# Angular Velocity Formula

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Angular velocity formula is the change in angular displacement of a given particle in a certain time interval.

Angular velocity of a particle is expressed as ‘ω’. The change in angular displacement is expressed as ‘dθ’.

The time taken for the angular displacement is t. Angular velocity of a particle is the rate of change of

angular displacement with respect to the time. This makes the angular velocity formula expressed as ω = dθ /

dt.

Example 1: Find the angular velocity of a block moving on a path given as θ=3t2-12t when t = 8

seconds.

Given is the path of the bock is θ = 3 t2 - 12 t.

The angular velocity formula is ω = dθ/dt.

ω = dθ/dt = 6 t - 12

For t = 8 seconds, the angular displacement of the block is

ω = 6 * 8 - 12 = 48 - 12 = 36 rad/seconds.

Hence the ω = 36 rad/seconds.

Example 2: Find the angular velocity of anobject moving on a path given as θ=t3-2 t2 + 1 when t = 6

seconds.

Given is the path of the bock is θ = t3 - 2t2 + 1.

The angular velocity formula is ω = dθ/dt.

ω = dθ/dt = 3 t2 - 4t

For t = 6 seconds the angular displacement of the block is

ω = (3 * 36)-(4 * 6) = 108-24 = 84 rad/seconds.

Hence the ω = 84 rad/seconds.