# Direction of Impulse: Final Momentum vs Initial Momentum

• tubworld
In summary, if an object moves at a certain speed and someone hits it back at another speed (towards the +ve x direction), how do we tell the direction of the impulse?

#### tubworld

How do we know the direction of the impulse(which is the change in momentum)? I thought let's say if an object travels at -ve x direction at a certain speed and someone hits it back at another speed (towards the +ve x direction), how do we tell the direction of the impulse? Isnt the direction always in the +ve direction in this case if we have defined our +ve and -ve directions as stated?So its always true that the impulse is in the final direction?

Cos final momentum - initial momentum = change in momentum =impulse. So it will always be in the direction of the final velocity right?

Yup, you are correct.

thanx alot!

That is only true if the impulse force succeeds in changing the direction of the motion of the object (if it acts against it to start with) - think of a bug hitting the windscreen of a truck, it will slow the truck down by a bit only momentarily without changing the direction of it's motion.

Nope, you are completely wrong!

Your statement "the impulse is in the final direction?" is, in general, false!

IF you are dealing with motion on a straight line and IF the impulse is enough to reverse the direction of motion then, yes, the impulse happens to be in the same direction as the final motion. However, in one dimension there are only two possible directions so there aren't that many possiblities!
Suppose you have an object moving along a line and you give it "hit" that slows it down to 1/2 its speed. In that case, the "final speed" is still in the same direction and opposite to the impulse. There are only two possible directions (same or opposite final speed) and impulse can take either!

If you work in two or three directions, it's much more complicated. Imagine a pool ball bouncing off a cushion. The impulse is perpendicular to the cushion but neither the initial nor final speeds are in that direction.

The best thing to say is "impulse is change in momentum: subtract the two momenta." Since momentum is mass*velocity and mass has no direction, as far as the direction is concerned, subtract the initial velocity from the final velocity.

In the example you gave: inital velocity -ve, final velocity +ve, ve-(-ve)= +2ve. The impulse is in the + direction, the same as the final velocity. In the example I gave, initial velocity is ve, final velocity is (1/2)ve, impulse is (1/2)ve- ve= (-1/2)ve, opposite to the final velocity.

For the pool table example, take initial velocity vector to be (vx, -vy), final velocity (vx,+vy). The impulse is the difference of those vectors: (vx, vy)- (vx,-vy)= (vx-vx, vy+vy)= (0, vy), not in the direction of either initial or final velocity.

Oh! Thanx for the explanation! I really UNDERSTAND now from your examples given! Appreciated! :)

## 1. What is the definition of momentum?

Momentum is a measure of an object's motion, calculated by multiplying its mass and velocity.

## 2. What is the law of conservation of momentum?

The law of conservation of momentum states that in a closed system, the total momentum before an event is equal to the total momentum after the event. This means that momentum is conserved and cannot be created or destroyed.

## 3. How does the direction of impulse affect the final momentum?

The direction of impulse has a direct effect on the final momentum. If the impulse is in the same direction as the initial momentum, the final momentum will be greater. If the impulse is in the opposite direction, the final momentum will be less.

## 4. How are final and initial momentum related?

Final momentum and initial momentum are related by the law of conservation of momentum. The initial momentum of a system will always be equal to the final momentum of the system, as long as there are no external forces acting on the system.

## 5. What factors affect the direction of impulse?

The direction of impulse is affected by the magnitude and direction of the force applied to an object, as well as the duration of the force. The angle at which the force is applied also plays a role in determining the direction of impulse.