# Impulse - Force Over Time

## Force and Change in Momentum

Force applied over time creates an impulse, a change in momentum. Impulse is defined in classical mechanics as a force multiplied by the amount of time it acts over. In calculus terms, the impulse can be calculated as the integral of force with respect to time. The symbol for impulse is J or Imp.

Force is a vector quantity (the direction matters) and impulse is also a vector in the same direction. When an impulse is applied to an object, it has a vector change in its linear momentum. Impulse is the product of the average net force acting on an object and its duration. J = Δt

Alternately, impulse can be calculated as the difference in momentum between two given instances. Impulse = change in momentum = force x time.

## Units of Impulse

The SI unit of impulse is the same as for momentum, the Newton second N*s or kg*m/s. The two terms are equal. English engineering units for impulse are pound-second (lbf*s) and slug-foot per second (slug*ft/s).

## The Impulse-Momentum Theorem

This theorem is logically equivalent to Newton's second law of motion: force equals mass times acceleration, also known as the force law. The change in momentum of an object equals the impulse applied to it. J = Δ p.

This theorem can be applied to a constant mass or to a changing mass. It is relevant especially to rockets, where the mass of the rocket changes as fuel is expended to produce the thrust.

## Impulse of Force

The product of average force and the time in which it is exerted is the impulse of force. It is equal to the change of momentum of an object that isn't changing mass.

This is a useful concept when you are studying impact forces. If you increase the time over which the change of force happens, the impact force also decreases. This is used in mechanical design for safety, and it is useful in sports applications as well. You want to reduce the impact force for a car hitting guardrail, for example, by designing the guardrail to collapse as well as designing parts of the car to crumple on impact. This lengthens the time of the impact and therefore the force.

If you want a ball to be propelled further, you want to shorten the time of impact with a racket or bat, raising the impact force. Meanwhile, a boxer knows to lean away from a punch so it takes longer in landing, reducing the impact.

## Specific Impulse

Specific impulse is a measure of the efficiency of rockets and jet engines. It is the total impulse that is produced by a unit of propellant as it is consumed. If a rocket has a higher specific impulse, it needs less propellant to gain altitude, distance, and speed. It is the equivalent of the thrust divided by the propellant flow rate. If the propellant weight is used (in Newton or pound), specific impulse is measured in seconds. This is often how rocket engine performance is reported by manufacturers.

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