(kinetic) Energy and Momentum

Question

What is the difference between kinetic Energy and Momentum? Both are based on an objetct's mass and velocity!

Answer 1

Momentum (vector): P = m V

Kinetic Energy (scalar): K = (1/2) m V²

In Physics we always look for quantities that are conserved (say before and after a collision) to help us do the calculations and predict the motion (velocity magnitude and direction) of the objects involved.

The conservation of the Kinetic energy only gives us 1 equation and we have two unknowns (V₁ & V₂).

Conservation of Momentum gives us another 1 equation.

Now we have two unknown and two equations.

Conservation of Momentum can give us up to 3 equations based on the dimension of the space that a collision happens (1D: linear collision, 2D: Billiard balls, 3D: Large Hadron Collider)

Answer 2

Both do indeed describe the state of motion of an object, but only Momentum is a vector, which includes the property of direction of motion. Energy is a scalar and as such is relative to a reference point.

For both there exist the principles of conservation: Momentum - Impulse and Energy - Work.