Tossing Coins: Can We Predict the Outcome?

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In summary: Yes, that should give pure rotation around a horizontal axis, allowing the problem to be reduced to a two dimensional treatment.
  • #1
quawa99
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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?
 
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  • #2
You about to enter a big quarter flipping contest?
 
  • #3
SteamKing said:
You about to enter a big quarter flipping contest?

Its just out of curiosity nothing more.
 
  • #4
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.
 
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  • #5
quawa99 said:
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.
 
  • #6
jbriggs444 said:
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.
 
  • #7
quawa99 said:
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.
 
  • #8
jbriggs444 said:
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
 
  • #9
quawa99 said:
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.
 
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1. Can we predict the outcome of tossing coins?

Yes, we can predict the outcome of tossing coins by using probability and understanding the factors that influence the outcome.

2. How does probability play a role in predicting the outcome of tossing coins?

Probability is the likelihood of a specific outcome occurring. In tossing coins, there are only two possible outcomes (heads or tails), so the probability of getting either outcome is 50%. By understanding this concept, we can make predictions about the outcome of tossing coins.

3. What factors influence the outcome of tossing coins?

The main factor that influences the outcome of tossing coins is the initial state of the coin. If the coin is perfectly balanced and flipped with consistent force and height, then the outcome is more likely to be random. However, external factors such as wind or the surface the coin lands on can also play a role.

4. Can we make accurate predictions every time when tossing coins?

No, even with a thorough understanding of probability and the factors that influence the outcome, there is still an element of chance involved in tossing coins. While we can make educated guesses, the outcome will ultimately be random.

5. How can the outcome of tossing coins be useful in real-life scenarios?

The outcome of tossing coins can be useful in decision-making processes. For example, if a decision needs to be made between two options, a coin toss can help to eliminate bias and make a fair choice. Additionally, it can be used in statistical analyses and simulations to model real-life scenarios.

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