# Angular Frequency Formula

Angular frequency is associated with the number of revolutions an object performs in a certain unit of time. In that sense is related to frequency but in terms of how many times it turns a full period of motion in radians units.

The formula of angular frequency is given by:

Angular frequency = 2 π / (period of oscillation)

ω = 2π / T = 2πf

Where we have:

ω: angular frequency

T: period

f: frequency

If the motion is alone a circle, we have:

Angular frequency = (angle change) / (time it takes to change the angle)

ω = dθ / dt

θ: is the angle change.

If we know the radius of the circle is R, then we can determine the velocity by:

v = Rω

Angular Frequency Formula Questions:

1) A mass is tied to a 2 meters' rod. After a small impulse, it begins to oscillate. What is the angular frequency?

Answer:The length of the rod is 2 meters, L = 2 m. The acceleration of gravity is 9.8 m/s^{2}. Substitute in the equation for T.

T = 2 π √2 m/9.8 m/s^{2}

T = 2.8 s

The next step is to substitute the period in the angular frequency equation

ω = 2π / T

ω = 2π / 2.8 s

ω = 2.24 rad/s

2) A mass circles half of a round square in a certain time t=0.8 s. What isthe angular frequency?

Answer: The angular change is given by the formula of ω. Half of the circle occurswhen only half of the 2π radians (full circle) are traveled by the mass,then the angles change is π radians.

ω = dθ / dt

ω = π rad / 0.8 s

ω = 3.92 rad/s

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