The moment of inertia of a thin rod about an axis perpendicular to the rod and passing through one end is given by (\frac{1}{3}mL^2).

The angular momentum of a rigid body rotating about a fixed axis is given by (I\omega).

The kinetic energy of a rigid body rotating about a fixed axis is given by (\frac{1}{2}I\omega^2).

The torque acting on a rigid body rotating about a fixed axis is given by (I\alpha).

The equation of motion for a rigid body rotating about a fixed axis is (I\alpha = \sum\tau).

The moment of inertia of a uniform disk about an axis perpendicular to the disk and passing through its center is given by (\frac{1}{2}mR^2).

The moment of inertia of a uniform sphere about an axis passing through its center is given by (\frac{2}{5}mR^2).

The angular velocity of a rigid body rotating about a fixed axis with constant angular acceleration (\alpha) and initial angular velocity (\omega_0) after time (t) is given by (\omega_0 + \alpha t).

The angular displacement of a rigid body rotating about a fixed axis with constant angular acceleration (\alpha) and initial angular velocity (\omega_0) after time (t) is given by (\omega_0 t + \frac{1}{2}\alpha t^2).

The relationship between the linear velocity (v) of a point on a rigid body rotating about a fixed axis and the angular velocity (\omega) of the body is given by (v = \omega r), where (r) is the distance from the point to the axis of rotation.

The relationship between the centripetal acceleration (a_c) of a point on a rigid body rotating about a fixed axis and the angular velocity (\omega) of the body is given by (a_c = \omega^2 r), where (r) is the distance from the point to the axis of rotation.

The moment of inertia of a uniform cylinder about an axis parallel to the cylinder's axis and passing through its center is given by (\frac{1}{2}mR^2).

The moment of inertia of a uniform rectangular plate about an axis perpendicular to the plate and passing through its center is given by (\frac{1}{12}m(w^2 + h^2)).

The moment of inertia of a uniform triangular plate about an axis perpendicular to the plate and passing through its vertex is given by (\frac{1}{12}mb^2).