Inertia and moment of inertia question

Dear Réginald Jean Louis:

inertia = mass.

You need to know how much torque the ball screw requires to deliver a force along the screw's axis (assuming the screw is vertical).

Basically, we need a little more information...

David A. Smith

Ignoring moment of inertia, let us suppose that you wish to lift a mass of 46 kg at a known rate (V specify it in meters/sec).

If you specified a motor capable of providing twice this power, you would have an estimate of the power required from the motor, which is

46 X 9.81 x V (m/s) X 2 = motor power in watts / 746 = nominal motor horse power

Brian W

Dear Réginald Jean Louis:

And power is torque * angular velocity.

David A. Smith

Not quite.

In basic terms, inertia is an indication of a certain body's resistance to rotate around a certain axis. Therefore it not only depends on the object's mass but also it's geometry (mass distribution).

How do we calculate it? Being "I" the inertia of a body, "In" the the n-th body's element's inertia and r the distance from the rotation axis to that body's element:

I = sum( In*(r^2) )

so, if a certain body is formed by 3 elements (inertia from body 1, 2 and 3 = I1, I2, I3) which are distanced from the axis of rotation (r1, r2, r3), then that body's inertia should be:

I = I1*r1*r1 + I2*r2*r2 + I3*r3*r3 For mor information you can look at

or any book on newtonian mechanics.

Well, being "w" the angular velocity, "a" the angular acceleration and "t" the time, then we have:

w = a*t

And being "T" the applied torque, "I" the body's inertia and "a" the angular acceleration, we have:

T = I*a

Solving the torque equation in order of "a" and replacing it in the angular speed equation, we end up with:

w = (T/I)*t

...which says that if there is any torque applied on that body (the body's inertia is always nonzero), it is only a matter of time before that system reaches the wanted angular velocity.

Of course the problem isn't as simple as that. But without any additi> Basically, we need a little more information...

Take care and hope this helps Rui Maciel

Correct, however the OP did distinguish between inertia and moment of inertia. You may have been correct that he/she did not know the difference. And it is unusual for the sleeve of a ball screw setup to be rotating... so moment of inertia wouldn't really apply.

David A. Smith