Angular Dynamics: 150Nm, 75rpm, 9 & 23 Revs. Determine Inertia & Friction

[MMCS]

A constant torque of 150Nm applied to a turbine rotor is sufficient to overcome the constant bearing friction and to give it a speed of 75rpm from rest after 9 revolutions. When the torque is removed, the rotor turns for a further 23 revolutions before stopping. Determine the moment of inertia of the rotor and the bearing friction

Equations

ω2²-ω1² / 2 * (9*2∏) = ang accel = 1963.5

On accelerating
150Nm - Inertia Torque - Bearing friction = 0

On decelerating
Inertia Torque = bearing friction

 

[haruspex]

ω2²-ω1² / 2 * (9*2∏) = ang accel

Fuller use of parentheses would help: (ω2²-ω1²) / (2 * 9*2∏)

= 1963.5

That's the acceleration in the first phase, right? What about the slowing down phase?

On accelerating
150Nm - Inertia Torque - Bearing friction = 0

OK, so flesh that out. Put in symbols for the two quantities to be determined and write out the torque equations using them.

 

[MMCS]

Ok so, decelleration

471.2²/(2*(23*2∏)) = -768.3

So two formulas

accelerating
150 - bearing friction - (1963.13 * Moment of inertia) = 0

decelerating
bearing friction - (768.3 * Moment of inertia) = 0

Combined

150 - (768.3*moment in inertia)-(1963.13*moment of inertia)=0
150-2731.4*moment of inertia = 0
moment of inertia = 0.0549
This is incorrect as i have the answer to be 198kgm²

however, if i use my value of 0.0549 to find bearing friction i get

bearing friction - 768.3 * moment of inertia = 0
bearing friction - 768.3 * 0.0549 = 0
bearing friction = 42.2, which i have to be the correct answer
it seems odd that solving them simultaneously would give me one correct answer and one incorrect, have i made a mistake?

 

[haruspex]

I didn't check the details of your arithmetic before. You seem to have used 75rpm as though it's revs per second. Looks like that error was self-cancelling in calculating the bearing friction but not in calculating the MI.