How to Calculate Power and Torque for a 15kg Load at 15 RPM?

[SuperPat]

Hi all
I am Belgian and I have difficulty with english formulas.
I'm trying to calculate the power and torque required of a motor to rotate a load.

Here is the problem:
I have a motor (axis up) on which is fixed a cylindrical load of 15Kg. The diameter of this load is 400mm
Calculate the power and torque of the motor to reach a rotation of 15RPM in 2 seconds?

Here is how I calculated:

I calculate the inertia of my load: J = 1/2 m r²
J = 1/2 x 15 x 0.2 x 0.2 = 0.3 Kg.m²

Angular velocity: omega = (pi x RPM) / 30
omega = (3.14 x 15) / 30 = 1.57 rad/s

acceleration: a = omega / t
a = 1.57 / 2 = 0.785 rad/s²

torque: c = J x a
c = 0.3 x 0.785 = 0.24 Nm

Power : P = c x omega
P = 0.24 x 1.57 = 0.38 watts

I don't believe a 0.38w motor with 0.24Nm torque
can rotate a mass of 15Kg at 15 rpm in 2s

I've searched, but I can't find the error.
Thanks for your help.

Patrick

 

[Delta2]

I think It can be done if the motor is frictionless, however real motors aren't and you should add in your result the torque due to the friction which is proportional to the weight of the load.

 

[SuperPat]

of course yes.
I would like first to calculate the motor characteristics and after add 50% power and torque to compensate the frictions and "yield"
But how to calculate ?
Is there an error in my calculation or should I use other formulas?
because 0.38W and 0.24Nm is not right for this heavy load.
Thanks

 

[Delta2]

I can't find any mistake in your calculations. Note that 15RPM is relatively low RPM it is just 1/4 of full rotation in 1 second.

 

[Delta2]

Ah it also matter the orientation of the axis of the motor, is the axis of rotation parallel to the direction of gravitational field? If yes then your calculations are correct (up to friction). If not then you have to calculate the torque of the weight of the load.

 

[SuperPat]

yes, the axis of rotation parallel to the direction of gravitational field.
I'am trying to test with a 10W motor and gearbox 1:6 ...
Thanks
Patrick

 

[Delta2]

BTW I am just a mathematician, I know about torque and power calculations but don't have engineering experience with motors, but something tells me that the negative torque due to friction might be a lot more than 0.24Nm.
I 'll page two more member which I think have more experience on this sector of technology
@berkeman @DaveE

 

[SuperPat]

Thank you very much
Patrick