Question

2. A uniform rod, of length 2a, hangs in a horizontal position being supported by two vertical strings, each of length I, attached to its ends, the other extremities being attached to fixed points. The rod is given an angular velocity w about a vertical axis through its center; find its angular velocity when it has turned through any angle and shew that will rise through a distance a’w2/6g. Prove also that the time of a small oscillation about the position of equilibrium is 2ntsqrt(1/3g).

Answer 1

To solve this problem, we need to use the equations of motion and principles of rotational motion.

Let's start by analyzing the system's potential energy, given by the following equation:

U = mgI
where:
* U is the potential energy
* I is the moment of inertia of the rod
* g is the acceleration due to gravity

We can now use the conservation of energy principle to determine the equation of motion of the rod. The potential energy at the initial position is equal to the kinetic energy of the system at any position, which gives us: