The rotational equivalents of
(i) Mass is moment of inertia, I = \(\sum\)mr²
(ii) Force is Torque \(\tau\) = I\(\alpha\)

Law of conservation of angular momentum states that, when no external torque acts on the body, the net angular momentum of a rotating body remains constant.

A pair of forces which are equal in magnitude but opposite in direction and separated by a perpendicular distance so that their lines of action do not coincide that causes a turning effect is called a couple.

(i) Position and direction of the axis of rotation.
(ii) Distribution of Mass.

(i) Mass of the body.
(ii) Size and shape of the body.
(iii) Distribution of mass about the axis of rotation.
(iv) Position and orientation of the axis of rotation.

The angular momentum is zero (L = 0), if the linear momentum is zero (p = 0) or if the particle is at the origin (\(\overrightarrow { r } \)=0) or if \(\overrightarrow { r } \) and \(\overrightarrow { p } \) are parallel or antiparallel to each other (θ = 0° or 180°).

The angular momentum of a point mass is defined as the moment of its linear momentum. In other words, the angular momentum L of a point mass having a linear momentum p at a position r with respect to a point or axis is mathematically written as, \(\overrightarrow { L } =\overrightarrow { r } \times \overrightarrow { p } \)

It is the combination of pure translational and pure rotational motion.
1. The rolling motion is the most commonly observed motion in daily life. The motion of wheel is an example of rolling motion.
2. Round objects like ring, disc, sphere etc. are most suitable for rolling. Let us study the rolling of a disc on a horizontal surface. Consider a point P on the edge of the disc.
3. While rolling, the point undergoes translational motion along with its center of mass and rotational motion with respect to its center of mass.

The concepts to form the integrand to find the moment of inertia are to be followed. Now, the origin is fixed to the left 'end of the rod and the limits are to be taken from 0 to l.

I =  \(\frac { M }{ l } \int _{ 0 }^{ l }{ { x }^{ 2 }dx } =\frac { M }{ l } \left[ \frac { { x }^{ 3 } }{ 3 } \right] _{ 0 }^{ l }=\frac { M }{ l } \left[ \frac { { l }^{ 3 } }{ 3 } \right] \)
I = \(\frac { 1 }{ 3 } \)Ml²

Sum of the clockwise moments is equal to sum of the anticlockwise moments when a body is in rotational equilibrium or algebraic sum of moments at any point is zero.