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The net force on an object equals the product of its mass and acceleration: ΣF = ma. Force and acceleration are both vectors pointing in the same direction. This law connects kinematics (how things move) to dynamics (why they move). It is the central equation of classical mechanics and underlies virtually every problem in the course.
Always start by identifying all forces on the object, then sum them as vectors to get the net force. Apply separately in each coordinate direction: ΣFx = max and ΣFy = may. Work many problems of increasing complexity before combining with energy or momentum methods.
From kinematics, you know how to describe motion — position, velocity, acceleration. From Newton's First Law, you know that objects do not change their velocity unless something forces them to. The Second Law is the missing link: it tells you *how much* the velocity changes when a force acts, and in what direction.
The equation ΣF = ma says that the net force on an object — the vector sum of every force acting on it — equals the object's mass multiplied by its acceleration. The key word is *net*. If you push a book to the right with 5 N and friction pushes back with 3 N, the net force is 2 N to the right, and that is the force that determines the acceleration. You never plug individual forces into F = ma; you always find the net force first.
Mass plays the role of resistance to acceleration. Think of it this way: if you apply the same net force to a basketball and a bowling ball, the basketball accelerates much more because it has less mass. Mass is not the same as weight — mass is how much stuff is in the object (measured in kilograms), while weight is the gravitational force pulling it down (W = mg, measured in Newtons). An astronaut on the Moon has the same mass but much less weight.
Because force and acceleration are both vectors, the Second Law works independently in each direction. For a problem with forces in two dimensions, you write ΣFx = max for the horizontal direction and ΣFy = may for the vertical direction. This decomposition is powerful: a ball rolling off a table has gravitational acceleration only in the y-direction, while its x-velocity stays constant. Each direction is governed by its own version of F = ma.
Nearly every problem in mechanics — from blocks on ramps to orbiting planets — starts with this law. The skill to develop is systematic: identify the object, list every force on it, sum those forces as vectors to get the net force, then apply a = ΣF/m. This process becomes second nature with practice, and it is the foundation for everything that follows in classical mechanics.