Momentum Calculator

Momentum conservation follows from Newton's third law: in any interaction, the force on object A from B is equal and opposite to the force on B from A. Over the same time interval, these forces produce equal and opposite impulses, so the total momentum of the system remains constant. This holds even when energy is not conserved (inelastic collisions).

Momentum $$p = mv$$ is a vector and is always conserved in isolated systems. Kinetic energy $$KE = \frac{1}{2}mv^2$$ is a scalar and is only conserved in elastic collisions. They are related by $$KE = p^2/(2m)$$. Two objects can have equal momentum but different kinetic energies if their masses differ.

Yes. Momentum is a vector quantity, so it can be positive or negative depending on the direction of velocity. Negative momentum simply means the object moves in the negative direction of your chosen coordinate system. The magnitude of momentum is always non-negative.

The de Broglie wavelength $$\lambda = h/p$$ assigns a quantum-mechanical wavelength to any moving particle. For macroscopic objects, this wavelength is incredibly small (less than $$10^{-30}$$ m) and unobservable. For electrons and other subatomic particles, it becomes significant and explains phenomena like electron diffraction.

Newton's second law in its general form is $$F = dp/dt$$ — force equals the rate of change of momentum. For constant mass, this simplifies to $$F = ma$$. The impulse-momentum theorem states that $$F \Delta t = \Delta p$$, connecting force, time, and momentum change.