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# How do you calculate angular momentum?

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As explained by Hyperphysics, angular momentum is calculated by finding the product of the moment of inertia and the angular velocity of a rotating body or system. The moment of inertia with respect to an axis is the product of the mass times the distance from the axis squared, and angular velocity is the rate of change of angular displacement.

## Keep Learning

Einstein Online defines angular momentum, for an object orbiting a central point, as the product of the object’s mass times its distance from the axis times the velocity at which it orbits around the center. Angular momentum is understood as the momentum of rotation, or an object’s resistance to change in rotation. Angular momentum is a vector quantity requiring both magnitude and direction. The direction of the angular momentum vector is the same as the axis of rotation of the object using the right-hand rule, explains Real World Physics.

Encyclopædia Britannica states that the total angular momentum for a given object or system isolated from external forces is a constant, which is known as the law of conservation of angular momentum. The units for angular momentum are kilogram meters squared per second (kg ? m2 / sec). A child’s yo-yo builds angular momentum as the string unwinds and the spool spins, causing the yo-yo to continue spinning after reaching the end of the string, states HowStuffWorks.

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## Related Questions

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The parallel axis theorem states that the "moment of inertia of any object about an axis through its center of mass is the minimum moment of inertia for an axis in that direction in space," according to HyperPhysics. It is also know as Steiner's theorem.

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Northwestern University explains that a ring has a higher moment of inertia than a solid disk of equal mass and outer radius because it has less mass at its center. According to the principles of inertia, bodies that have more mass at the center have lower levels of moment of inertia, which is directly related to the rate at which an object can spin.

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The moment of inertia of a sphere is I = 2/5 MR^2 for a solid sphere and I = 2/3 MR^2 for a thin spherical shell. This moment of inertia can be derived from the moment of inertia of a thin disk by summing the moments of inertia of a series of infinitely thin disks throughout the volume of the sphere.