The formula for Moment of Inertia of a square based pyramid is (1/12)*m*(h^2 + 4a^2), where m is the mass of the pyramid, h is the height, and a is the length of one side of the base.
Moment of Inertia is a measure of an object's resistance to changes in its rotational motion. In a square based pyramid, it determines the pyramid's stability and how difficult it is to rotate it around its central axis.
Moment of Inertia is directly proportional to the mass and the square of the distance between the rotation axis and the mass. In a square based pyramid, the distribution of mass and the distance between the rotation axis and the corners of the base affect the Moment of Inertia.
Yes, the Moment of Inertia of a square based pyramid can be calculated using calculus. The formula mentioned earlier is derived using integration techniques.
Moment of Inertia can be measured experimentally by using a torsion pendulum. The pyramid is attached to the pendulum, and the time period of oscillation can be measured. The Moment of Inertia can then be calculated using the formula: I = (T^2 * k)/4π^2, where T is the time period and k is a constant determined by the geometry of the pendulum.