Calculate the angle through which a point rotates given arc length and radius.
Angular displacement (θ) is the angle through which a point or line rotates about a specified axis. It is the rotational equivalent of linear displacement, measured in radians, degrees, or revolutions.
The fundamental relationship is: θ = s / r, where s is arc length and r is radius. One complete revolution equals 2π radians or 360 degrees.
Angular displacement is essential in robotics, machinery design, and physics problems involving circular motion and rotation.
Where: θ = angular displacement (rad), s = arc length (m), r = radius (m)
Wheel with radius 1.5 m rolls 9.42 m. Angular displacement?
Arc length (s) is the actual distance traveled along the circle. Angular displacement (θ) is the angle rotated. They relate by: θ = s / r.
Radians are the natural unit for angular measures in calculus and physics, simplifying mathematical expressions.
Yes, the sign indicates direction. Positive is typically counterclockwise, negative is clockwise.
When a wheel rolls, the angular displacement tells how many rotations occurred. For steering wheels and mechanical parts.
Related Tools
Calculate angular acceleration.
Calculate angular momentum.
Calculate angular velocity.
Calculate belt length.
Calculate centrifuge parameters.
Calculate circular motion.