Question

derive relation between linear velocity and angular velocity.

Answer 1

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Answer 2

DERIVATION OF RELATION BETWEEN ANGULAR AND LINEAR VELOCITY.

Consider a body spins about an axis traveling through a point O and perpendicular (⊥) to the plane of the paper. Let P be the position of a particle internally in the body. If the body rotates via an angle 0 in a time interval of t, the particle at P gets to P'.

⇒ Linear displacement PP' = r∅

⇒linear velocity, v= $\frac{PP'}{t}$= r∅/t -------i

⇒angular velocity ω= ∅/t--------ii

∴ replacing the values of ω in eq-i

∴ v= rω

HENCE THE RELATION BETWEEN THE LINEAR AND ANGULAR VELOCITY IS V=rω.