[xheavenlyx]

Wow, this is an interesting problem.

I can just think of one possible way if its difficult to measure density / volume. However i suspect the shaft SHOULD have its data sheet somewhere in the office (which gives all the important details like weight).

Anyway, here is a try from my side, (correct anything if its wrong):

I will be assuming the following data:
1. your "Shaft" is a cylinder.
2. Your shaft is connected to a motor which can rotate it.
3. You have all the motor specifications like RPM, Power (kW) etc.

We will use this formula to get the weight:

For cylinder rotating along length..I (Moment of Inertia) is:
So Mass(kg) = ( I_z * 2 ) / r²

How to find I (Moment of Inertia) ?:

torque = I_z x Alpha (Angular Acceleration in rad/s)
I_z= Torque in N.m / Angular Acceleration in rad/s²

How to find torque and Angular Acceleration?:

Torque-N.m = (60,000 * Power in kWh) / ( 2 * pi * RPM motor rotation speed )

Get power from Motor datasheet, or it will be printed on the motor in kW! Run the motor at constant speed to get RPM from a hand-held tachometer (Use same speed for other calculations).

For Angular Acceleration:

use this formula: final A.velocity in rad/s = Initial A.velocity in rad/s + Angular Acceleration * time in seconds.

to use this, start the machine (Initial A.vel = 0) and calculate the time it takes to reach a constant final A.vel in RMP. Convert this final Angular Velocity to RPM by dividing the rad/s with 2pi. Then substitute in above formula to get Angular Acceleration in rad/s².



Do the above and (hopefully) you will get the shaft mass.