Vehicle taking a tun on a leel oad iii. A ehicle on a speed beake i. Reolution of eath aound the sun. Electon eoling aound the nucleus in an atom i. A chaged paticle descibing a cicula path in a magnetic field ii. Coin placed on disk iii. Ca moing on a smooth banked oad ix. Passenge sitting in a tuning ca he centipetal foce ension in the sting Fictional foce exeted by the oad on the tyes Weight of the body o a component of weight Gaitational foce exeted by the sun Coulomb attaction exeted by the potons on electons Magnetic foce exeted by the magnetic field In this case fictional foce gies necessay centipetal foce. N sin θ gies necessay centipetal foce. Necessay centipetal foce is poided by seat and passenge. 6

7 Chapte 0 : Cicula Motion Classical hinking. Angula displacement. he angula displacement in cicula motion is dimensional quantity. dimensionless quantity. unitless and dimensionless quantity. unitless quantity.. Angula displacement is measued in mete. time. adian. steadian. 3. A flywheel otates at a constant speed of 3000.p.m. he angle descibed by the shaft in one second is 3 π ad 30 π ad 00 π ad 3000 π ad. Angula elocity and angula acceleation 4. Diection of α is tangent to path. pependicula to path. paallel to the path. along the path. 5. What is the angula speed of the seconds hand of a watch? 60 ad/s π ad/s π/30 ad/s ad/s 6. he angula elocity of a paticle otating in a cicula obit 00 times pe minute is.66 ad/s 0.47 ad/s 0.47 deg/s 60 deg/s 7. A body of mass 00 g is eoling in a hoizontal cicle. If its fequency of otation is 3.5.p.s. and adius of cicula path is 0.5 m, the angula speed of the body is 8 ad/s 0 ad/s ad/s 4 ad/s 8. What is the angula elocity of the eath? π π ad/s ad/s π π ad/s ad/s An electic moto of hose-powe geneates an angula elocity of 5 ad/s. What will be the fequency of otation? 0 0/π 0/π he atio of angula speeds of seconds hand and hou hand of a watch is : : : :. A body moes with constant angula elocity on a cicle. Magnitude of angula acceleation is ω constant zeo ω. A wheel haing a diamete of 3 m stats fom est and acceleates unifomly to an angula elocity of 0.p.m. in 5 seconds. Angula acceleation of the wheel is 4.4 ad s 3.3 ad s. ad s. ad s.3 Relation between linea elocity and angula elocity 3. he ecto elation between linea elocity, angula elocity ω and adius ecto is gien by ω + ω ω. ω 4. A wheel has cicumfeence C. If it makes f.p.s., the linea speed of a point on the cicumfeence is πfc fc fc/π fc/60 5. A body is whiled in a hoizontal cicle of adius 0 cm. It has angula elocity of 0 ad/s. What is its linea elocity at any point on cicula path? 0 m/s m/s 0 m/s m/s 6. A paticle moes in a cicula path, 0.4 m in adius, with constant speed. If paticle makes 5 eolutions in each second of its motion, the speed of the paticle is 0.6 m/s. m/s.6 m/s 3.6 m/s 7

8 Std. XII : iumph Physics 7. A paticle P is moing in a cicle of adius with a unifom speed. C is the cente of the cicle and AB is a diamete. When passing though B, the angula elocity of P about A and C ae in the atio : : A C : B P 4 :.4 Unifom Cicula Motion (U.C.M.) 8. In unifom cicula motion, both elocity and acceleation ae constant. elocity changes and acceleation is constant. elocity is constant and acceleation changes. both elocity and acceleation change. 9. A paticle moes along a cicula obit with constant angula elocity. his necessaily means, its motion is confined to a single plane. its motion is not confined to a single plane. nothing can be said egading the plane of motion. its motion is one-dimensional. 0. Select the WRONG statement. In U.C.M. linea speed is constant. In U.C.M. linea elocity is constant. In U.C.M. magnitude of angula momentum is constant. In U.C.M. angula elocity is constant.. If a paticle moes in a cicle descibing equal angles in equal inteals of time, the elocity ecto emains constant. changes in magnitude only. changes in diection only. changes both in magnitude and diection.. A paticle moes along a cicle with a unifom speed. Afte the position ecto has made an angle of 30 with the efeence position, its speed will be 3 3. A ca taels due noth with a unifom elocity. As the ca moes oe muddy aea, mud sticks to the tye. he paticles of the mud as it leaes the gound ae thown etically upwads. etically inwads. towads noth. towads south..5 Acceleation in U.C.M. (Radial acceleation) 4. A paticle in U.C.M. possesses linea acceleation since its linea speed changes continuously. both magnitude and diection of linea elocity change continuously. diection of linea elocity changes continuously. its linea speed does not change continuously. 5. he acceleation of a paticle in U.C.M. diected towads cente and along the adius is called centipetal acceleation. centifugal acceleation. gaitational acceleation. tangential acceleation. 6. In an inetial fame of efeence, a body pefoming unifom cicula motion in clockwise diection has constant elocity. zeo angula acceleation. centipetal acceleation. tangential acceleation. 7. An electic fan has blades of length 30 cm as measued fom the axis of otation. If the fan is otating at 00.p.m., the acceleation of a point on the tip of the blade is about 600 cm/s 4740 cm/s 370 cm/s 5055 cm/s 8. he diamete of a flywheel is. m and it makes 900 eolutions pe minute. Calculate the acceleation at a point on its im. 540 π m/s 70 m/s 360 π m/s 540 m/s 9. he angula speed (in e/min) needed fo a centifuge to poduce an acceleation of 000 g at a adius am of 0 cm is (ake g 0 m/s ) 500 e/min 4000 e/min 000 e/min 3000 e/min 8

9 Chapte 0 : Cicula Motion 30. If the angle between tangential acceleation and esultant acceleation in non U.C.M. is α, then diection of the esultant acceleation will be tan a t tan a a at tan a tan a t a α a α 3. A ca is moing along a cicula oad at a speed of 0 m/s. he adius of cicula oad is 0 m. If the speed is inceased at the ate of 30 m/s, what is the esultant acceleation at that moment? 0 m/s 50 m/s 50 m/s 80 m/s.6 Centipetal and centifugal foces 3. he foce equied to keep a body in unifom cicula motion is centipetal foce. centifugal foce. fictional foce. beaking foce. 33. A ehicle moing on a hoizontal oad may be thown outwad due to gaitational foce. nomal eaction. fictional foce between tyes and oad. lack of pope centipetal foce. 34. Select the WRONG statement. Centifugal foce has same magnitude as that of centipetal foce. Centifugal foce is along the adius, away fom the cente. Centifugal foce exists in inetial fame of efeence. Centifugal foce is called pseudo foce, as its oigin cannot be explained. 35. An impotant consequence of centifugal foce is that the eath is, bulged at poles and flat at the equato. flat at poles and bulged at the equato. high tides and low tides. ising and setting of sun. 36. Fats can be sepaated fom milk in a ceam sepaato because of cohesie foce. gaitational foce. centifugal foce. iscous foce. 37. When a ca is going ound a cicula tack, the esultant of all the foces on the ca in an inetial fame is acting away fom the cente. acting towads the cente. zeo. acting tangential to the tack. 38. Place a coin on gamophone disc nea its cente and set the disc into otation. As the speed of otation inceases, the coin will slide away fom the cente of the disc. he motion of coin is due to adial foce towads cente. non-conseatie foce. centifugal foce. centipetal foce. 39. If p is the magnitude of linea momentum of a paticle executing a unifom cicula motion, then the atio of centipetal foce acting on the paticle to its linea momentum is gien by m. 40. A acing ca of mass 0 kg goes aound a cicula tack (hoizontal) of adius 0 m. he maximum thust that tack can withstand is 0 5 N. he maximum speed with which ca can go aound is 0 m/s 00 m/s 50 m/s 0 m/s 4. wo paticles of equal masses ae eoling in cicula paths of adii and espectiely with the same speed. he atio of thei centipetal foces is 4. A 0 kg object attached to a nylon cod outside a space ehicle is otating at a speed of 5 m/s. If the foce acting on the cod is 5 N, its adius of path is m 4 m 6 m m 9

10 Std. XII : iumph Physics 43. he beaking tension of a sting is 50 N. A body of mass kg is tied to one end of a m long sting and whiled in a hoizontal cicle. he maximum speed of the body should be 5 m/s 0 m/s 7.5 m/s 5 m/s 44. A poton of mass kg goes ound in a cicula obit of adius 0. m unde a centipetal foce of N. hen the fequency of eolution of the poton is about cycles pe second cycles pe second cycles pe second cycles pe second 0.7 Banking of oads 45. he safety speed of a ehicle on a cue hoizontal oad is µg µ g µ g µ/(g) 46. he safe speed of a ehicle on a hoizontal cue oad is independent of mass of ehicle. coefficient of fiction between oad suface and tye of ehicle. adius of cue. acceleation due to gaity. 47. he ail tacks ae banked on the cues so that esultant foce will be deceased. weight of tain may be educed. centifugal foce may be balanced by the hoizontal component of the nomal eaction of the ail. fictional foce may be poduced between the wheels and tacks. 48. he angle of banking of the oad does not depend upon acceleation due to gaity. adius of cuatue of the oad. mass of the ehicle. speed of the ehicle. 49. Fo a banked cued oad, the necessay centipetal foce on any ehicle is poided by etical component of nomal eaction of the ehicle. hoizontal component of the nomal eaction of the ehicle. both etical and hoizontal components of the nomal eaction of the ehicle. weight of the ehicle. 50. If the adius of the cicula tack deceases, then the angle of banking inceases. deceases. fist inceases then deceases. does not change..8 Conical Pendulum 5. When the bob of a conical pendulum is moing in a hoizontal cicle at constant speed, which quantity is fixed? Velocity Acceleation Centipetal foce Kinetic enegy 5. he peiod of a conical pendulum is equal to that of a simple pendulum of same length l. moe than that of a simple pendulum of same length l. less than that of a simple pendulum of same length l. independent of length of pendulum. 53. Conside a simple pendulum of length m. Its bob pefoms a cicula motion in hoizontal plane with its sting making an angle 60 with the etical. he centipetal acceleation expeienced by the bob is 7.3 m/s 5.8 m/s 0 m/s 5 m/s 54. A paticle of mass kg is eoled in a hoizontal cicle of adius m with the help of a sting. If the maximum tension the sting can withstand is 6π N, then the maximum fequency with which the paticle can eole is 3 Hz Hz 4 Hz 5 Hz.9 Vetical Cicula Motion 55. When a paticle is moed in a etical cicle, it has constant adial and tangential acceleation. it has aiable tangential and adial acceleation. it has only constant adial acceleation. it has only constant tangential acceleation. 56. Fo a paticle moing in a etical cicle, kinetic enegy is constant. potential enegy is constant. neithe K.E. no P.E. is constant. both kinetic enegy and potential enegy ae constant.

11 Chapte 0 : Cicula Motion 57. If a stone is tied to one end of the sting and whiled in etical cicle, then the tension in the sting at the lowest point is equal to centipetal foce. the diffeence between centipetal foce and weight of the stone. the addition of the centipetal foce and weight of the stone. weight of the stone. 58. If a body is tied to a sting and whiled in etical cicle, then the tension in the sting at the highest position is maximum. minimum. between maximum and minimum alues. zeo. 59. A body of mass m is suspended fom a sting of length l. What is minimum hoizontal elocity that should be gien to the body in its lowest position so that it may complete one full eolution in the etical plane with the point of suspension as the cente of the cicle l g 3l g 4l g 5l g 60. If the oebidge is concae instead of being conex, the thust on the oad at the lowest position will be m m mg + mg m g g 6. A moto cycle is going on an oe bidge of adius R. he die maintains a constant speed. As moto cycle is descending, nomal foce on it inceases deceases emain the same fluctuates 6. A paticle of mass m tied with sting is eoling in etical cicula motion with same speed. Maximum possibility of beaking the sting is at point B A m A D B C D C 63. A body of mass m is tied to a sting of length l and whiled in a etical cicle. he elocity of the body at the lowest position is u. hen the tension in the sting at a position when the sting makes an angle θ with the etical is mu l mu + mg cos θ l mu + mg(cos θ 3) l mu + mg(3cos θ ) l 64. A motocyclist ides in a hoizontal cicle along the inne wall of cylindical chambe of adius. If the coefficient of fiction between the tyes and the wall is µ, the minimum angula speed to peent him fom sliding down is µ g g µ µ g µ g 65. A paticle is moing in a etical cicle. If is the elocity of paticle at highest point and is the elocity of paticle at lowest point, then the elation between and is < Kinematical equations in cicula motion in analogy with linea motion 66. Calculate the angula acceleation of a centifuge which is acceleated fom est to 350.p.s. in 0 s. 0 ad s 0 ad s 5 ad s 30 ad s 67. A wheel otates with constant acceleation of.0 ad/s. If the wheel has an initial angula elocity of 4 ad/s, then the numbe of eolutions it makes in the fist ten seconds will be appoximately, 6 4 0

12 Std. XII : iumph Physics Miscellaneous 68. A ca is moing at a speed of 7 km/h. he diamete of its wheel is 0.5 m. If the wheels ae stopped in 0 otations applying bakes, then angula etadation poduced by the bakes would be 45.5 ad/s 33.5 ad/s 5.48 ad/s 50.9 ad/s 69. A paticle of mass kg is otating by means of a sting in a etical cicle. he diffeence in the tensions at the bottom and the top would be kg wt kg wt > kg wt < kg wt 70. A paticle does unifom cicula motion in a hoizontal plane. he adius of the cicle is 0 cm. If the centipetal foce F is kept constant but the angula elocity is doubled, the new adius of the path (oiginal adius R) will be R/4 R/ R 4R he physics of.. A tapeze act in a cicus. Citical hinking. Angula displacement. A wheel otates with a constant angula elocity of 300.p.m. he angle though which the wheel otates in one second is π ad 5 π ad 0 π ad 0 π ad. Fo a paticle in a non-unifom acceleated cicula motion, elocity is adial and acceleation is tansese only. elocity is tansese and acceleation is adial only. elocity is adial and acceleation has both adial and tansese components. elocity is tansese and acceleation has both adial and tansese components.. Angula elocity and angula acceleation 3. A wheel completes 000 eolutions to coe the 9.5 km distance. hen the diamete of the wheel is.5 m.5 cm 7.5 cm 7.5 m In a cicus, a man hangs upside down fom a tapeze, legs bent oe the ba and ams downwad, holding his patne. Is it hade fo the man to hold his patne when the patne hangs staight downwad and is stationay o when the patne is swinging though the staight-down position? he answe is at the end of this chapte. 4. he atio of angula speed of second hand to that of the minute hand of a clock is 60 : : 60 : : 6 5. What is the angula speed of the minute hand of the clock in degees pe second? A paticle is descibing the cicula path of adius 0 m in eey s. he aeage angula speed of the paticle duing 4 s is 0 π ad s 4 π ad s π ad s π ad s 7. Calculate the angula acceleation if a flywheel gains a speed of 540.p.m. in 6 seconds. 3π ad s 6π ad s 9π ad s π ad s

13 Chapte 0 : Cicula Motion 8. A paticle is in cicula motion in a hoizontal plane. It has angula elocity of 0 π ad/s at the end of s and angula elocity 5 π ad/s at the end of 4 s. he angula acceleation of paticle is 5 π ad/s.5 π ad/s 7.5 π ad/s π ad/s 9. Angula displacement (θ) of a flywheel aies with time as θ t + 3t adian. he angula acceleation at t s is gien by 4 ad/s 8 ad/s 6 ad/s 6 ad/s.3 Relation between linea elocity and angula elocity 0. he linea elocity of a paticle on the N-pole of the eath is zeo. 486 km/h infinite. 5 m/s. o enable a paticle to descibe a cicula path, what should be the angle between its elocity and acceleation? A body eoles n times in a cicle of adius π cm in one minute. Its linea elocity is 60 n cm/s n 60 cm/s π n 60 cm/s π n 60 cm/s 3. he second s hand of a watch has length 6 cm. Speed of end point and magnitude of diffeence of elocities at two pependicula positions will be 6.8 and 0 mm/s 8.88 and 4.44 mm/s 8.88 and 6.8 mm/s 6.8 and 8.88 mm/s 4. wo cas C and C ae going ound in concentic cicles of adii R and R. hey complete the cicula paths in the same time. Speed of C hen Speed of C R /R R /R can not be detemined as data is insufficient 5. A wheel is 0.5 m in adius. When it makes 5 eolutions pe minute, its linea speed at a point on cicumfeence is π π m/s m/s 8 π m/s π m/s 4 6. A stone tied to the end of a sting of length 50 cm is whiled in a hoizontal cicle with a constant speed. If the stone makes 40 eolutions in 0 s, then the speed of the stone along the cicle is π/ ms π ms π ms 4π ms 7. he adius of the eath is 6400 km. he linea elocity of a point on the equato is nealy 600 km/h 675 km/h 500 km/h 800 km/h 8. What is the alue of linea elocity if ω 3i ˆ 4j ˆ + kˆ and 5i ˆ 6j ˆ + 6kˆ? 6i ˆ + j ˆ 3kˆ 8i ˆ 3j ˆ + kˆ 4i ˆ 3j ˆ + 6kˆ 6i ˆ j ˆ + 8kˆ 9. If the equation fo the displacement of a paticle moing on a cicula path is gien by θ t , whee θ is in adian and t is in seconds, then the angula elocity of the paticle at t s is 8 ad/s ad/s 4 ad/s 36 ad/s.4 Unifom Cicula Motion (U.C.M.) 0. A paticle coes equal distances aound a cicula path in equal inteals of time. Which of the following quantities connected with the motion of the paticle emains constant with time? Displacement Velocity Speed Acceleation. A paticle pefoming unifom cicula motion has adial elocity and adial acceleation. adial elocity and tansese acceleation. tansese elocity and adial acceleation. tansese elocity and tansese acceleation. 3

14 Std. XII : iumph Physics. Assetion: In cicula motion, the centipetal and centifugal foces acting in opposite diection balance each othe. Reason: Centipetal and centifugal foces don t act at the same time. Assetion is ue, Reason is ue; Reason is a coect explanation fo Assetion Assetion is ue, Reason is ue; Reason is not a coect explanation fo Assetion Assetion is ue, Reason is False Assetion is False but Reason is ue. 4.5 Acceleation in U.C.M. (Radial acceleation) 3. A ca is taelling at a gien instant 40 m/s on a cicula oad of adius 400 m. Its speed is inceasing at the ate of 3 m/s. Its tangential acceleation is 4 m/s 3 m/s 5 m/s m/s 4. Fo a paticle in cicula motion, the centipetal acceleation is less than its tangential acceleation. is equal to its tangential acceleation. is moe than its tangential acceleation. may be moe o less than its tangential acceleation. 5. If a body moes with constant speed along a cued path, its tangential acceleation is zeo. is paallel to its elocity. pependicula to its elocity. can make any abitay angle with its elocity. 6. An aicaft executes a hoizontal loop of adius km with a steady speed of 900 km/h. Ratio of its centipetal acceleation to acceleation due to gaity is A tun table which is otating unifomly has a paticle placed on it. As seen fom the gound, the paticle goes in a cicle with speed 0 cm/s and acceleation 0 cm/s. he paticle is now shifted to a new position whee adius is half of the oiginal alue. he new alues of speed and acceleation will be 0 cm/s, 0 cm/s 0 cm/s, 80 cm/s 40 cm/s, 0 cm/s 40 cm/s, 40 cm/s 8. A paticle is moing on a cicula path with constant speed, then its acceleation will be zeo. extenal adial acceleation. intenal adial acceleation. constant acceleation. 9. wo paticles A and B ae located at distances A and B espectiely fom the cente of a otating disc such that A > B. In this case, if angula elocity ω of otation is constant then both A and B do not hae any acceleation. both A and B hae same acceleation. A has geate acceleation than B. B has geate acceleation than A. 30. A paticle goes ound a cicula path with unifom speed. Afte descibing half the cicle, what is the change in its centipetal acceleation? π π 3. a and a t epesent adial and tangential acceleations espectiely. he motion of the paticle is unifomly cicula only if a 0 and a t 0 a 0 and a t 0 a 0 and a t 0 a 0 and a t 0.6 Centipetal and centifugal foces 3. A body is eoling with a constant speed along a cicle. If its diection of motion is eesed but the speed emains the same, then which of the following statements is tue? he centipetal foce will not suffe any change in magnitude. he centipetal foce will hae its diection eesed. he centipetal foce will suffe change in diection. he centipetal foce would be doubled. 33. A cylindical essel patially filled with wate is otated about its etical cental axis. Its suface will ise equally. ise fom the sides. ise fom the middle. loweed equally.

15 Chapte 0 : Cicula Motion 34. A ca of mass 840 kg moes on a cicula path with constant speed of 0 m/s. It is tuned though 90 afte taelling 660 m on the oad. he centipetal foce acting on the ca is 34 N 640 N 84 N 00 N 35. A body of mass 500 g is eoling in a hoizontal cicle of adius 0.49 m. he centipetal foce acting on it (if its peiod is s) will be N 8.0 N 0.8 N 0.08 N 36. he atio of centipetal foces on two electons which ae eoling aound nucleus of hydogen atom in nd and 3 d obits espectiely is 7 : 8 8 : 6 8 : 7 6 : A mass kg descibes a cicle of adius.0 m on a smooth hoizontal table at a unifom speed. It is joined to the cente of the cicle by a sting, which can just withstand 3 N. he geatest numbe of eolutions pe minute the mass can make is A paticle pefoms unifom cicula motion in a hoizontal plane. he adius of the cicle is 0 cm. he centipetal foce acting on the paticle is 0 N. Its kinetic enegy is 0. J 0. J.0 J.0 J 39. A coin placed on a otating tun-table slips when it is placed at a distance of 9 cm fom the cente. If the angula elocity of the tuntable is tippled, it will just slip if its distance fom the cente is 7 cm 9 cm 3 cm cm 40. A body is kept on a hoizontal disc of adius m at a distance of m fom the cente. he coefficient of fiction between the body and the suface of disc is 0.4. he speed of otation of the disc at which the body stats slipping is (g 0 m/s ) ad/s 4 ad/s 0. ad/s 0.4 ad/s 4. A small coin is kept at the im of a hoizontal cicula disc which is set into otation about etical axis passing though its cente. If adius of the disc is 5 cm and µ s 0.5, then the angula speed at which the coin will just slip is 5 ad/s 7 ad/s 0 ad/s 4.9 ad/s 4. A sting beaks unde a load of 4 kg. A mass weighing 00 g is attached to the end of this sting which is one mete long and otated hoizontally. he angula elocity of otation when the sting beaks, is nealy (g 0 m/s ) 6 ad/s 4 ad/s ad/s 0 ad/s 43. A bend in a leel oad has a adius of 00 m. he maximum speed with which a ca tuning this bend without skidding, if coefficient of fiction between the tyes and the suface of the oad is 0.8, will be (g 9.8 m/s ) 0 m/s 4 m/s 8 m/s 3 m/s 44. When the oad is dy and the coefficient of fiction is µ, the maximum speed of a ca in a cicula path is 0 ms. If the oad becomes wet and µ µ, then what is the maximum speed pemitted? 5 ms 0 ms 0 ms 5 ms 45. A ca moes at a speed of 36 km h on a leel oad. he coefficient of fiction between the tyes and the oad is 0.8. he ca negotiates a cue of adius R. If g 0 ms, then the ca will skid (o slip) while negotiating the cue if the alue R is 0 m m 4 m 6 m 46. On a dy oad, the maximum pemissible speed of a ca in a cicula path is ms. If the oad becomes wet, then the maximum speed is 4 ms. If the coefficient of fiction fo dy oad is µ, then that fo the wet oad is 9 µ µ 3 µ µ 5

16 Std. XII : iumph Physics 47. A body moes along cicula path of adius 50 m and the coefficient of fiction is 0.4. What should be its angula elocity in ad/s if it is not to slip fom the suface? (g 9.8 m/s ) A cate of egg is located in the middle of the flat bed of a pick up tuck as the tuck negotiates an unbanked cue in the oad. he cue may be egaded as an ac of cicle of adius 35 m. If the coefficient of fiction between the cate and the flat bed of the tuck is 0.6, the speed with which the tuck should tun so that the cate does not slide oe the bed is 4.3 m/s 0.3 m/s.3 m/s 5.3 m/s 49. he maximum fictional foce between the tyes of a ca and the oad is 0.5 mg. he ca negotiates a cue of adius 0 mete. he elocity is 0 m/s 7 m/s 4.9 m/s 4. m/s 50. A ca of mass 000 kg moes on a cicula path with constant speed of m/s. It tuned though 90 afte taelling 47 m on the oad. he centipetal foce acting on the ca is 30 N 480 N 640 N 80 N 5. A oad is 0 m wide. Its adius of cuatue is 50 m. he oute edge is aboe the lowe edge by a distance of.5 m. his oad is most suited fo the elocity.6 m/s 4.6 m/s 6.6 m/s 8.6 m/s 5. A tain has to negotiate a cue of adius 400 m. he speed of the tain is 7 km/hou. he hoizontal distance is to be aised with espect to the inne adius by h. If distance between ail is l m, the alue of h will be (g 0 m/s ) 5 cm 0 cm 5 cm.5 cm.7 Banking of oads 53. On a ailway cue, the outside ail is laid highe than the inside one so that esultant foce exeted on the wheels of the ail ca by the tops of the ails will hae a hoizontal inwad component. be etical. equilibate the centipetal foce. be deceased. 54. A moto cyclist moes ound a cicula tack with a cetain speed and leans at an angle θ. If he doubles the speed, then he has to lean inwad at an angle θ. hen θ 4 θ θ θ tan θ 4 tan θ tan θ 4 tan θ 55. A ailway tack is banked fo a speed, by making the height of the oute ail h highe than that of the inne ail. If the distance between the ails is l and the adius of cuatue of the tack is, then h l g h tan sin l g h tan l h lg g 56. A ca is moing on a cicula path and takes a tun. If R and R be the eactions on the inne and oute wheels espectiely, then R R R < R R > R R R 57. A ailway line is banked with an angle of 0.0 adians. he height of the oute ail oe inne ail, if the distance between the two ails of.5 m, will be 0.05 m m 0.05 m m 6

17 Chapte 0 : Cicula Motion 58. If angle of banking is sin (0.) and nomal eaction is 000 N then the weight of the ca is N N 000 N 000 N 59. A bus is moing in a cicula hoizontal tack of adius 0 m with a constant speed 0 m/s. A plumb bob is suspended fom the oof of the bus by a light igid od of length.0 m. he angle made by the od with the tack is (ake g 0 m/s ) zeo A oad is 8 m wide. Its adius of cuatue is 40 m. he oute edge is aboe the lowe edge by a distance of. m. he most suited elocity on the oad is nealy 5.7 ms 8 ms 36. ms 9.7 ms 6. A cicula oad of adius 000 m has banking angle 45. If the coefficient of fiction between tye and oad is 0.5, then the maximum safe speed of a ca haing mass 000 kg will be 7 m/s 4 m/s 99 m/s 86 m/s 6. While diing aound cue of adius 7.3 m, an enginee notes that a pendulum in his ca hangs at an angle of 30 to the etical. he speed of the ca is (appoximately) 0 m/s 5 m/s 5 m/s 6.7 m/s 63. A boy on a cycle pedals aound a cicle of adius 0 m at a speed of 0 m/s. he combined mass of the body and the cycle is 90 kg. he angle that the cycle makes with the etical so that is may not fall is (g 9.8 m/s ) Fo taffic moing at 60 km/hou along a cicula tack of adius 0. km, the coect angle of banking is tan tan (50 / 3) tan (50 / 3) tan ( ) 65. A cicula acing ca tack has a adius of cuatue of 500 m. he maximum speed of the ca is 80 km/h. he angle of banking θ is (g 0 m/s ) θ tan (0) θ tan (0.5) θ tan (0.3) θ tan (0.) 66. A cyclist with combined mass 80 kg goes aound a cued oad with a unifom speed 0 m/s. He has to bend inwad by an angle θ tan (0.50) with the etical. he foce of fiction acting at the point of contact of tyes and oad suface is (g 0 m/s ) 300 N 400 N 800 N 50 N 67. he maximum safe speed fo which a banked oad is intended, is to be inceased by 0 %. If the angle of banking is not changed, then the adius of cuatue of the oad should be changed fom 30 m to 36.3 m. m 43. m 63. m 68. A cyclist going aound a cicula oad of adius 0 m is obseed to be bending inwad 30 with etical. Fictional foce acting on the cyclist is (Gien: g 0 m/s, mass of the cyclist is 90 kg) 53 N 800 N 559 N 50 N 69. he maximum speed with which a ehicle can negotiate a cued oad, which is banked at an angle θ tan (0.4), is 54 km/h. If the same oad is flat and ehicle has to negotiate the cue with same maximum speed, the coefficient of fiction between the oad and tyes of the ehicle should be Conical Pendulum 70. A mass of 0 kg is whiled in a hoizontal cicle by means of a sting at an initial speed of 5.p.m. Keeping the adius constant, the tension in the sting is quadupled. he new speed is nealy 4.p.m. 0.p.m..5.p.m. 7.p.m. 7

18 Std. XII : iumph Physics 7. Conside a simple pendulum of length m. Its bob pefoms a cicula motion in hoizontal plane with its sting making an angle 60 with the etical. he peiod of otation of the bob is (ake g 0 m/s ) s.4 s.98 s.4 s 7. he length of the sting of a conical pendulum is 0 m and it has a bob of mass 50 g. he angle that the sting makes with the etical is 30. If the bob coes one eolution in 3 s, then the coesponding centipetal foce acting on the bob will be 0 N N 00 N 5 N 73. In a conical pendulum, when the bob moes in a hoizontal cicle of adius with unifom speed, the sting of length L descibes a cone of semietical angle θ. he tension in the sting is gien by / mgl (L ) L mgl mgl (L mgl ) (L ).9 Vetical Cicula Motion 74. An aeoplane, flying in the sky, suddenly stats eoling in a etical cicle of adius 4 km. At the highest point of the cicle, the pilot expeiences weightlessness. Its elocity at the highest point will be 00 m/s 00 m/s 300 m/s 400 m/s 75. A hollow sphee has adius 6.4 m. Minimum elocity equied by a motocyclist at bottom to complete the cicle will be 7.7 m/s 0. m/s.4 m/s 6.0 m/s 76. A bucket full of wate is eoled in a etical cicle of adius 4 m such that wate does not fall down. he time of one eolution is 0 second 8 second 4 second 6 second 77. A paticle of mass m is otating by means of a sting in a etical cicle. he diffeence in tensions at the top and the bottom would be 6 mg 4 mg mg 3 mg 78. A kg stone at the end of a sting m long is whiled in a etical cicle at a constant speed of 4 m/s. he tension in the sting will be 5 N when the stone is (ake g 0 m/s ) at the top of the cicle at the bottom of the cicle halfway down at any position othe than that in, and 79. A 40 kg child sits on a swing suppoted by two chains, each 3 m long. If the tension in each chain at lowest point is 350 N, then the child s speed at the lowest point is [ake g 0 m/s ] 4.7 m/s 3 m/s 7. m/s 9. m/s 80. An aeoplane flying in the sky with a unifom speed of 00 m/s moes in a etical cicle of adius 400 m. he mass of the pilot is 70 kg. he foce exeted by the pilot on the seat at the highest point of the cicle will be [ake g 0 m/s ] 3000 N 6300 N 7700 N 630 N 8. In the aboe poblem, the foce exeted by the pilot on the seat at the lowest point of the cicle will be [ake g 0 m/s ] 4500 N 6300 N 7700 N 770 N 8. A woman weighing 600 N is sitting in a ca which is taelling at a constant speed on a staight oad. he ca suddenly goes oe a hump in the oad (hump may be egaded as an ac of a cicle of adius. m). If the woman expeiences weightlessness, calculate the speed of the ca. [ake g 0 m/s ] m/s 8 m/s 5 m/s 5 m/s 83. A body of mass kg is moing in a etical cicula path of adius m. he diffeence between the kinetic enegies at its highest and lowest positions is [ake g 0 m/s ] 0 J 0 J 4 5 J 0 ( 5 ) J 84. he maximum and minimum tensions in the sting whiling in a cicle of adius.5 m with constant elocity ae in the atio 5 : 3. Its elocity is 98 m/s 7 m/s 490 m/s 4.9 m/s 8

19 Chapte 0 : Cicula Motion 85. A student weighing 667 N ides a steadily otating Feis wheel (student sits upight). At the highest point, the magnitude of the nomal foce N on the student fom the seat is 556 N. he magnitude of N, if the wheel s speed is doubled, is 3 N N 444 N 33 N 86. A body slides down a fictionless tack which ends in a cicula loop of diamete D. hen the minimum height h of the body in tems of D so that it may just complete the loop is h 5 D h 3 D h 4 5 D h D 87. A fictionless tack ABCDE ends in a cicula loop of adius R. A body slides down the tack fom point A which is at a height h 5 cm. Maximum alue of R fo the body to successfully complete the loop is h A E 5 5 cm cm 4 0 cm cm Assetion: Fo looping a etical loop of adius, the minimum elocity at the lowest point should be 5g. D R B Reason: Velocity at the highest point would be zeo. Assetion is ue, Reason is ue; Reason is a coect explanation fo Assetion Assetion is ue, Reason is ue; Reason is not a coect explanation fo Assetion Assetion is ue, Reason is False Assetion is False but Reason is ue. C.0 Kinematical equations in cicula motion in analogy with linea motion 89. A flywheel at est is eached to an angula elocity of 36 ad/s in 6 s with a constant angula acceleation. he total angle tuned duing this inteal is 6 ad 44 ad 08 ad 7 ad 90. An engine equies 5 s to go fom a speed of 600.p.m. to 00.p.m. with constant acceleation. How many eolutions does it make in this peiod? A wheel of a ehicle is otated to a unifom angula acceleation about its axis. Initially its angula elocity is zeo. It otates though an angle θ in the fist s and in the next 3 s, it otates though an additional angle θ. he θ atio of θ is When a ceiling fan is switched off, its angula elocity educes to 50% while it makes 36 otations. How many moe otations will it make befoe coming to est? (Assume unifom angula etadation) Miscellaneous 93. A paticle is moing in a cicle of adius centeed at O with constant speed. What is the change in elocity in moing fom A to B if AOB 60? O sin 30 cos 30 sin 60 cos B A 9

20 Std. XII : iumph Physics 94. A paticle moes along a cicle of adius 0/π m with a constant tangential acceleation. If the elocity of the paticle is 80 m/s at the end of the nd eolution afte motion has begun, the tangential acceleation is 40 π m/s 40 m/s 640 π m/s 60 π m/s 95. A stone of mass kg tied to a light inextensible sting of length (0/3) m is whiling in a cicula path in a etical plane. If the atio of the maximum tension in the sting to the minimum tension is 4 and if g is taken to be 0 m/s, the speed of the stone at the highest point of the cicle is 5 m/s 0 m/s 0 m/s 0 3 m/s he physics of.. Riding the bicycle in a loop the loop. Competitie hinking. Angula elocity and angula acceleation. Which of the following statements is false fo a paticle moing in a cicle with a constant angula speed? [AIEEE 004] he elocity ecto is tangent to the cicle. he acceleation ecto is tangent to the cicle. he acceleation ecto points to the cente of the cicle. he elocity and acceleation ectos ae pependicula to each othe.. If ω E and ω H ae the angula elocities of the eath otating about its own axis and the hou hand of the clock espectiely, then [MH CE 009] ω E 4 ω H ω E ω H ω E ω H ω E ω E 3. A fan is making 600 eolutions pe minute. If afte some time it makes 00 eolutions pe minute, then incease in its angula elocity is [BHU 999] 0π ad/s 0π ad/s 40π ad/s 60π ad/s 0 he stunt of iding the bicycle in a loop-theloop, assuming that the loop is a cicle, what is the least speed the ide could hae at the top of the loop to emain in contact with it thee? he answe is at the end of this chapte. 4. Angula elocity of hou am of a clock, in ad/s, is [MH CE 005] π π π π he atio of angula speed of a second-hand to the hou-hand of a watch is [K CE 05] 3600 : 70 : 7 : 60 : 6. he diffeence between angula speed of minute hand and second hand of a clock is [MH CE 05] 59π 59π ad / s ad / s π 59π ad / s ad / s

21 Chapte 0 : Cicula Motion 7. he elation between linea speed, angula speed ω and angula acceleation α in cicula motion is [MH CE 00] α a ω α a ω α ω a α a ω 8. he angle tuned by a body undegoing cicula motion depends on time as θ θ 0 + θ t + θ t. hen the angula acceleation of the body is [Oissa JEE 009] θ θ θ θ.3 Relation between linea elocity and angula elocity 9. If the body is moing in a cicle of adius with a constant speed, its angula elocity is [CPM 975; R PE 999] / / / 0. wo paticles of mass M and m ae moing in a cicle of adii R and. If thei time peiods ae same, what will be the atio of thei linea elocities? [MH CE 00] MR : m M : m R : :. If the length of the second s hand in a stop clock is 3 cm, the angula elocity and linea elocity of the tip is [Keala PE 005] ad/s, m/s ad/s, 0.34 m/s 0.47 ad/s, m/s ad/s, m/s. A wheel of diamete 0 cm is otating at 600 pm. he linea elocity of paticle at its im is [MH CE 004] 6.8 cm/s 6.8 cm/s 0.68 cm/s 68.4 cm/s 3. he angula elocity of a wheel is 70 ad/s. If the adius of the wheel is 0.5 m, then linea elocity of the wheel is [MH CE 000] 0 m/s 0 m/s 35 m/s 70 m/s 4. An athlete completes one ound of a cicula tack of adius 0 m in 40 s. he distance coeed by him in min 0 s is [Keala (Med.) 00] 70 m 40 m 0 m 0 m 5. he length of second s hand in a watch is cm. he change in elocity of its tip in 5 seconds is [MP PM 987, 03] π zeo cm/s 30 π π cm/s cm/s Unifom Cicula Motion (U.C.M) 6. When a body moes with a constant speed along a cicle, [MH CE 003] its linea elocity emains constant. no foce acts on it. no wok is done on it. no acceleation is poduced in it. 7. In unifom cicula motion, [MP PM 994] both the angula elocity and the angula momentum ay. the angula elocity aies but the angula momentum emains constant. both the angula elocity and the angula momentum emains constant. the angula momentum aies but the angula elocity emains constant. 8. A sphee of mass m is tied to end of a sting of length l and otated though the othe end along a hoizontal cicula path with speed. he wok done in full hoizontal cicle is [C PM 993; JIPMER 000] 0 m π l mg (π) m ( l ) 9. If a paticle moes with unifom speed then its tangential acceleation will be [MH CE 008] zeo ω infinite 0. A paticle moes in a cicula path with deceasing speed. Choose the coect statement. [II JEE 005] Angula momentum emains constant. Acceleation a is towads the cente. Paticle moes in a spial path with deceasing adius. he diection of angula momentum emains constant.

22 Std. XII : iumph Physics. A body moes along a cicula path with cetain elocity. What will be the path of body in following figue? [MH CE 00] Moe adially out. Moe hoizontally out. Fall etically down. Moe tangentially out.. A paticle comes ound a cicle of adius m once. he time taken by it is 0 s. he aeage elocity of motion is [JIPMER 999] 0.π m/s π m/s m/s zeo 3. he tangential elocity of a paticle making p otations along a cicle of adius π in t seconds is [MH CE 009] πp πp t t π p π p t t 4. If K.E. of the paticle of mass m pefoming U.C.M. in a cicle of adius is E. he acceleation of the paticle is [MH CE 00] E m Em E m 4E m 5. Assetion: If a body moing in a cicula path has constant speed, then thee is no foce acting on it. Reason: he diection of the elocity ecto of a body moing in a cicula path is changing. [EAMCE 004] Assetion is ue, Reason is ue; Reason is a coect explanation fo Assetion Assetion is ue, Reason is ue; Reason is not a coect explanation fo Assetion Assetion is ue, Reason is False Assetion is False but Reason is ue..5 Acceleation in U.C.M (Radial acceleation) 6. he centipetal acceleation is gien by [R PE 999] / / B A 7. Angle between adius ecto and centipetal acceleation is [MH CE 00] 0 c π c π c none of these 8. Fo a paticle in unifom cicula motion, the acceleation a at a point P(R, θ) on the cicle of adius R is (Hee θ is measued fom the x-axis) [AIEEE 00] ˆ i + ˆj R R ˆ cos i sin ˆj R R ˆ sin i cos ˆj R R ˆ cos i sin ˆj R R 9. wo cas of masses m and m ae moing in cicles of adii and espectiely. hei speeds ae such that they make complete cicles in the same time t. he atio of thei centipetal acceleation is [AIEEE 0] m : m m : m : : 30. A paticle moes in a cicle of adius 5 cm with constant speed and time peiod 0. π s. he acceleation of the paticle is [CBSE PM (Pelims) 0] 5 m/s 5 m/s 5 m/s 36 m/s 3. If a cycle wheel of adius 0.4 m completes one eolution in one second, then acceleation of the cycle is [MH CE 999] 0.4 π m/s 0.8 π m/s 0.4 π m/s.6 π m/s 3. A paticle moes in a cicle of adius 5 cm at two eolutions pe second. he acceleation of the paticle in m/s is [MNR 99; D PM 999; UPSEA 000; R PE 003; Pb PE 004; CBSE PM PM (Pelims) 0] π 8π 4π π 33. Cetain neuton stas ae belieed to be otating at about e/s. If such a sta has a adius of 0 km, the acceleation of an object on the equato of the sta will be [NCER 98] m/s m/s m/s m/s