# Why doesn't a spinning coin flip over?

• hihiip201
In summary, the conversation discusses the concept of conservation of angular momentum and how it relates to a spinning coin or top. The speaker also mentions the use of Euler's equations and the potential to win money with this knowledge.

#### hihiip201

As titled:

I would be satisfied with a qualitative explanation(pure physical), but it would be nice if someone can also provide the mathematical model.

thanks

Are you asking why it doesn't stop spinning and flop over onto one of its sides? Just not sure what you mean by "flip over".

Remember conservation of angular momentum.

ehild

Drakkith said:
Are you asking why it doesn't stop spinning and flop over onto one of its sides? Just not sure what you mean by "flip over".

oh sorry I should be more clear.

I meant why doesn't it fall down on the ground(flat) as a stationary coin would.

It follows from Euler's equations. If there is an Omega_z (z is the axis of the coin), and I_z is larger than I_x and I_y, Omega_x and Omega_y follow SHO, and oscillate without flipping over.
You can win money with that, just don't get caught.

## 1. Why doesn't a spinning coin flip over?

The spinning motion of a coin creates a gyroscopic effect, which helps to stabilize the coin and prevent it from flipping over. This is due to the conservation of angular momentum, where the axis of rotation of the coin remains unchanged as long as there is no external force acting upon it.

## 2. How does the shape of a coin affect its ability to spin without flipping over?

The shape of a coin plays a crucial role in its ability to spin without flipping over. A coin's circular shape and evenly distributed mass allow it to maintain a stable axis of rotation and resist any external forces that may cause it to flip over. In contrast, a non-circular or unevenly weighted object would be more likely to flip over when spun.

## 3. Can a spinning coin ever flip over?

While a spinning coin may appear to defy gravity and remain upright indefinitely, it is not completely immune to external forces. If there is enough friction or air resistance acting on the coin, it may eventually slow down and lose its gyroscopic effect, causing it to flip over. However, under normal conditions, a spinning coin should not flip over.

## 4. Does the speed of the spin affect a coin's stability?

Yes, the speed of the spin can affect a coin's stability. A faster spinning coin will have a stronger gyroscopic effect, making it more resistant to external forces and less likely to flip over. On the other hand, a slower spinning coin may not have enough angular momentum to maintain its stability and may flip over more easily.

## 5. How does gravity play a role in a spinning coin's stability?

Gravity has a minimal effect on a spinning coin's stability. The gyroscopic effect of the spinning motion is strong enough to overcome the force of gravity and keep the coin upright. However, if the coin is spinning at a very slow speed, gravity may eventually cause it to topple over. Overall, the shape and speed of the spin have a greater impact on a coin's stability than gravity does.