## 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/sec^{2} and is equal to dω/dt.