Formula for moment of inertia
Moment of inertia is a measure of an object’s resistance to rotational motion around a given axis.
The formula for the moment of inertia (I) of an object depends on its shape and the axis about which the moment of inertia is being calculated.
Some common formulas for different shapes:
Moment of inertia of a point mass (m) located at a distance (r) from the axis of rotation:
I = mr^2
Moment of inertia of a uniform rod of length (l) and mass (m) about an axis perpendicular to the rod and passing through its end: I
= (1/12) * m * l^2
Moment of inertia of a uniform disk of mass (m) and radius (r) about an axis passing through its center and perpendicular to its plane:
I = (1/2) * m * r^2
Moment of inertia of a uniform sphere of mass (m) and radius (r) about an axis passing through its center and perpendicular to its surface:
I = (2/5) * m * r^2
Note that these formulas are for an object with uniform mass distribution, if the object has a non-uniform mass distribution, the moment of inertia can be calculated using more complex methods.