# Difference between Impulse and Momentum

1. Aug 9, 2013

What's the difference between impulse and momentum ?

When do we use impulse or when do we say a body has impulse ?

2. Aug 9, 2013

### andron2000

Hello.

If a body experiences an impulse, its momentum changes. So if a force acts on an object in a short amount of time, that object will experience an impulse, and subsequently its momentum will change.

3. Aug 9, 2013

### technician

momentum is a property of moving objects...mass x velocity.
To change momentum requires a force acting for a length of time.
The quantity Force x time is called impulse and it equals the change in momentum.
So I would say impulse is used to link force with momentum.

4. Aug 9, 2013

### mark.watson

F = ma, where a = Δv/Δt. Therefore FΔt = mΔv.

The left hand side is the impulse and the right hand side is the momentum. Both are vector quantities.

5. Aug 9, 2013

### Jolb

technician and mark.watson both are on the right track, but I would say technician is assuming a constant force, while mark.watson is giving an infinitesimal form of the actual definition:

The definition of impulse I is
$$\vec{I}=\int \vec{F} \ dt$$ Impulse is a time integral of force.
Momentum, on the other hand, is a property of an object. If an impulse I is imparted on an object, it will change that object's momentum by $\vec{I}$. To be more explicit, if the object initially has momentum $\vec{p}$, and then an impulse $\vec{I}$ acts on that object, its final momentum will be $\vec{p}+\vec{I}$. So an impulse is basically momentum transferred.

Last edited: Aug 9, 2013
6. Aug 9, 2013

### Staff: Mentor

Impulse is to momentum as work is to kinetic energy.

Work-energy theorem: ΔK = W (the change in an object's kinetic energy equals the work done on it)

Impulse-momentum theorem: Δp = I (the change in an object's momentum equals the impulse acting on it)

7. Aug 9, 2013

### Jolb

Well, work can go into potential energy too, e.g. stretching a spring.

8. Aug 17, 2013