Question
Derive an expression for centripetal acceleration experienced by a particle revolving in circular orbit of radius r with constant angular speed ω.
Solution
Let a particle revolve in a circular orbit of radius r with constant angular speed 
.
Let the particle starts from A and at any instant t, the particle be at B and undergo angular displacement θ = ωt.
Linear speed of particle is v = rω.
Therefore the velocity of particle in vector form is,
Therefore, acceleration is directed along BO towards the centre. That is why it is known as centripetal acceleration.
.Let the particle starts from A and at any instant t, the particle be at B and undergo angular displacement θ = ωt.
Linear speed of particle is v = rω.
Therefore the velocity of particle in vector form is,
Therefore, acceleration is directed along BO towards the centre. That is why it is known as centripetal acceleration.
