# What is the Magnitude of the Initial Angular Momentum of the Merry-Go-Round?

August 19, 2023
David Sunnyside

In physics, the rotational equivalent of linear momentum is called angular momentum (or simply angular momentum). It is a vector quantity that consists of both magnitude and direction. An object or system of objects may have either orbital angular momentum, as the Earth does, or spin angular momentum, as the merry-go-round does. Angular momentum is conserved under the same conditions as linear momentum, so in any event that does not affect the object's trajectory the total angular momentum of the system remains unchanged.

For a point particle, angular momentum can be represented as the cross product of its position vector r displaystyle mathbf r and the linear momentum vector p displaystyle mathbf p of the particle. The angular momentum vector, L displaystyle mathbfL , is therefore perpendicular to both r displaystyle mathbfr and p displaystyle mathbfp .

A person who runs 2 meters toward a circular merry-go-round, jumps on it, and starts to spin at its initial velocity has an initial angular momentum of. This is because, in addition to a mass, the initial angular momentum of a body consists of its moment of inertia times its initial angular velocity.

Since this angular momentum is conserved, the merry-go-round will continue to rotate with the same angular speed as it had before the child jumped on. As a result, the angular momentum of the system of the merry-go-round and the person together will remain constant. This is a basic example of angular momentum conservation.

David Sunnyside
Co-founder of Urban Splatter • Digital Marketer • Engineer • Meditator