Table of Contents
Angular Displacement Defined
Angular displacement is the angle through which an object has rotated about a fixed axis, measured in radians, degrees, or revolutions. One complete revolution equals 2 pi radians or 360 degrees. It is the rotational analog of linear displacement (distance traveled).
Angular displacement is used extensively in engineering design of gears, motors, robotic arms, and satellite attitude control. In physics, it connects to angular velocity and acceleration through the rotational kinematic equations, which mirror the linear equations of motion.
Rotational Kinematic Equations
Where theta is angular displacement, omega_0 is initial angular velocity, alpha is angular acceleration, and t is time. These equations assume constant angular acceleration.
Unit Conversions
| From | To | Multiply by |
|---|---|---|
| Radians | Degrees | 180/π = 57.296 |
| Degrees | Radians | π/180 = 0.01745 |
| Revolutions | Radians | 2π = 6.2832 |
| RPM | rad/s | 2π/60 = 0.10472 |
FAQ
Is angular displacement a vector?
Infinitesimal angular displacements are vectors (they obey vector addition), but finite angular displacements are not true vectors because they do not commute (order of rotations matters). However, for rotations about a single fixed axis, angular displacement behaves like a scalar with a sign convention.
How many radians in one revolution?
One complete revolution equals 2 pi radians, approximately 6.2832 radians. The radian is defined as the angle subtended by an arc equal in length to the radius of the circle, making it a natural unit for rotational mathematics.
What is the difference between angular displacement and angular distance?
Angular displacement is a signed quantity (can be positive or negative depending on direction) measured from start to finish position. Angular distance is always positive and represents the total angle swept, regardless of direction changes. For motion in one direction, they are equal in magnitude.