I would like to build a Moment of Inertia machine:
A machine that rotates an object (with a DC motor) and can also record the angular velocity and use this to find the moment of inertia.

Initially I used an energy approach, relating P in (VI) and P out (KE/time)x efficiency and rearrange to get the moment of inertia in terms of rotation time, voltage and current. The issue is that efficiency is not constant. I may need to substitute an expression for the efficiency, or have a completely new approach involving torque. Also in the first way the torque isn’t in the equation which is unsettling for the fixed torque motor.

I have not started building the project, so although I would really like to build it, if it’s too complicated for a yr12 project I may choose something else.

How can I calculate the efficiency of a DC motor, depending on perhaps the speed, torque, voltage etc?
Any advice is greatly appreciated.

  • \$\begingroup\$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. You haven't actually asked aquestion. Show us what you have already done. Please nderstand that this is a question and answer site, not a forum. \$\endgroup\$
    – RussellH
    Feb 2, 2023 at 4:16
  • \$\begingroup\$ Sorry, I would like to know how you can calculate the efficiency of a DC motor, depending on perhaps the speed, torque, voltage etc. \$\endgroup\$
    – Karim
    Feb 2, 2023 at 4:23
  • 1
    \$\begingroup\$ Karim, Edit your question and add the question in your comment to it. \$\endgroup\$
    – RussellH
    Feb 2, 2023 at 4:26
  • 1
    \$\begingroup\$ Why not just drive your DC motor with a constant current, which -- for a high-enough quality motor -- should give you a constant torque out? \$\endgroup\$
    – TimWescott
    Feb 2, 2023 at 4:44
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    \$\begingroup\$ just measure P while spinning up an unloaded motor. Then you can subtract that amount from the amount taken with an object attached. You can also weigh the motor, estimate it's materials, and calculate an average specific heat for it, which would let you ballpark efficiency by measuring resulting temperatures. \$\endgroup\$
    – dandavis
    Feb 2, 2023 at 6:00

2 Answers 2


Method for calculating DC-Motor efficiency:

First of all we need to understand that a DC-Motors efficency is depending on the load torque applied to the motor. In below example of a motor performance curve you can see that each load-torque will have its very own efficiency.

example performance curve of 12V brushed dc-motor

To calculate the efficiency for each load point you can use following formula:

enter image description here

(it is important to use SI-Units as indicated in [ ] brackets, otherwise you have to adjust factor pi/30 accordingly)

  • \$\begingroup\$ That efficiency curve causes so many problems. That is a curve for a motor that does not utilize speed or torque control, but instead uses a fixed input voltage. If the motor is being controlled electronically, then that graph is not very helpful, because the voltage will be changed continuously on the fly during operation. \$\endgroup\$
    – user57037
    Feb 8, 2023 at 18:56

The output power of the motor is speed * torque where speed is in rad/sec and torque is in Nm.

The input power of the DC motor is V * I where 'V' is input voltage and 'I' is input current.

The main power loss in the motor is due to the resistance in the current path. That power loss is P = I^2 * R where P is the power loss, I is the input current and R is the resistance in the conductive path.

The output torque of the motor is Kt * I where Kt is the torque constant of the motor, and I is the input current.

So you can estimate the output power of the motor if you know Kt, I, and speed. And you can estimate the power loss in the motor if you know I and R. Be advised that R is not constant with temperature. As the motor winding heats up, R will increase by about 4 percent every 10 degrees C.


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