# Does a moving body possess impulse?

1. Nov 27, 2016

### Ali Hamaiz

We generally consider impulse during a colliion but if a body is simply accelerating e.g a car moving with a acceleration will it have impulse?
If a body has an acceleration it may have a change in velocity there will be impulse and if moving with uniform velocity it may not have impulse. I am a little bit confused at the concept of impulse .

Last edited: Nov 27, 2016
2. Nov 27, 2016

### hilbert2

Are you familiar with the Dirac delta function $\delta(x)$, which is also called "impulse function" and is defined by $\int_a^b \delta(x-x_0 ) = 1$ if $a \leq x_0 \leq b$ and $\int_a^b \delta(x-x_0 ) = 0$ if $x_0 < a$ or $x_0 > b$ ?

If the time dependence of the acceleration of a body has the form of Dirac delta: $a = v\delta (t-t')$, there is a sudden change in velocity by $v$ at time $t'$ - just like in a collision between two rigid bodies.

3. Nov 27, 2016

### Cutter Ketch

I'm interested in the way you phrased the question. You say "will it have impulse" as if impulse is a property of the car. That's the wrong way to think of it. Impulse is the action. It is the time integral of the force. It is how much you pushed.

A car being accelerated is accelerating because it is being acted on by a force. Whatever force there is that is causing the acceleration is certainly applying an impulse.

Now we equate that impulse with something that is a property of the car: momentum. Impulse, i.e. Force integrated over time causes a change in momentum i.e. m delta v

That these are equal does not mean they are the same thing. Impulse is the action. Change in momentum is the result of that action. Some force applied over time imparted an impulse and as a result the car gained momentum.

Does that help?

4. Nov 27, 2016

### Cutter Ketch

P.S.: we talk of impulse in a collision but we do not explicitly know the forces involved. Even though we can't write down the force as a function of time and do the integral, there is nothing wrong with talking about the impulse that we know must have happened.

We do know the change in momentum, so we can infer what the impulse, the force integrated over time must have been. In other words they say "impulse" but in a before and after problem you are expected to immediately equate that term with change in momentum.

5. Nov 28, 2016

### Ali Hamaiz

I get it cutter ketch what you said and the conclusion is a moving body does not possess impulse but i am confused will it have impulse during a collision or it will act on it .

Thanks ,

6. Nov 28, 2016

### Dragon27

A body possesses momentum. When the body is being acted upon by a force (e.g. when it accelerates, or is accelerated by some force field, or collides, or whatever) it receives impulse. And by the impulse-momentum theorem the change in the body's momentum equals the impulse that it received during the interaction. Basically, "impulse" is the measure of the action of force on the body, and it translates into the change of momentum of the body. This is the standard terminology in English language.
It may be different in other languages. For instance, in my native language (Russian) the word "импульс" (which has the same latin origin as the word "impulse") means "momentum". The integral of the force (what is called "impulse" in English) in Russian may be called "импульс силы" (literally, "the impulse of the force").

7. Nov 28, 2016

### jbriggs444

What @Dragon27 said. We use the word "momentum" to refer to what a body has (mv). We use the word "impulse" to refer to the amount of of momentum transferred from or to the body, usually by an external force acting over some [brief] period of time. [The word "impulse" implies a transfer over a brief interval. If the interval were longer, we'd likely be talking about forces and accelerations instead]

This is similar to the way we use the word "kinetic energy" to refer to what a body has (1/2 mv2) and "work" to refer to what is added or subtracted by an external force acting over some distance.

8. Nov 28, 2016

### Ali Hamaiz

I understood everything :) , thanks great explanation .

9. Nov 28, 2016

### hilbert2

In Finnish we also sometimes use the word "impulssi" for momentum (I've heard at least one professor use that word), but the usual term is "liikemäärä", which literally translates to "amount of motion".