# Calculating size of electric motor needed

#### Kalus

I'm a little confused as how to calculate the power of motor you would need in a certain scenario.

Imagine you have an electric motor sitting upright (so spindle pointing towards the sky) with a metal disc attached to the spindle. Now imagine that you have some metal rod that is being pressed down on the disc exerting a frictional force at a distance from the center of r/2 (where r is radius).

I know the equation that power= torque*angular velocity... but im unsure what to include as torque.

Obviously the frictional force(F_f) exerts a "stopping" torque of F_f * r/2 but would you also need to calculate the torque to get the disc spinning on its own, E.g Torque= I*angular acceleration?

If so, how do you calculate angular acceleration?

Also, if you came up with a resistive torque of X, then would the torque of the motor need to be X+1 or whatever to get the thing to actually spin up?

Many thanks, Kalus

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#### Gordianus

Few electric motors provide a constant torque, but let's say you have one of those and its useful torque is T. The difference T-F_f*r/2 is the net torque which is equal to the product I*gama, where I is the total moment of inertia and gama the angular acceleration.
Therefore, as long as you don't mind about acceleration time, you need a motor whose torque is barely higher than the resisting torque.

#### Kalus

Ok, im still a little confused about the torque needed to make the disc start though.

If consider having no normal force on the disc for a moment, what would the torque required be to start the disc in motion?
Would it be Torque= Moment of Inertia* Angular Acceleration?

Does that mean that then when you include normal force, that to get it moving, at the start it would be Torque to start motion > Torque to overcome inertia + Torque to overcome normal friction force?

Many Thanks, Andy

#### wywong

You don't need to consider inertia unless you need to reach a certain speed within a certain time. As long as the torque exceeds the friction, the motor will start to turn and build up speed gradually.

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