In need of help with a physics problem, anything is appreciated.

Question

Answer 1

To determine the angular acceleration of the rod, we first need to calculate the torque. To calculate the torque, we know that the gravitational force will be given by Mg and the distance to the axis of rotation is L/2. Therefore, we see that the torque will be MgL/2 in the into the page (clockwise) direction. The rotational inertia (also known as the moment of inertia) of a rod about its end is given by 1/3 ML², which can be calculated either from the moment of inertia of a rod about its center, 1/12 M L² , and the Parallel Axis theorem, or directly from the moment of inertia integral. Thus, I=1/3 M L², so utilizing Newton's second law for rotation, we see that angular acceleration is (MgL/2)/ I, which is 3g/(2L). Therefore, the translational speed at the end of the rod will be given by α*r= 3g/(2L) * L=3/2 g. Thus the end is accelerating faster than an object in free fall.