# Inertia and moment of inertia question

Hi everybody.
Ok I have some questions that need answer:
1) I read on the web what is inertia but never found how to calculate it.
2) If I have a motor with ball screw attach to the shaft. A metal sheet that weight 100 pound is attach to the ball scew nut. How can I determine how much torque the motor should deliver so I can have a angular speed of x rad/sec?
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Dear R�ginald Jean Louis:

inertia = mass.

that
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
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N:dlzc D:aol T:com (dlzc) wrote:

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 http://en.wikipedia.org/wiki/Inertia 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 additional knowledge of the motor in question (structural resistance?), that is the only thing that can be calculated, which isn't much.
So, as the parent post said:

Take care and hope this helps Rui Maciel
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Dear rui maciel:
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object's
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
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On Mon, 12 Apr 2004 01:17:29 -0400, "R�ginald Jean Louis"

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
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Dear R�ginald Jean Louis:
wrote:

it.
that
And power is torque * angular velocity.
David A. Smith
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