Question

derive the expression for liner and angular velocity​

Answer 1

Explanation:

We know that angular displacement is the angle traced by a particle under the circular motion. Since the direction of the displacement is along the axis, that’s why angular displacement is an axial vector.

A particle in a circular motion exhibits two types of displacements; these are:

Along the circumference: Linear Displacement (s).

Making an angle θ: Angular Displacement.

If ‘r’ is the radius of the circle, then the relation between angular and linear displacement is:

S = Rθ or θ = Sr

Sr

…..(1)

Linear velocity is defined as the rate of change of linear displacement. For a particle P, it is given by:

v = ΔSΔt

ΔSΔt

….(2)

Angular velocity of the particle is the rate of change of angular displacement, i.e., how fast an angle is changing. It is given by:

ω = ΔθΔt

ΔθΔt

…(3)

In this article, we will derive the relation between linear velocity and angular velocity.

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