Calculate angular momentum using two methods: enter moment of inertia and angular velocity for rotational systems, or enter mass, velocity, and radius for linear-to-angular conversion. Your results include the angular momentum (L) in kg·m²/s, helping you solve rotational physics problems with ease.
Angular Momentum (L)
--
Method Used
--
Formula Applied
--
Factor 1
--
Factor 2
--
Angular momentum (L) is the rotational equivalent of linear momentum. It describes the quantity of rotation an object has, taking into account its mass distribution, speed, and the distance from the axis of rotation. It is sometimes called the moment of momentum or rotational momentum.
There are two common formulas. For rotating bodies: L = I × ω, where I is the moment of inertia (kg·m²) and ω is the angular velocity (rad/s). For a point mass moving in a curved path: L = m × v × r, where m is mass, v is linear velocity, and r is the perpendicular radius from the axis.
Angular momentum is measured in kilogram-square-meters per second (kg·m²/s), which is equivalent to joule-seconds (J·s). Both units are dimensionally identical and used interchangeably in physics.
The law of conservation of angular momentum states that if no external torque acts on a system, its total angular momentum remains constant. A classic example is a figure skater spinning faster when they pull their arms in, reducing their moment of inertia while keeping angular momentum constant.
Angular momentum is the rotational analog of linear momentum. For a point mass, angular momentum L = r × p, where p = mv is the linear momentum and r is the position vector from the axis. When the motion is perpendicular to the radius, this simplifies to L = m × v × r.
Moment of inertia (I) measures how mass is distributed relative to the axis of rotation — the farther the mass from the axis, the larger the moment of inertia. Since L = I × ω, a larger moment of inertia at the same angular velocity produces greater angular momentum.
Yes. The sign of angular momentum depends on the direction of rotation. By convention, counterclockwise rotation is typically positive and clockwise is negative. In vector form, angular momentum is a pseudovector pointing along the axis of rotation according to the right-hand rule.
Angular momentum appears in many everyday phenomena: planets orbiting the Sun, gyroscopes maintaining orientation, spinning tops, bicycle wheels staying upright, and the Earth's rotation on its axis. In engineering, it is critical in the design of flywheels, turbines, and satellites.