Impulse is the change in momentum of an object. Impulse is interchangeably symbolized as change in momentum, , or simply . This falls out of the mathematical definition of impulse:
In investigations of the processes that cause an object's momentum to change, such as cars colliding, or a ball bouncing, impulse is the path to studying the forces involved in the change.
As it is an expression of momentum, an acceptable unit for impulse is the , however common units for impulse include the Newton-second ().
When a force is applied to an object, no matter what the state of that object's motion is, acceleration will occur. This is in fact Newton's second law, . The equation for impulse, can in fact be derived from this law:
Since and see below, we have the following theorem:
where represents impulse, represents applied force, and represents the time over which the force is applied.
A force of was applied to an object for . Calculate the impulse experienced by the object.
Let represent impulse, force, and the time that the force acted. Then
Newton's second law states that the acceleration of an object due to a net force is in the same direction as that force and inversely proportional to the mass of the object, or, mathematically, .
Since an acceleration causes a change in velocity, a reformulation of Newton's second law is possible in terms of velocity.
The equality of the two formulations of Newton's second law is best demonstrated through a simple example.
A 2 ball is dropped near the surface of a planet. If find the average force on the ball throughout its fall.
Finally, evaluate Newton's second law:
An object which was initially at rest has a momentum of after being influenced by a force for . Calculate the magnitude of the force that acted upon the object.
The is equivalent to the , so substitute that value, along with the provided time, into to obtain: