Angular Displacement Calculator

Angular Displacement Calculator

Calculate the angle through which a point rotates given arc length and radius.

Circular Motion Analysis

Angular Displacement (radians)
2.5000

What is Angular Displacement?

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.

How to Calculate

θ = s / r

Where: θ = angular displacement (rad), s = arc length (m), r = radius (m)

Example

Wheel with radius 1.5 m rolls 9.42 m. Angular displacement?

θ = 9.42 / 1.5 = 6.28 rad (≈ 2π rad = 1 revolution)

FAQ

What's the difference between arc length and 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.

Why use radians instead of degrees?

Radians are the natural unit for angular measures in calculus and physics, simplifying mathematical expressions.

Can angular displacement be negative?

Yes, the sign indicates direction. Positive is typically counterclockwise, negative is clockwise.

How does this apply to everyday objects?

When a wheel rolls, the angular displacement tells how many rotations occurred. For steering wheels and mechanical parts.

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