Chapter 17: Circular Motion

Angular Displacement θ
The angle θ, through which the object has moved is known as its angular displacement.

θ=arc/radius = s/r

Radian

One radian (rad) is defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.

1 rad = 57.3⁰

Angular Speed ω

The angular speed is defined as the rate of change of angular displacement.

Angular speed ω = Δθ/Δt

Centripetal force

Centripetal force is the name given to that force which causes a change in direction of velocity toward the center of the circular motion. It is the net force that acts on an object to keep it moving along a circular path.

The figures shows the angle between two radii OA and OB and V_A and V_B.

So,

DE/CD = AB/OA

ΔV/V_A = Δs/r

ΔV= Δs (V_A /r)

Dividing both sides by Δt

ΔV/Δt = (Δs/Δt) (V_A/r)

A= v²/r

Centripetal force = mv²/r = mrω²