How is the angular momentum calculated in a collision?

Angular momentum is calculated as the product of the moment of inertia and angular velocity.

In a collision, the total angular momentum before the collision is equal to the total angular momentum after the collision, assuming no external torques act on the system. This is known as the conservation of angular momentum.

The moment of inertia, I, is a measure of an object's resistance to rotational motion and is calculated as the sum of the products of each particle's mass and its distance from the axis of rotation squared. Mathematically, it can be expressed as:

I = Σmr²

where m is the mass of each particle and r is its distance from the axis of rotation.

The angular velocity, ω, is the rate at which an object rotates about an axis and is measured in radians per second. Mathematically, it can be expressed as:

ω = Δθ/Δt

where Δθ is the change in angle and Δt is the change in time.

Therefore, the angular momentum, L, can be calculated as:

L = Iω

In a collision, if the moment of inertia and angular velocity of the system remain constant, the angular momentum before the collision is equal to the angular momentum after the collision. This can be expressed mathematically as:

L1 = L2

where L1 is the angular momentum before the collision and L2 is the angular momentum after the collision.