f = 1 = ωa T 2 When a body performs uniform circular motion its speed remains constant but Centripetal Acceleration – velocity continuously changes due to change of direction. Hence a body is continuously accelerated and the acceleration experienced by the body is known as centripetal acceleration (that is the acceleration directed towards the center). v2 a P2 v1 r ∆v ∆v O C B θ ∆s v v R v2 v1 θ θ P1 A Consider a particle performing uniform circular motion with speed v. When the particle changes its position from P1 to P2 its velocity changes from v1 to v2 due to change of direction. The change in velocity from P1 to P2 is which is directed towards the center of the circular path according to ∆v triangle law of subtraction of vectors. From figure and are similar, hence applying the condition of similarity ∆OP1P2 ∆ABC BC = P1 P1 AB O P1 or, = ∆v ∆s v r or, = v∆s ∆v r Dividing both sides by = v∆s ∆t, ∆v r∆t ∆t Taking limit 0 both sides, ∆t Lim = v Lim ∆v ∆θ
f = 1 = ωa T 2 Centripetal Acceleration – When a body performs uniform circular motion its speed remains constant but velocity continuously changes due to change of direction. Hence a body is continuously accelerated and the acceleration experienced by the body is known as centripetal acceleration (that is the acceleration directed towards the center). v2 a P2 r v1 ∆v ∆v O θ ∆s C B R v2 θ v1 v θ v P1 A Consider a particle performing uniform circular motion with speed v. When the particle changes its position from P1 to P2 its velocity changes from v1 to v2 due to change of direction. The change in velocity from P1 to P2 is ∆v which is directed towards the center of the circular path according to triangle law of subtraction of vectors. From figure ∆OP1P2 and ∆ABC are similar, hence applying the condition of similarity BC = P1 P1 AB O P1 or, ∆v = ∆s v r or, ∆v = v∆s r Dividing both sides by ∆t, ∆v = v∆s ∆t r∆t Taking limit ∆t 0 both sides, Lim ∆v = v Lim ∆θ
CLASS%20XI%20PHYSICS.docx