Impulse & Momentum - Dynamics

The Principle of Linear Impulse & Momentum

The equation of motion (F = ma) will be integrated to give the principle of linear impulse and momentum. This is a vector equation that relates change in the velocities magnitude and direction, also relates force and time.

Linear Momentum: L = m v where m is mass and v is velocity. Units are mass-velocity, Kg*m/s or slug*ft/s

Linear Impulse: the effect of a force is measured over a period of time. I = ∫F dt The units are force-time, N-s or lb-s


∑mv1 + ∑∫F dt = ∑mv2 This is the Principle of linear impulse and momentum

This equation states that the initial momentum plus the impulses of all external forces is equal to the final momentum. This equation can also be written in to the x, y, and z components for the velocity and force.


If the sum of the external impulses that act on the system are equal to zero then the conservation of linear momentum can be written...

∑mv1 = ∑mv2

This equation is helpful when dealing with objects that collide/interact.

Impulsive forces: these forces are present when there is an explosion, or the striking of one object on another.

Non-impulsive forces: a force that is very small compared to the impulsive forces such as weight or a spring that has a small deformity.

Example: A soccer ball that is kicked. The force of the foot kicking the ball is an impulsive force because the momentum of the ball is changed drastically. The balls weight is a non-impulsive force and has a negligible effect on the change in momentum.



For more topics on Dynamics click here