Impulse (`Delta vecv`)

vCalc Reviewed
Equation / Last modified by Administrator on 2017/11/26 07:05
vCalc.Impulse (`Delta vecv`)

The Impulse calculator computes the impulse (J) as a function of a mass (m), velocity (v) and angle of impact (θ).ImpulseDeltavecv-illustration.png

INSTRUCTIONS: Choose the preferred units and enter the following:

  • (m) This is the mass of the object.
  • (v)  This is the velocity of the object.
  • (θ) This is the angle of impact of the object.

Impulse (J): The calculator returns the Impulse (J) in Newton•Seconds.

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The Math / Science

This is the formula for the impulse applied to a mass, where impulse is the change in the mass's momentum. The inputs are mass (m), velocity(v), and angle of impact (θ). 

Since the mass is not changing in this example and the magnitude of the velocity is not changing, the change in momentum, `Delta`p, is solely due to the change in direction of velocity due to impact with as surface at angle `theta`.  This example assumes perfect rebound from the surface, so that the speed of the mass before and after impact are exactly equal.

Impulse is the product of the net force and the time interval for which the force acts.  Furthermore, impulse shows how much the force changes the momentum of a body. When a net force acts on a body it will result in an acceleration which alters the motion of the body. A large net force will cause a larger acceleration than a small net force. The total change in motion of the object can be the same if the large and small forces act for different time intervals. The combination of the force and time that it acts is a useful quantity which leads us to define impulse.

 J = F • Δt


  • F is the net force on the system
  • Δt is the duration of the force.

Forces produce either acceleration or deceleration on moving bodies, and the greater the force acting on an object, the greater its change in velocity and, hence, the greater its change in momentum. However, changing momentum is also related to how long a time the force acts. If a brief force is applied to a stalled automobile, a change in its momentum is produced . The same force applied over an extended period of time produces a greater change in the automobile's momentum.