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From Newtons's second law for rotational motion, viz., \(\mathcal{T}=I\alpha\text{,}\) we have derived above that net rotational impulse equals chave in angular momentum.

From this, we can deduce that if rotational impulse is zero, then angular momentum cannot change.

This statement is called the principle of the conservation of angular momentum. One simple situation in which \(\vec J_{\text{rot,net,ext}}=0\) is when no external torques are acting on a body, e.g., a rotating body in outer space. Such a body will continue to rotate forever at the same rotation velocity. Another situation in which \(\vec J_{\text{rot,net,ext}}=0\) is when line of force on the body passes through the axis of rotation, e.g., force by Sun on rotating Earth is approximately like that, and hence, Earth continues to rotate at approximately constant angular speed about an axis towards the North star.

As a concrete example, suppose a spherical rotating star of moment of inertia \(I_i\) and angular speed \(\omega_i\) suddenly collapses to moment of inertia \(I_f\) and ends up rotating at angular speed \(\omega_f\) under a force pointed towards the center. Since centrally pointed force will have zero torque, and hence zero rotational impulse, we can say that angular momentum of the star will be cnserved. Therefore, we must have

An important class of problems where principle of the conservation of angular momentum is very useful is in collisions. In a collision forces are internal and hence \(\vec J_{\text{rot,net,ext}}=0\text{.}\) We will see some examples in the next section.

Principles of onservation of momentum, energy, and angular momentum are mire fundamental than Newton's laws of motion and apply to systems where Newton's laws do not hold, e.g. in quantum mechanics.