Impulse is defined as a quantity which describes the effect of a net force that acts upon an object. Think of it as a moving force. It is the product of the average net force that acts an object, includes the duration, and is a force-time integral with a vector quantity. That is because force is a vector in the impulse momentum theory and time is a scalar.

Impulse is represented by J.

Momentum is defined as a quantity which describes the resistance an object has to stopping. Think of it as moving inertial. It is the product of an object’s mass and velocity and is a vector quantity as well since velocity is a vector and mass is a scalar.

Momentum is represented by P.

### What Does the Impulse Momentum Theory State?

The impulse momentum theory takes these definitions into account and states that the change in momentum of an object equals the impulse that is applied to it. That statement can be reflected by the following equation: J = Δp.

If mass is constant, then the equation shifts to this equation within the theorem: F̅Δt = mΔv.

If the mass is changing, then the theorem would be expressed in this manner: F dt = m dv + v dm.

Because impulse is a quantity which is closely related to momentum, applying force for an amount of time allows an object with momentum to have the value of that momentum change to a new value. The impulse is equal to the change in momentum that occurs.

When determining the change in value, the first step is to define a positive direction. Then the variables of impulse and momentum are determined so that the new value can be calculated.

### Does the Principle of Conservation Apply?

When dealing with physics, the term “conservation” refers to something which does not change. Within an equation, that means the variable with a conserved quality to it will remain constant over time. The value remains the same before and after an event occurs.

In mechanics, angular momentum, energy, and momentum are three fundamental quantities which are traditionally conserved. The conservation of momentum is used to describe collisions which occur between objects, but only if it is an isolated system. There cannot be an external impulse that has the capability of applying force to the system.

That means the principle of conservation does not apply within the impulse momentum theory because the “impulse,” or force, is acting upon the object with momentum by its very calculation.

Until the impulse is applied, however, the principle of conservation could apply to the object in events which occur before the equations in this theorem are applied.

That means a collision which occurs within the isolated system does not have this theory applied to it. The collisions act upon the momentum of each other because they are an *internal force* instead of an *external force.* That means the momentum is conserved.

### How We Use Impulse Momentum Theory

We see the impulse momentum theory applied every day in some way as it is an equivalent to Newton’s second law. The application for variable mass allows momentum and impulse to be used as analysis tools, which are applied to vehicles that use rocket or jet engine propulsion. By creating a performance parameter, the units of propellant being expelled can be calculated so that a specific impulse can be determined.

We also see impulse momentum theory applied in various daily activities. If you play tennis, then this theory applies because the tennis ball being hit by a racket is given impulse. The momentum of the ball shifts to a new value because a large force (the racket, powered by the swing of an arm) is applied to the tennis ball for a specific amount of time.

Using a golf club to hit a golf ball would be another action of impulse that changes the momentum value.

It is important to remember that an item which is stationary still has momentum on our planet because our planet is always moving. The size of our planet negates tangible awareness of that movement, such as the rotation of the planet or how it orbits the sun, but the evidence of its existence is still present. The surface of the Earth at the equator moves at a speed of nearly 1,000 miles per hour as it rotates and the planet orbits the sun at a speed of about 67,000 miles per hour.

In summary, impulse momentum theory allows us to calculate a new value when a force is applied to the current value.