# Conservation of linear momentum and rotational motion

1. Dec 10, 2012

### kavan

When you open a door you apply force in any particular direction and as a result you get rotational motion of the door. My question is how linear momentum is conserved in this case as linear momentum seems to have generated rotational motion? To clarify my question further, if we fix a rod from one end such that it can freely rotate about that end and then hit another end of the rod with a speeding ball with some linear momentum along any direction(say x).. the momentum will be transferred to the rod which will start to rotate...now the rotating rod will have linear momentum with components in both directions(say x and y). How did the momentum along the y direction come into picture when originaly there was none?8

Last edited: Dec 10, 2012
2. Dec 10, 2012

### jbriggs444

Linear momentum is conserved in a closed system as long as there are no external forces on the system. In the case of a hinged door or rod there is an external force from the hinge.

The force from the hinge has a component in the y direction.

3. Dec 12, 2012

### kavan

We can include the external force within the system by suitably expanding it. Imagine collision case, a ball hitting the door makes one system on which there are no external force.

Didnt get that. If originally there were no momentum in y direction from where the momentum in y direction comes once the door starts rotating.

4. Dec 13, 2012

### jbriggs444

The hinge connects the door to... what exactly? If you are expand the system to include the wall the hinge is screwed into then you have to include the motion of the wall in your calculations.

5. Dec 23, 2012

### kavan

Plz see the screenshot attached. How did linear momentum of the ball converted into angular momentum of the rotating road. I hope I've clarified my question.

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6. Dec 23, 2012

### Staff: Mentor

Even before the collision, the ball has angular momentum about the hinge. Angular momentum is conserved during the collision. (Linear momentum is not. As already pointed out, you cannot ignore the force of the hinge on the door.)

7. Dec 23, 2012

### Darwin123

And the wall is attached to the building. And the building is attached to the earth.

Linear momentum is conserved in the door, wall, building, earth system.

Now excuse me. I hear my Noether calling.

8. Dec 24, 2012

### D'Alembert

As for converting linear to angular momentum you have to know that everything that has linear momentum has angular momentum too and the other way round.

When it comes to the collision the energy of the ball is given to the door as momentum. The only motion that the door can perform is a rotation and therefore all of the energy goes in it. During the rotation the door's linear momentum is conserved within the system door-hinge. The angular momentum is conserved for itself in the rotation.

When you calculate it you will see that the angular momentum of the ball in relation to a random point is the same as the angular momentum of the door related to the same point.

The linear momentum of the rotating door cannot be described so well using Newtonian mechanics. Instead you need the term of constraints since the hinge is a constraint for the door.

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