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Conservation of linear momentum 
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#1
Dec1012, 11:41 AM

P: 5

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



#2
Dec1012, 01:12 PM

P: 928




#3
Dec1212, 10:10 AM

P: 5




#4
Dec1312, 06:42 AM

P: 928

Conservation of linear momentum
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
Dec2312, 07:45 AM

P: 5

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.



#6
Dec2312, 08:47 AM

Mentor
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#7
Dec2312, 07:04 PM

P: 741

Linear momentum is conserved in the door, wall, building, earth system. Now excuse me. I hear my Noether calling. 


#8
Dec2412, 05:04 AM

P: 8

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 doorhinge. 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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