How is angular displacement calculated in circular motion?

Angular displacement is calculated by measuring the angle through which an object rotates.

In circular motion, an object moves along a circular path with a fixed radius. Angular displacement is the angle through which the object rotates from its initial position. It is measured in radians and is denoted by the symbol θ.

To calculate angular displacement, the initial and final positions of the object must be determined. The initial position is taken as the reference point, and the angle between the reference point and the final position is measured. This angle is the angular displacement.

Angular displacement can be positive or negative depending on the direction of rotation. If the object rotates in a clockwise direction, the angular displacement is negative. If the object rotates in an anti-clockwise direction, the angular displacement is positive.

Angular displacement is related to linear displacement by the formula θ = s/r, where s is the linear displacement and r is the radius of the circular path. This formula is derived from the fact that the arc length of a circle is proportional to the angle it subtends at the centre.

In summary, angular displacement is the angle through which an object rotates in circular motion. It is measured in radians and can be positive or negative depending on the direction of rotation. Angular displacement is related to linear displacement by the formula θ = s/r.