Rotatoy Motion Hoizontal Cicula Motion In tanslatoy motion, evey point in te body follows te pat of its pecedin one wit same velocity includin te cente of mass In otatoy motion, evey point move wit diffeent velocity wit espect to te axis of otation e paticle on te axis of otation will ave zeo velocity 3 e anle descibed by te adius vecto in a iven inteval of time is called te anula displacement 4 Anula displacement is a vecto passin tou te cente and diected alon te pependicula to te plane of te cicle wose diection is detemined by it and scew ule (It is a pseudo vecto) 5 Anula displacement is measued in adians 6 e ate of cane of anula displacement is called anula velocity (ω) ω θ t = ads 7 Anula velocity is a vecto lyin in te diection of anula displacement = 8 Linea velocity (V) ω 9 Rate of cane of anula velocity is called anula acceleation (α) Unit is ads cane in anula velocity α = time = 0 Linea acceleation = adius anula acceleation a α Resultant acceleation a = ω wee a = adial acceleation and a = tanential acceleation Compaison of linea and anula quantities anslatoy motion Rotatoy motion

v = u + at ω = ω + αt s = ut + at = + v u as u + v s = Mass (m) F = ma Impulse = Ft Linea momentum p Wok = FS Powe = FV mv = mv p E = m KE = mv = mv θ = ωt + αt ω = ω + αθ θ = ω + ω Moment of inetia (I) oque τ =I α Anula impulse =τ t Anula momentum W P = τθ = τω I ω = I ω L E = I Rotational KE = ω I 3 If a paticle makes n otations pe second θ = πn L = Iω 4 Anula velocity is a pseudo vecto (o) axial vecto v = ω and v = ω = 0

5 Rate of cane of anula velocity is called anula acceleation (α ) Unit is ad s cane in anula velocity = time α e anula acceleation is a pseudo (o) axial vecto 6 e diection anula acceleation (α ) is alon te cane in anula velocity a = α and a = a α = 0 7 e diection α will be same as tat of ω if it is inceasin and opposite to tat of ω if it is deceasin 8 Unifom cicula motion a anential acceleation is due to cane in te speed and nomal acceleation is due to te cane in te diection dv b anential acceleationa = = α is is alon te tanent dawn alon te dt cicula pat c Fo vetical cicula motion te tanential acceleation is iven by a = α = sinθ v d Radial (o) nomal (o) centipetal acceleation a = = ω = 4π n e In unifom cicula motion: (ω =constant) i) anential acceleation is zeo ( a = 0) ii) omal acceleation a = constant 9 In non unifom cicula motion et acceleation = + (o) v a = + ( α ) a a a and a = a i + a j 0 a = 0 and a = 0 unifom linea motion a = 0 and a 0 - acceleated (o) non unifom linea motion a 0 and a = 0 unifom cicula motion t

3 a 0 and a 0 - non unifom cicula motion 4 e foce wic makes a body move ound a cicula pat wit unifom speed is called te centipetal foce is is always diected towads te cente of te cicle mv Centipetal foce= = mω = 4π n m 5 A body movin ound a cicula pat wit unifom speed expeiences an inetial o pseudo foce wic tends to make it o away fom te cente is foce is called te centifual foce and tis is due to te inetia of te body 6 Centifual foce = centipetal foce (but tese ae not action and eaction) 7 o wok is done by centipetal foce 8 e kinetic eney of te body evolvin ound in a cicula pat wit unifom speed is E If F is te equied centipetal foce, ten 9 Uses of centifual foces and centifual macines i) Ceam is sepaated fom milk (ceam sepaato) ii) Sua cystals ae sepaated fom molasses iii) Pecipitate is sepaated fom solution iv) Steam is eulated by Watt s ovene v) Wate is pumped fom a well (Electical pump) vi) Hematocentifue, Ginde, Wasin macine, etc E F = 30 e anle tou wic a cyclist sould lean wile takin sap tunins is iven by te elation v θ = an 3 Safe speed on an unbanked oad wen a veicle takes a tun of adius is v = µ wee µ = coefficient of fiction 3 e maximum speed tat is possible on cuved unbanked tack is iven by = v /a Wee = eit of cente of avity and a = alf te distance between weels

33 Anle of bankin At cuves te oute ede of te oad is slitly above te lowe ede e anle made by te tilled oad wit te oizontal is called anle of bankin mv sinθ = and cosθ = m v anθ = Fo small anles, tanθ = sinθ v v l = = l 34 Conical Pendulum: Let be te tension in te stin a b mv sinθ = And cosθ = m v ω an θ = = an θ = ω = ω = c ime peiod = π (O) And fequency n = π d sin m m ( l sin ) = = θ ω θ ω l = π