Register to reply

Conservation of linear momentum

by kavan
Tags: conservation laws, rotation
Share this thread:
kavan
#1
Dec10-12, 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
Phys.Org News Partner Physics news on Phys.org
Engineers develop new sensor to detect tiny individual nanoparticles
Tiny particles have big potential in debate over nuclear proliferation
Ray tracing and beyond
jbriggs444
#2
Dec10-12, 01:12 PM
P: 965
Quote Quote by kavan View Post
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
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.

How did the momentum along the y direction come into picture when originaly there was none?
The force from the hinge has a component in the y direction.
kavan
#3
Dec12-12, 10:10 AM
P: 5
Quote Quote by jbriggs444 View Post
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.
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.


Quote Quote by jbriggs444 View Post
The force from the hinge has a component in the y direction.
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.

jbriggs444
#4
Dec13-12, 06:42 AM
P: 965
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.
kavan
#5
Dec23-12, 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.
Attached Thumbnails
Screenshot_2012-12-23-19-07-39.png  
Doc Al
#6
Dec23-12, 08:47 AM
Mentor
Doc Al's Avatar
P: 41,487
Quote Quote by kavan View Post
How did linear momentum of the ball converted into angular momentum of the rotating road.
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.)
Darwin123
#7
Dec23-12, 07:04 PM
P: 741
Quote Quote by jbriggs444 View Post
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.
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.
D'Alembert
#8
Dec24-12, 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 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.


Register to reply

Related Discussions
Conservation of angular momentum vs. linear momentum General Physics 7
Hockey puck momentum, conservation of linear momentum Introductory Physics Homework 1
Linear momentum conservation vs mecanical energy conservation General Physics 1
Linear momentum conservation vs angular momentum conservation Classical Physics 2
Conservation of momentum in combination of angular and linear momentum General Physics 16