## Electric motors momentum and load

hi,

this is not a question from Hw its pure interest.
1.lets say i have an electric motor with a shaft radius r lengh L, and at its end there is a metal disk with radius R and thickness b. if the motor supplies torque τ what would be the momentum on the disk?
i was thinking that i the motor gives momentum τ on a shaft then its gives a force of F1=τ/r and so the momentum of the disk is M1=τ/r * (R-r) ? please correct me

2. using the same data, when a motor is given and it is suppose to supply 3000 RPM under no load, how can i calculate the reduce in RPM if it is loaded by a full metal disk distanced L from the motor on its shaft?

thanks a lot for your help
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 There are a lot of words flying around here rather loosely, so let us be careful. First of all, you have not specified what kind of electric motor you have, and that may, or may not become an important issue down the road. It is usually a good idea to spell it out up front. Your first question was, what is the momentum of the disk? Momentum (with no qualifier) is usually understood to mean linear momentum, and there is no linear momentum because there is no linear velocity of the center of mass of the disk (I am assuming that the whole assembly is anchored on a floor or a bench). If your question was intended to be, what is the angular momentum of the disk? then the answer is different. It depends on the motor speed, ω, expressed in rad/s. The angular momentum, H = J ω where J = ∫M r2 dm = mass moment of inertia of the disk The distance out along the shaft that the weight load of the disk is placed has no significant impact on the speed of the motor. While it is not a good idea to hang a very heavy pulley a long way out from the motor bearing, that loads the bearing and will affect bearing wear and possibly alignment. It will not affect motor speed. The sort of load that affects motor speed is that which requires the motor to do work such as powering a fan, a saw, or other machine.
 hi, thank you for your comment! i am talking abut a 24v dc motor, running around 4000 RPM. I see that the specifications says RPM without load and RPM with a load, which is like 500 RPM lower than without a load so im wondering why? I was talking about angular momentum, sorry about that.. so if the motor shaft is turning in 4000RPM the disk's angular momentum depends on its momentum of inertia i understand correctly? Thank you!

## Electric motors momentum and load

The angular momentum of the disk depends upon the angular velocity (shaft speed) and the mass moment of inertia for the disk. Please note that momentum and moment of inertia involve two different words that only sound alike but one ends with "um" whereas the other does not.

Your motor was probably designed for a particular application for which the specs you found apply. The 500 rpm drop is required to develop the power required to support the rated load, whatever it originally was.