Question

explain angular frequency and derive it

Answer 1

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:

Q1) 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/s2. Substitute in the equation for T.

T = 2 π √2 m/9.8 m/s2

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

Answer 2

Angular frequency (ω), also known as radial or circular frequency, measures angulardisplacement per unit time. Its units are therefore degrees (or radians) per second. Hence, 1 Hz ≈ 6.28 rad/sec. Since 2π radians = 360°, 1 radian ≈ 57.3°.