Angular velocity and angular acceleration

Hey Aspirant!

Angular acceleration is the change in angular velocity divided by time, while tangential acceleration is the change in linear velocity divided by time.

Angular acceleration does not change with radius, but tangential acceleration does.

Measure of how angular velocity changes over time. The rotational analogue of linear acceleration. A vector quantity with counterclockwise defined as the positive direction.

Linear acceleration of a rotating object that is perpendicular to its radial acceleration is tangential acceleration.

If the body is a point mass, and even if frames are stationary, still the angular velocity and accelerations may or may not come out to be the same.

Consider for example, the case of a uniform circular motion, if the angular velocity is measured about an axis which does NOT pass through the centre, it will be a function of time, this is because the torque of the centripetal force will NOT be zero about such an axis.

On the other hand, consider a point mass moving in a straight line. The angular velocity about axes (passing through all points on a parallel line and perpendicular to the plane of motion) will be the same.It mainly has to do with the expression for torque which comes from what Force the point mass is experiencing. If the torque depends on which axis is chosen, then ω and α will change.If it is not a point mass, then firstly you can not measure ω and α about points which are not on the object/rigid body (unless its acting as the Instantaneous Centre). But, about all points on the rigid body, ω and α will be the same.

Hope it solves your query.

Best of luck.