How the moment of inertia of gearwheel and its shaft can be determined experimentally?

Question

or any similar answer near to the question

Answer 1

If you can accelerate the wheel and shaft with a known torque, you can calculate the moment of inertia, but measuring or controlling the applied torque is not necessarily easy to do. You might consider applying torque by suspending a known weight by a flexible cord with a few turns of the cord wrapped around the shaft or around a drum mounted on the shaft. Attach or belt a small DC tachometer generator to the shaft. Gently release the weight and record shaft speed vs time with a chart recorder. You can then calculate the moment of inertia from the torque and the rate of acceleration.

If you can accurately measure the power required to spin the assembly at an initial speed, you can cut power to the motor used to spin the assembly and record the coast-down speed vs time. Calculate the initial stopping torque from the known power required to overcome friction at the initial speed. You will need to know the inertia of the motor.

Another method is to suspend the gearwheel and shaft assembly by attaching a piano wire to the center of the end of the shaft that is farthest from the gear wheel. Attach the wire in such a manner that it twists when the gear and shaft assembly is turned. Turn the gear and release it, allowing the springiness of the wire to rotate the gear back towards the original position. The rotation of the gear will overshoot the original position and exhibit rotary oscillation. The moment of inertia can be calculated from the measured period of oscillation. You may need a wheel and shaft assembly with a known moment of inertia to calibrate the setup. I have seen this method used, but I don't know the details of the necessary calculations.

Edit 1:

My answer and the other answer are both "proper answers." What more do you want? Here is some additional infromation on the two methods I described:

Method of applying a known torque:

http://needmore.physics.indiana.edu/~ric...

Torsion pendulum method:

Moment of Inertia Measuring Instrument U.S. Patent No. 3693413

To view the patent, go to Google advanced patent search and enter the number.

http://www.google.com/advanced_patent_se...

http://www.space-electronics.com/Literat...

Answer 2

Spin the assembly up with a motor and calculate the time to reach a steady state RPM.  Then, knowing the torque applied from the motor and the change in angular speed, the inertia of the assembly can be determined.

Torque = Inertia * angular acceleration