# Torque & Inertia calculation for a wheel

• George_J
In summary, George is looking for help understanding how to calculate torque needed to rotate a wheel around its own axis. He has a good idea of what he needs to do, but feels that something is missing.
George_J
Hello!

Before I start I want to apologize for my english and not having a scanner (lol).

I'm calculating the torque needed to rotate a wheel* around its own axis from above, ( see the link at the end of post). I have quite an good idea to how I'm supposed to calculate it but I feel that something is missing.

My picture explains it in a very simplistic matter, the wheel is intersecting the ground just to magnify the contact surface and the wheel is also bearing a Force (m*g) and also a torque. The contact surface I explained as a simple rectangle with a center, the longest path is from the center to one of the corners, will be the lever for the torque applied. I hope my picture explains it better than I do. The path can be calculated easily with Pythagoras and the Torque in this case is called ''force couple'' or ''pure moment'' , sadly I don't know the exact name since I'm studying in Swedish. & with that I can calculate the power needed for this rotation.

The purpose is to purchase a motor that can handle the torque/power. I could always just buy a very strong motor but that is not the purpose of my ''research''. But anyhow I really think something is missing here. The inertia perhaps ? I can't put my finger on it and I'm very bad at dynamics..

I have datasheets to all available motors, which includes their torque, inertia and much more, I just need some hints in what is missing in my calculation..
For those wondering I'm building a monorail robot, and it should approximately weigh 30ish kg. The wheels are supposed to be 10-15 cm in diameter.

Now I humbly ask for your help, and I hope I don't come over as an arrogant person asking such a big favor..

* http://www.cleaningshop.com.au/contents/media/l_19097_utility_cart_wheels.jpg
(This picture is not accurate the axis of the wheel will be aligned with the wheels center. As of now anyway.)

Hello George, and

What I am missing here is the required acceleration: the torque not only has to overcome friction, but also has to provide some useful acceleration I suppose. If the wheels are any good and the surface is smooth, I expect the acceleration to need more torque than the friction !

I don't follow the way you (ab?)use the extensiveness of the contact surface. Better to assume its size doesn't come into the calculations.

Someone somewhere will have written a paper on the rolling resistance of a bicycle wheel and how it's affected by tyre pressure.

## What is torque?

Torque is a measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation.

## How is torque related to a wheel?

In the context of a wheel, torque is the force that causes the wheel to rotate around its axis. It is necessary for a wheel to have torque in order for it to turn.

## What is inertia?

Inertia is a measure of an object's resistance to change in its state of motion. In other words, it is the tendency of an object to continue moving in the same direction and at the same speed, or to remain at rest, unless acted upon by an external force.

## How is inertia related to a wheel?

In the context of a wheel, inertia is the property that causes the wheel to resist changes in its state of motion. This is important because it allows the wheel to maintain a constant speed and direction of rotation.

## How do you calculate torque and inertia for a wheel?

To calculate torque for a wheel, you need to know the force applied to the wheel and the distance from the axis of rotation. To calculate inertia for a wheel, you need to know the mass of the wheel and its distance from the axis of rotation. Both of these calculations involve using specific formulas and units, which can vary depending on the specific situation and type of wheel being analyzed.

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