Impulse and Momentum Calculator

The impulse-momentum theorem states that the impulse applied to an object equals the change in its momentum: J = Δp = m·Δv. This means that a force applied over a time interval causes a proportional change in an object's momentum. It connects Newton's second law to the concepts of impulse and momentum.

Impulse equals the change in momentum: J = p₂ − p₁ = m·v₂ − m·v₁ = m·Δv. Simply multiply the object's mass by the difference between its final and initial velocities. The unit of impulse is N·s, which is equivalent to kg·m/s.

When you know the force applied and the duration, impulse is calculated as J = F × Δt — force multiplied by the time interval. For example, a 10 N force applied for 3 seconds produces an impulse of 30 N·s. This is the other common form of the impulse equation.

They are related but not the same. Momentum (p = m·v) describes an object's current state of motion at a given instant. Impulse (J = Δp) is the change in momentum resulting from a force acting over time. They share the same units (N·s = kg·m/s), which can cause confusion, but impulse is always a change while momentum is an instantaneous quantity.

To stop an object, you need to reduce its momentum to zero. For example, a ball with mass 0.16 kg moving at 2.5 m/s has momentum p = 0.16 × 2.5 = 0.4 kg·m/s. The impulse needed to stop it is −0.4 N·s (opposite direction). Enter mass = 0.16 kg, v₁ = 2.5 m/s, and v₂ = 0 into the calculator to verify.

Impulse is measured in Newton-seconds (N·s) and momentum in kilogram-meters per second (kg·m/s). These units are equivalent: 1 N·s = 1 kg·m/s. This equivalence follows directly from the impulse-momentum theorem and confirms that impulse and change in momentum are the same physical quantity expressed in different unit forms.

Yes — direction matters in momentum and impulse calculations since both are vector quantities. A negative velocity simply means the object is moving in the opposite direction to the defined positive axis. For example, if a ball bounces back, its final velocity would be negative relative to its initial direction, resulting in a larger magnitude impulse.

Force is related through the equation F = mΔv / Δt, which is simply a rearrangement of the impulse-momentum theorem. A larger force applied over the same time produces a greater impulse and therefore a bigger change in momentum. This is why airbags in cars increase the time of impact — reducing the peak force experienced by passengers even though the total impulse remains the same.