Impulse

Impulse describes the cumulative effect of a force acting on an object over a specific interval of time. It is calculated by multiplying the force applied by the duration for which it acts, and the result is exactly equal to the change in the object's Momentum. This equivalence — known as the impulse-momentum theorem — is one of the most practically useful relationships in mechanics, and it's what the Impulse Calculator computes directly.

Because impulse equals the change in momentum, the same change in momentum can be produced by a large force acting briefly or a smaller force acting over a longer time. This is the physical reason airbags, crumple zones, and padded flooring reduce injury — they extend the time of impact, which reduces the peak force experienced for the same momentum change.

Impulse connects directly back to Newton's Second Law, since force itself is defined as the rate of change of momentum. Integrating force over time to get impulse is simply the inverse operation, making impulse one of the most direct practical applications of Newton's laws, alongside the Momentum Calculator for analyzing collisions.

J = F × Δt

Where J is impulse (in newton-seconds, N·s), F is force (in newtons, N), and Δt is the time interval over which the force acts (in seconds, s).

Equivalently, by the impulse-momentum theorem:

J = Δp = m × (v_f − v_i)

A baseball with a mass of 0.145 kg is hit by a bat, changing its velocity from −20 m/s (incoming) to +35 m/s (outgoing, in the opposite direction) over a contact time of 0.0015 seconds.

Change in momentum: Δp = m × (v_f − v_i) = 0.145 × (35 − (−20)) = 0.145 × 55 = 7.975 kg·m/s

By the impulse-momentum theorem, the impulse delivered by the bat is also 7.975 N·s. The average force during contact can then be found by rearranging J = FΔt:

F = J ÷ Δt = 7.975 ÷ 0.0015 ≈ 5,317 N

• Equal to the change in momentum: impulse and ΔMomentum are the same quantity, connected by the impulse-momentum theorem J = Δp.
• Force and time trade off: the same impulse can result from a large force over a short time or a small force over a longer time, which is why extending impact time reduces peak force.
• Shares units with momentum: newton-seconds (N·s) and kilogram-meters per second (kg·m/s) are dimensionally equivalent.
• A vector quantity: impulse has direction, so reversing an object's motion (like a bounced ball) requires a larger impulse than simply stopping it.
• Explains real-world safety design: airbags, cushioned flooring, and crumple zones all work by increasing collision time to lower the force delivered to the body.