Question

establish the relationship between the linear and angular velocity

Answer 1

Hint-

v=ds/dt

v=ds/dt

. What does this

s

s

represent(i.e. which 'path' is your object on)? We know angular velocity is the rate of change of angular displacement, i.e.

ω=dθ/dt

ω=dθ/dt

.What is the relation between

s

s

and

θ

θ

? Are they proportional? Plug in the known data in the first equation.

I believe this should be sufficient

Answer 2

Thus, for a given angular velocity ω, the linear velocity v of the particle is directly proportional to the distance of the particle from the centre of the circular path (i.e) for a body in a uniform circular motion,