Nov 19, 2008
Question on page 8 example
In reviewing my notes, I was wondering why it was necessary to sum the moments instead of simply summing the forces in the x direction as we had done in the previous example. With the sum of the forces in x, I get Fx = -3kx =m x(double dot) and I'm wondering why this is not a valid EOM.
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2 comments:
I think that it's because we are assuming no slip at C and we must sum the moments about that point. otherwise, we would have more variables than I would know how to deal with.
Additionally, my intuition tells me that for a valid Equation of Motion, the mass would play a part in that. (heavier object, less motion, etc.) but i could be wrong - it happens more frequently than i would like.
--to kmjones--
It is perfectly fine to sum forces in the x-direction:
Fx = -3kx + f = m*x_dot_dot
(Note that you left off the friction force in your summation.) The equation involves the friction force f. To eliminate that force, you can then do a summation of moments about O:
MO = f*R = IO*alpha
Solve this equation for f and substitute back into the first. You then need to do your kinematics to get the single differential equation in terms of x.
As Andy points out, this approach requires you to deal with an additional variable (the friction force). By summing moments about the contact point C, you avoid having to deal with the friction force f in arriving at the EOM. The EOM is the same regardless of which of the two approaches that you take.
Let us know if this is not clear.
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