Question

What is the derivation for v=rw?

Answer 1

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 + Δt → Time at which the object is at Q

Let POQ = Δθ and
---- ----- ------
oQ= r. + ∆r

It means that an object describes an arc PQ of length Δl in time interval Δt.

: v=∆L
---
∆t. ....1

(i)= ∆ø
-----
∆t
∆ø= (i)∆t ...2

Also, ∆ø=∆l
---- [angle =arc
r. ------
radius ]

From equations (i) and (ii),

(i)∆t=v∆t
--------
r
v=r(i)