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Concept

Newton’s second law

The net force tells you how motion changes, not which way an object is moving.

Add the forces first

For a constant-mass object in an inertial frame, Newton’s second law is

∑F⃗=ma⃗.\sum \vec{F} = m\vec{a}.

The left side is the vector sum of external forces. It is not necessarily the largest force or the force you happen to be interested in.

Apply it one direction at a time

Choose positive directions and use signs consistently:

∑Fx=max,∑Fy=may.\sum F_x = ma_x, \qquad \sum F_y = ma_y.

An object can accelerate along one axis while its forces balance along another. A block on a fixed straight slope is a useful example.

Zero force does not mean zero velocity

Zero net force means zero acceleration. An object may remain at rest or continue with constant velocity.

Similarly, an object moving to the right can have a net force to the left. In that case its rightward velocity decreases. The force describes the change in velocity, not the velocity itself.

Ask a better question

Before substituting numbers, ask: “What does the given motion tell me about acceleration?” Use that answer with your force diagram to build the equations.