Calculate the angle through which an object moves on a circular path.
Angular displacement is the angle (in radians, degrees, or revolutions) through which a point or line has been rotated in a specified sense about a specified axis. It is the circular analog of linear displacement.
When an object moves along a circular path, the distance it travels along the edge is the arc length (s). The ratio of this arc length to the radius (r) of the circle gives the angular displacement in radians. This relationship is fundamental to understanding rotational motion in physics and engineering.
θ (Theta) = Angular displacement (radians)
s = Arc length (linear distance)
r = Radius of the circular path
Angular displacement is a vector quantity that represents the change in angle, while angular distance is the total angle covered. For a full circle returning to start, displacement is 0 but distance is 2π radians.
Radians are the natural unit for angles in physics because they relate arc length directly to radius without arbitrary factors. Most physics formulas (like v = ωr) require radians.
There are exactly 2π radians in one full revolution, which is approximately 6.28318 radians.
Yes. By convention, counter-clockwise rotation is positive and clockwise rotation is negative.
Arc length is always proportional to radius for a fixed angle. Doubling the radius doubles the arc length for the same angular displacement.
Multiply radians by 180/π to get degrees. For example, π radians = 180°, so 1 radian ≈ 57.3°.
Angular displacement is undefined when radius is zero, as there is no circular path. The calculator returns 0 for safety.
Angular displacement is used in robotics, mechanical engineering, planetary motion analysis, gyroscope calculations, and any rotational dynamics problem.
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