How Does Moment of Inertia Affect Motor Size Requirements?

[schip666!]

All this recent talk of torque and horsepower leads me to show my ignorance and ask for enlightenment (I tried to post this yesterday but it seems I failed, sorry if its a dup):

Say I want to spin a nicely balanced wheel. I can calculate the moment of inertia but can't quite grasp how that helps me figure out how big a motor I need. My problem is dimensional analysis:

moment of inertia == kg·m²
energy (joules) == kg·m²·s² (or Newton-Meter)
torque(joules/radian) == kg·m²·s² (where wiki sez: "A torque of 1 N·m applied through a full revolution will require an energy of exactly 2π joules.")

So... ignoring friction, the torque of the motor only influences the acceleration of the wheel? Then it is just friction that prevents me from driving my truck tire with a cell-phone vibrator motor? Or is there another conversion I must yet undergo?

 

[rcgldr]

A torque of 1 N·m applied through a full revolution will require an energy of exactly 2π joules."

That explains the torque required, but there's no stated period of time for that amount of energy to be added. Power is the rate of energy change per unit time. So if the 2n joules could be applied in one second at constant power, then the power would be 2n watts.

 

[diazona]

So... ignoring friction, the torque of the motor only influences the acceleration of the wheel? Then it is just friction that prevents me from driving my truck tire with a cell-phone vibrator motor?

Yeah, pretty much. If you disregard friction and other resistance forces, you could spin anything with even a tiny motor. But it would take ages to spin up to any reasonable velocity, and there's a decent chance the motor would blow out before long. (Working against a large load puts a lot of stress on the internal parts of a small motor)

Like rcgldr said, in practice you usually have to consider timing, e.g. how quickly you want to achieve a certain angular velocity, and that tells you what power your motor needs to provide.

 

[schip666!]

Excellent! Thank you both. But further clarification needed, as usual:

In order for me to be able to decide that a certain motor will spin my erstwhile lumpen truck wheel I need to measure the friction that needs to be overcome. To do so would be pretty much equivalent to measuring a lever-arm from the outside circumference, say by hooking a spring scale to the wheel and pulling until something gives? Then I can work out how fast I want to get things going by adding torque above and beyond with the 2pi joules routine?

I should have taken physics and mechanical engineering back when I had functioning brain cells...instead I wasted them on learning the C language. Thanks again.

 

[PJC01]

First of all, don't worry about showing your ignorance. Asking questions and seeking enlightenment is the foundation of scientific inquiry.

To answer your question, the moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is essentially a measure of how much mass is concentrated at the center of rotation. The larger the moment of inertia, the more torque is required to accelerate the object. This is why a larger motor is needed to spin a wheel with a larger moment of inertia.

In terms of dimensional analysis, you are correct that both moment of inertia and torque have the same units of kg·m²·s². However, it is important to note that torque is a measure of force applied at a distance, while moment of inertia is a measure of mass and its distribution. In order to calculate the torque needed to spin a wheel, you would need to know the moment of inertia and the desired angular acceleration.

As for your question about driving a truck tire with a cell-phone vibrator motor, it is not just friction that prevents this. The cell-phone vibrator motor simply does not have enough torque to overcome the moment of inertia of the truck tire. This is because the tire has a much larger moment of inertia due to its larger mass and distribution of that mass. Additionally, the motor may not have enough power to sustain the rotation of the tire.

In summary, both moment of inertia and torque play important roles in rotational motion, and understanding their relationship is crucial in determining the size and power of a motor needed to spin a wheel.