# Angular impulse

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The **angular impulse** in physics is the product of the average of a briefly applied force *F* times the radius of a rigid body *R* times the brief time period delta *t*:

where the final angular velocity is just after the impulse, and the initial angular velocity is just before the impulse.

## Example

Suppose a rotating cylinder of radius R_{2} is joined with a stationary cylinder of radius R_{1}. Both feel an impulsive force until the continue rotating without slippage at different angular velocities. The above formula permits calculation of the respective angular velocities as follows:

Thus:

But:

and:

and thus can be solved in terms of the initial angular velocity of the rotating cylinder .