Linear Velocity of a Rotating Body:
Consider a body rotating about its axis as shown in fig:
ω = Angular velocity of the body in rad/s
r = radius of the circular path in meters
v = Linear velocity of the particle on the periphery in m/s
After one second, the particle will move v meters along the circular path and the angular displacement will be ω rad.
We know that length of arc = Radius of arc x Angle subtended in rad.
∴ v = rω
Linear Acceleration of a Rotating Body:
Consider a body rotating about its axis with a constant angular acceleration. We know that linear acceleration.
a = dv/dt = (d/dt)(v)
We also know that in motion of rotation, the linear velocity,
v = rω
Now substituting the value of v in equation (i),
a = (d/dt)(rω) = r.(dω/dt) = rα
α = Angular acceleration in rad/sec2 and is equal to dω/dt.