Momentum Calculator

About the Momentum Calculator

Linear momentum is the product of an object's mass and its velocity. It is a vector quantity that measures how much motion an object has.

Enter mass in kilograms and velocity in metres per second. Momentum is returned in kilogram-metres per second (kg·m/s).

How to use this calculator

1. Enter the mass of the object, usually in kilograms.
2. Enter the velocity, usually in meters per second.
3. Check that the velocity sign matches direction, because momentum is a vector quantity.
4. Read the momentum result, which is given in kilogram meters per second, \(\mathrm{kg\cdot m/s}\).

The formula explained

The formula \(p = m \cdot v\) computes linear momentum, where mass is multiplied by velocity. It shows how much motion an object has in a given direction.

• p = momentum, measured in \(\mathrm{kg\cdot m/s}\)
• m = mass of the object, usually in \(\mathrm{kg}\)
• v = velocity of the object, usually in \(\mathrm{m/s}\)

Step by step method

1. Write down the mass and velocity with their units.
2. Multiply mass by velocity using \(p = m \cdot v\).
3. Keep the sign of velocity, since a negative velocity gives a negative momentum.
4. State the final momentum with the correct units, \(\mathrm{kg\cdot m/s}\).

Worked example

Problem. A cart has a mass of 4.5 kg and moves at 3.2 m/s. Find its momentum.

1. Use the formula \(p = m \cdot v\).
2. Substitute the values, \(p = 4.5 \cdot 3.2\).
3. Calculate the product, \(p = 14.4\,\mathrm{kg\cdot m/s}\).

Tips and common mistakes

• Make sure mass is in kilograms and velocity is in meters per second before calculating.
• If the object is moving in the opposite direction, use a negative velocity so the momentum has the correct sign.

Frequently asked questions