Two massless sticks of length 2r, each with a mass m fixed at its middle, are hi

Question

Two massless sticks of length 2r, each with a mass m fixed at its middle, are hinged at an end. One stands on top of the other, as shown below. The bottom end of the lower stick is hinged at the ground. They are held such that the lower stick is vertical, and the upper one is tilted at a small angle with respect to the vertical. They are then released. At this instant, what are the equations of motion for the angular accelerations of the two sticks (use theta 1 and theta 2 to denote the angular displacements of the two sticks – Hint: the equation of motion should be derived by using these angles as generalized coordinates)? Work in the approximation where is very small.

Explanation / Answer

For top stick

=> F * R = I * angular acceleration

=>    mg * r * sin = m * r2 * angular acceleration

=>     angular acceleration = g * sin/r

For bottom stick

=>    mg * r * sin = m * (3r)2 * angular acceleration

=>     angular acceleration = g * sin/9r

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