Momentum

Momentum is the product of an object's mass and its velocity, representing the "quantity of motion" that object carries. A larger mass or a higher velocity both increase momentum, which is why a slow-moving freight train can be far harder to stop than a fast-moving bicycle despite the bicycle's higher speed. The Momentum Calculator computes this value directly from mass and velocity inputs.

Momentum is a vector quantity, meaning its direction matters as much as its size — an object's momentum always points in the same direction as its velocity. This becomes especially important when analyzing collisions or explosions, where momentum in each direction must be tracked and summed separately.

One of the most powerful properties of momentum is that it is conserved in any closed system with no external forces acting on it: the total momentum before a collision equals the total momentum after. This conservation law, combined with Newton's Second Law, explains why forces and Velocity changes are so tightly linked, and it's the principle behind the Impulse Calculator, which relates force and time to the resulting change in momentum.

p = m × v

Where p is momentum (in kilogram-meters per second, kg·m/s), m is mass (in kilograms, kg), and v is velocity (in meters per second, m/s).

A soccer ball with a mass of 0.43 kg is kicked and travels at a velocity of 25 m/s. Its momentum is:

p = m × v = 0.43 kg × 25 m/s = 10.75 kg·m/s

If a heavier bowling ball of 7 kg were rolled at just 1.5 m/s, it would have a momentum of 7 × 1.5 = 10.5 kg·m/s — remarkably close to the soccer ball's momentum despite moving over 16 times slower, illustrating how mass and velocity trade off in determining momentum.

• Depends equally on mass and velocity: doubling either mass or velocity doubles momentum, since the relationship is directly proportional to both.
• Conserved in closed systems: total momentum before and after a collision or explosion stays constant, as long as no external force interferes.
• Directly tied to Newton's Second Law: force is the rate of change of momentum over time, making momentum a more general concept than force alone.
• Impulse changes momentum: applying a force over a time interval produces a change in momentum equal to that impulse.
• A vector quantity: momentum has direction as well as magnitude, which is essential when analyzing motion in multiple directions, such as angled collisions.