What is the derivation for v=rw?

Dear Student!!

**Relation between linear velocity and angular velocity**

Let *ω*→ Uniform angular velocity of point object moving along PQ

*v* → Linear speed

*r* → Radius of circular path

*t* → Time at which the object is at point P

*t* + Δ*t* → Time at which the object is at Q

Let POQ = Δ*θ* and

It means that an object describes an arc PQ of length Δ*l* in time interval Δ*t*.

Also,

From equations (i) and (ii),

**
**