Tossing Coins: Can We Predict the Outcome?

[quawa99]

Is it possible to determine which side of a coin is going to turn up when you toss one?If possible what all information would be required to do so?

 

[SteamKing]

You about to enter a big quarter flipping contest?

 

[quawa99]

You about to enter a big quarter flipping contest?

Its just out of curiosity nothing more.

 

[quawa99]

Assuming that we know the impulse imparted to the coin,the point of application of impulse ,the dimensions and mass of the disc:
1)The angular velocity of the coin can be calculated.
2)The time of flight can be calculated.

Based on the above two values we can find out the angle the coin rotates which can help us know which face of the coin is facing up.
I have neglected air resistance and considered the angular velocity to be constant.Tell me if this is correct or not.

 

[jbriggs444]

Assuming that we know the impulse imparted to the coin,the point of application of impulse ,the dimensions and mass of the disc:
1)The angular velocity of the coin can be calculated.
2)The time of flight can be calculated.

You also need to know

1) The height above the floor and the orientation of the coin when the impulse is applied.
2) Any existing rotation and velocity of the coin when the impulse is applied.
3) Details on the coin and floor surface that control how the coin bounces when it hits the floor at various possible orientations with various impact speeds and various rotation rates.

In addition, it is not clear that imparting the impulse will result in a pure rotation about a single horizontal axis.

 

[quawa99]

In addition, it is not clear that imparting the impulse will result in a pure rotation about a single horizontal axis.

It doesn't need to rotate purely about a horizontal axis does it?
Anyway the impulse will give the center of mass a linear vertical velocity plus some angular moment about a horizontal axis passing through it.So the coin undergoes rotational as well as translatory motion.The angular momentum about the axis passing through the center of mass should remain constant as gravity is the only force which cannot cause any torque.Hence the angular velocity will remain constant.

 

[jbriggs444]

It doesn't need to rotate purely about a horizontal axis does it?
Anyway the impulse will give the center of mass a linear vertical velocity plus some angular moment about a horizontal axis passing through it.So the coin undergoes rotational as well as translatory motion.The angular momentum about the axis passing through the center of mass should remain constant as gravity is the only force which cannot cause any torque.Hence the angular velocity will remain constant.

The impulse will not neccessarily give an angular moment about a horizontal axis. It may include a component about a vertical axis.

Angular velocity in three dimensions is more complex than in two.

 

[quawa99]

The impulse will not neccessarily give an angular moment about a horizontal axis. It may include a component about a vertical axis.

What if the disc is kept horizontal and a perfectly vertical impulse is given

 

[jbriggs444]

What if the disc is kept horizontal and a perfectly vertical impulse is given

Yes, that should give pure rotation around a horizontal axis, allowing the problem to be reduced to a two dimensional treatment.