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Beside the importance of understanding Newton's third law conceptually, it comes in crucially when solving dynamics problem with multiple objects interacting with one another.

Acceleration Constraints

In general, in a problem with multiple objects, each object would have its own acceleration \vec{a}_A, \vec{a}_B, c\dots When multiple objects are connected or in contact, the acceleration are often related in some ways.

In the video below, I am solving the following problem.

Consider two books: the lower book has mass m_2 and is resting on a nearly frictionless surface while the upper has mass m_1 . Suppose the coefficient of static friction between the books is \mu_s .

With what maximum force can the upper book be pushed horizontally so that the books move together without slipping?