Problems posed in terms of velocity and position use kinetic energy and work. Problems posed in terms of time use impulse and momentum. Consider:

When it is integrated:

where left-hand side of the equation is called linear impulse and the right-hand side is the change in linear momentum. Similarly for rotation:

When it is integrated:

where left-hand side of the equation is called angular impulse and right-hand side of the equation is the change in angular momentum. The angular momentum, or moment of momentum, is a function of the inertial properties and angular velocity of the rigid body, similar to the relationship between linear momentum, mass, and velocity. This relation is given in the Moment of Momentum section.

The relationship given in Eq. 2↑ is called the principle of linear impulse and momentum. It states that the change of linear momentum of a body over a time period t₁ to t₂ is equal to the linear impulse acting on it during that time period. Similarly, the relationship given in Eq. 4↑ is called the principle of angular impulse and momentum. It states that the change of angular momentum of a body over a time period t₁ to t₂ is equal to the angular impulse acting on it during that time period.

Recall from physics that momentum must be conserved. So, if the force on the object is zero or if the force is an internal force, F = 0. Thus, mv₂ − mv₁ =  0, so internal forces impart no impulse to a rigid body.