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Momentum Calculator

Calculate momentum ($p$), mass ($m$), or velocity ($v$) using the formula $p = mv$.

Momentum ($p = mv$)

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What is Momentum?

In physics, momentum is a fundamental concept often described as "mass in motion." It is a measure of how much motion an object has and how hard it is to stop that object. A heavy object moving quickly has a large momentum, while a light object moving slowly has a small momentum. A stationary object (with zero velocity) has zero momentum, regardless of its mass.

Momentum is a vector quantity, meaning it has both magnitude (how much) and direction. A car traveling north has a different momentum from an identical car traveling east at the same speed.

The Momentum Formula

The formula for calculating momentum is a straightforward multiplication:

  • $p$: Momentum, measured in kilogram-meters per second (kg·m/s).
  • $m$: Mass of the object, measured in kilograms (kg).
  • $v$: Velocity of the object, measured in meters per second (m/s).

This calculator allows you to solve for any one of these three variables if you know the other two.

The Law of Conservation of Momentum

One of the most important principles in all of physics is the Law of Conservation of Momentum. This law states that in an isolated system (one with no external forces acting on it), the total momentum of the system remains constant.

This principle is most often seen in collisions. Consider two billiard balls rolling on a table:

  • Before they collide, each ball has its own momentum ($p_1$ and $p_2$). The total momentum of the system is $p_{initial} = p_1 + p_2$.
  • When they collide, they exert forces on each other, but these are *internal* forces.
  • After they bounce off and move in new directions, they have new momentums ($p_3$ and $p_4$). The total momentum is now $p_{final} = p_3 + p_4$.

The law of conservation of momentum guarantees that $p_{initial} = p_{final}$. This is why, when a cannon fires, the cannon recoils backward. To conserve momentum (which was zero before firing), the forward momentum of the cannonball must be balanced by an equal and opposite backward momentum of the cannon.

Momentum, Force, and Kinetic Energy

Momentum is closely related to other key physics concepts:

  • Force: A force is not just $F=ma$; it can also be defined as the rate of change of momentum. The concept of Impulse ($J$) is the change in momentum ($\Delta p$), which is equal to the force applied multiplied by the time it was applied ($J = \Delta p = F \times \Delta t$). This is why a boxer "rolls with the punch"—by increasing the time ($\Delta t$) of the impact, they reduce the peak force ($F$) experienced.
  • Kinetic Energy: Momentum and kinetic energy ($KE = \frac{1}{2}mv^2$) both describe motion, but they are not the same. An object can have momentum without having kinetic energy (impossible, as $v=0$ means both are 0), but the relationship is not linear. If you double an object's velocity, you double its momentum ($p \propto v$), but you *quadruple* its kinetic energy ($KE \propto v^2$). For a deeper dive, the Wikipedia article on Momentum is an excellent resource.