Angular Momentum Calculator

Angular momentum measures the rotational equivalent of linear momentum, depending on how mass is distributed relative to an axis of rotation. This calculator applies two distinct formulas based on the scenario: For a point mass moving in a circular path, the equation is L = m * v * r, where L is angular momentum, m is mass, v is tangential velocity, and r is the radius of the circular path. For a rigid body rotating about a fixed axis, the formula uses its rotational inertia: L = I * omega, where I represents the moment of inertia and omega denotes the angular velocity in radians per second.

Imagine a spinning solid disk serving as a flywheel in a mechanical system. The moment of inertia (I) of the disk is calculated as 2.5 kg*m^2, and it rotates at an angular velocity (omega) of 12 rad/s. To find the angular momentum, we apply the rigid body formula: L = I * omega. Substituting the values yields L = 2.5 * 12, which equals 30 kg*m^2/s. If we evaluate a moving body instead—such as a 4 kg mass traveling at 5 m/s along a 3-meter radius circle—the moving body formula L = m * v * r yields 4 * 5 * 3, resulting in 60 kg*m^2/s.

Always verify that your units are consistent before entering values into the calculator. Standard SI units require mass in kilograms, velocity in meters per second, radius in meters, and angular velocity in radians per second. When dealing with rigid bodies, make sure you select the correct moment of inertia formula for the specific geometry, such as a hollow cylinder, solid sphere, or rod, as improper inertia values will invalidate your final angular momentum result.