# Impulse

on . Posted in Classical Mechanics

Impulse, abbreviated as J, is the change in momentum of an object.  Momentum is a vector quantity that describes an object's motion and is calculated as the product of its mass and velocity.  Impulse is defined as the change in momentum of an object over a given period of time and is equal to the force applied to the object multiplied by the time during which the force is applied.  Impulse is often associated with the concept of Newton's second law of motion, which states that the rate of change of momentum of an object is directly proportional to the force applied to it and occurs in the direction of the force.

Impulse is useful in various areas of physics, such as in analyzing collisions, where it helps determine how the velocities of objects change during the collision.  In a collision, the total impulse before the collision is equal to the total impulse after the collision, provided no external forces are acting on the system.  This principle is known as the law of conservation of linear momentum.

### Impulse with force formula

$$J = F \; \Delta t$$     (Impulse with Force)

$$F = J \;/\; \Delta t$$

$$\Delta t = J \;/\; F$$

Symbol English Metric
$$J$$ = Impulse $$lbf\;/\;sec$$ $$N\;/\;s$$
$$F$$ = Force $$lbf$$ $$N$$
$$\Delta t$$ = Time Change $$sec$$ $$s$$

### Impulse with mass formula

$$J = m \; \Delta v$$     (Impulse with Mass)

$$m = J \;/\; \Delta v$$

$$\Delta v = J \;/\; m$$

Symbol English Metric
$$J$$ = Impulse $$lbf\;/\;sec$$ $$N\;/\;s$$
$$m$$ = Mass $$lbm$$ $$kg$$
$$\Delta v$$ = Velocity Change $$ft\;/\;sec$$   $$m\;/\;s$$

### Impulse with Time formula

$$J = F \; \Delta t$$     (Impulse with Time)

$$F = J \;/\; \Delta t$$

$$\Delta t = J \;/\; F$$

Symbol English Metric
$$J$$ = Impulse $$lbf\;/\;sec$$ $$N\;/\;s$$
$$F$$ = Force $$lbf$$ $$N$$
$$\Delta t$$ = Time Differential $$sec$$ $$s$$

Tags: Momentum