# Mechanical equivalent of a coil

• Yoni
In summary, the conversation discusses the similarities between a swing and a RCL circuit in terms of harmonic motion and resonant frequency. The question is raised about whether the mechanical equivalents of a capacitor and coil can be determined based on these analogies. The idea of using a long wire folded into a coil is suggested as a way to increase inductance without increasing mass. However, the expert suggests further research on the topic and directs the person to resources on mechanical analogs of inductance and capacitance.
Yoni
Hi. This is a simple one (I think):

We all know a swing, or simple mass on a spring, moves in harmonic motion, and has a specific resonative frequency. We also know that the RCL circuit (which includes a coil and a capacitor) reacts similarly to an external oscillator, also with a specific frequency which gives the highest output. Both systems are equivalents, right?
So my question is: If we decide the mechanical velocity is equivalent to the current, and the spring equivalent to the capacitor, what is the mechanical equivalent of a coil?

Your question makes some assumptions that might need refined. We might say, for example, that the spring compliance is analogous to capacitance, but I would not say that a spring is equivalent to a capacitor. But, that aside, do you see any relationship between the mass and inductance?

Thanks for your amendment.
Mass, ha? Yes, this is what I thought. This is all under the analogy that velocity transforms to current. Can you therefore somehow conclude that under a different analogy that inductance would be like the elasticity of the spring (I mean with regards to current being analogous to some other variable)? Or is the previous analogy the only valid one?

Also, regarding the original analogy: taking a long conductive wire and folding it in circles, creating a coil, would increase inductance without lengthening the wire... am I right? Is there a way to increase "mechanical inductance" (meaning mass) without actually increasing mass itself?

If my assumptions above are correct, I thought that putting the mass on a table and rolling it with static friction generating angular momentum would accomplish that. Are my thoughts correct?

Yoni said:
Also, regarding the original analogy: taking a long conductive wire and folding it in circles, creating a coil, would increase inductance without lengthening the wire... am I right? Is there a way to increase "mechanical inductance" (meaning mass) without actually increasing mass itself?

If my assumptions above are correct, I thought that putting the mass on a table and rolling it with static friction generating angular momentum would accomplish that. Are my thoughts correct?

I believe you are correct about other analogies, but I am at least twenty years away from looking at this and feel out of my depth without reviewing. So, I'm going to pass and ask you to Google "mechanical analog inductance" or "mechanical analog capacitance" and see what you find.

## What is the mechanical equivalent of a coil?

The mechanical equivalent of a coil is the amount of energy that can be converted from mechanical energy to electromagnetic energy, or vice versa, by a coil.

## How is the mechanical equivalent of a coil calculated?

The mechanical equivalent of a coil can be calculated by the formula E = 1/2LI^2, where E is the energy in joules, L is the inductance in henrys, and I is the current in amperes.

## What factors affect the mechanical equivalent of a coil?

The mechanical equivalent of a coil can be affected by factors such as the number of turns in the coil, the material of the coil, and the strength of the magnetic field.

## What is the significance of the mechanical equivalent of a coil?

The mechanical equivalent of a coil is significant because it helps us understand the relationship between mechanical and electromagnetic energy and how they can be converted from one form to another.

## How is the mechanical equivalent of a coil used in practical applications?

The mechanical equivalent of a coil is used in many practical applications, such as in electric motors, generators, and transformers. It also plays a crucial role in the development of new technologies in the field of electromagnetism.

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