Momentum Calculator

What is Momentum?

Momentum ($p$) is often described as "mass in motion." It is a measurement of how difficult it is to stop a moving object.

A heavy truck moving slowly has high momentum. A small bullet moving fast also has high momentum. If you want to stop either of them, you need to apply a force against their direction of motion.

The Formula

• p (Momentum): Measured in kg·m/s (Kilogram meters per second).
• m (Mass): The weight of the object in Kilograms (kg).
• v (Velocity): The speed in meters per second (m/s).

Momentum vs. Kinetic Energy

This is the most common confusion in physics. Both depend on mass and velocity, but they scale differently.

• Momentum ($mv$): Scales linearly with speed. If you double your speed, your momentum doubles. It is a Vector (direction matters).
• Kinetic Energy ($\frac{1}{2}mv^2$): Scales exponentially with speed. If you double your speed, your energy quadruples. It is a Scalar (direction doesn't matter).

Impulse: Changing Momentum

To change an object's momentum (speed it up or slow it down), you must apply a Force for a specific amount of time. This is called Impulse ($J$).

Formula: Impulse = Force × Time

This explains why airbags save lives. In a car crash, your momentum must go from "60 mph" to "0 mph."

• Dashboard: Stops you in 0.01 seconds. Huge Force required = Injury.
• Airbag: Slows you down over 0.1 seconds. Lower Force required = Survival.

Conservation of Momentum

In a closed system (like two billiard balls colliding), the total momentum before the collision must equal the total momentum after the collision.

If a moving white ball hits a stationary 8-ball perfectly, the white ball stops dead, and the 8-ball moves away with the exact same speed the white ball had. Momentum was transferred, not lost.