Suppose there is a rod balancing on a table. The rod tips past vertical and begins to fall. Derive an equation for the force on the bottom of the rod as a function of the angle between the rod and the table. Assume that the rod does not slip, even if this implies a very large coeffecient of static friction.
The rod has length L and mass M. Its mass is evenly distributed along its length.
sum of forces, sum of moments. Parallel axis theorem.
The Attempt at a Solution
Here is a free body diagram of the rod/table.
Taking the sum of the forces in the vertical direction yields:
N = M(a + g). a is the vertical acceleration of the center of mass.
This doesn't make any sense to me, because it seems to be implying that the pendulum is falling faster than under free fall! How can this be? I know that the normal force is non-zero because the force of friction must counteract the moment caused by it (in order to not slip at the point of rotation) but why on earth is it greater than g?
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