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What is difference between angular and tangential velocity?

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Angular velocity

“Time rate of change of angular displacement is known as angular velocity.”It is denoted by ω,its formula is given by:

angular velocity

Unit of angular velocity is radian per second (rad s-1) .

angular velocity

Very often we are interested in knowing how fast or how slow a body is rotating.It is determined by its angular velocity which is defined as the rate at which the angular displacement is changing with time.If Δθ is the angular displacement during the time interval Δt ,the average angular velocity ωav during this interval is given by:

average angular velocity

The instantaneous angular velocity ω is the limit of the ratio Δθ/Δt as Δt ,following instant t,approaches to zero.

Thus:

instantaneous angular velocity

In the limit when Δt approaches zero,the angular displacement would be infinitesimally small.So it would be a vector quantity.Its direction is along the axis of rotation and given by right hand rule.

Types of angular velocity:

Average angular velocity:

“Total rate of change of angular displacement is called average angular velocity.”

Uniform angular velocity:

“If rate of change of angular displacement is constant is called uniform angular velocity.”

Non uniform angular velocity:

“If rate of change of angular displacement is not constant is called non uniform angular velocity.”

Instantaneously angular velocity:

“Angular velocity at particular instant of time is called instantaneous angular velocity.”

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