This is the motion about a fixed axis. In such systems, the force gets replaced by a moment about the fixed axis i.e. (force x distance from fixed axis) which is called Torque.

So excitation of Newton's law states that the sum of the torques applied to a rigid body or a system must be equal to sum of the torques consumed by the different elements of the system in order to produce angular displacement (θ), angular velocity (ω) and angular acceleration (α) in them. As previously stated, spring and friction behaves in same manner in rotational systems. The property of system which stores kinetic energy in rotational system is called Inertia and denoted by 'J' i.e. moment of inertia. Opposing torque due to inertia 'J' is proportional to the angular acceleration (α) of that inertia.

Taking Laplace,

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