An ID-card sliding on a low friction table

[EngineeringFuture]

TL;DR Summary

This is a question about why a rigid body slides horizontally when the only force applied to it is the vertically-acting gravity. The topics explored are mechanics, the relationship between linear and angular momentum, the nature of rigid bodies and their centers of mass, and other related topics.

I hold my identification card on a low-friction surface by one of its edges. I slightly lean it, and it starts to fall. Before it falls over, I place my finger against the card, and this prevents it from falling all the way over. Then, I withdraw my finger without pushing or pulling the card and let the ID-card fall all the way over and flat. Then, once the card has fallen completely flat on the table, something interesting happens: the card starts to move along the table in the direction of the horizontal component of the circular motion it was making. In fact, even if the table is slightly uphill, the card will move along the direction of the horizontal component of the circular motion it was making.

When I look at this from a perspective of Conservation of Momentum, this makes sense. The card still has momentum from gravity making it fall, and this momentum is why it is moving. There doesn't need to be any acceleration to cause the motion of the card because nearly every particle(I don't know if it is pivoting about completely stationary particles on the card or not) comprising the card is already moving in the horizontal direction and will keep moving in the horizontal direction until a force stops it. The center of mass of the card is moving horizontally already and will keep moving horizontally until friction stops it.

However, from the perspective of a rigid body, it doesn't make sense that the card as a whole accelerates simply because it stops rotating. Gravity acts vertically on the card. There are no other external forces applied to the card. Angular momentum can't be converted to linear momentum. How should I view the linear acceleration of the card once it stops falling?

 

[Lnewqban]

Welcome, @EngineeringFuture !
It seems to me that the air caught in between the card and the table is forced to move horizontally in the direction opposite to the following movement of the sliding card.
Therefore, that should be the external force initially accelerating the card horizontally.

 

[Baluncore]

Angular momentum can't be converted to linear momentum.

That is not true when an object, rotating about a horizontal axis, has frictional traction on a solid horizontal surface.
Think of the bounce of a spinning ball.

 

[A.T.]

However, from the perspective of a rigid body, it doesn't make sense that the card as a whole accelerates simply because it stops rotating.

As @Lnewqban noted, the card moves on an air cushion, which can get complicated. Even the air motion created while the card falls can have an effect.

Is the pivoting card edge free to move along the table, or are you blocking it one way with a finger?

 

[A.T.]

Angular momentum can't be converted to linear momentum.

That is not true when an object, rotating about a horizontal axis, has frictional traction on a solid horizontal surface.
Think of the bounce of a spinning ball.

That's not converting angular to linear momentum. That's exchanging angular and linear momentum with the surface.

 

[EngineeringFuture]

Welcome, @EngineeringFuture !
It seems to me that the air caught in between the card and the table is forced to move horizontally in the direction opposite to the following movement of the sliding card.
Therefore, that should be the external force initially accelerating the card horizontally.

Are you implying that the card wouldn't slide in a vacuum?

 

[Lnewqban]

Are you implying that the card wouldn't slide in a vacuum?

I would not.

 

[EngineeringFuture]

I would not.

Then it's simple enough to test if we can find a bored astronaut. I think it would slide in a vacuum.

 

[EngineeringFuture]

As @Lnewqban noted, the card moves on an air cushion, which can get complicated. Even the air motion created while the card falls can have an effect.

Is the pivoting card edge free to move along the table, or are you blocking it one way with a finger?

The pivoting edge is free to move along the table

 

[Lnewqban]

... I think it would slide in a vacuum.

Why?

 

[A.T.]

Then it's simple enough to test if we can find a bored astronaut.

Why an astronaut? You need a vacuum not zero g. A simple vacuum bell, like every school has, doesn't create a good vacuum, but might be enough to show a difference in the behavior.

I think it would slide in a vacuum.

In a vacuum it will depend more on the amount of friction. With very low friction the pivoting edge will slide even while the card still rotates.

 

[Baluncore]

How are you going to put your finger in the bell jar?

 

[A.T.]

How are you going to put your finger in the bell jar?

You need a remote controlled release mechanism.

 

[Vanadium 50]

How are you going to put your finger in the bell jar?

How long can you hold your breath?

You guys seem to want to make it more complicated than it needs to be. Astronauts? Start with a thin layer of dust or flour and see what it does, Takes a minute, and if that doesn't add clarity, then you call NASA.

 

[tech99]

The card falling is rather like a slender radio mast falling. In this case the foot kicks forward. It is not on an air cushion or it would move much further.