is there an effect on rotational inertia of a bar pendulum if extra mass is added to it .what happans if the added mass is located exactly at the orignal center of mass of the pendulum
Yes, adding extra mass to a bar pendulum can have an effect on its rotational inertia. The rotational inertia, also known as the moment of inertia, is a measure of an object's resistance to changes in its rotation. When additional mass is added to a pendulum, the distribution of mass changes, and therefore, its rotational inertia changes as well.
If the added mass is located exactly at the original center of mass of the pendulum, the rotational inertia will remain the same. This is because adding mass at the center of mass does not change the distribution of mass around the axis of rotation. As a result, the moment of inertia remains unaffected. The pendulum will continue to swing with the same period and behave as if no extra mass was added.
To calculate the rotational inertia of a pendulum, you need the mass distribution and the geometry of the system. The formula to compute the rotational inertia of a simple pendulum is I = mL², where I represents the moment of inertia, m is the mass, and L is the distance between the axis of rotation and the center of mass.
Keep in mind that this analysis assumes a simple and idealized pendulum without considering additional factors like friction or air resistance, which can affect the motion and stability of a real-life pendulum.