Newton’s First and Second Laws

Objective: Describe motion when external net force is zero.

Newton’s first law states that an object remains at rest or continues at constant velocity in a straight line unless an external net force acts, within an inertial reference frame. Inertia is resistance to a change in velocity; mass quantifies inertia in the Newtonian model. Friction and drag often slow everyday objects, giving the misleading impression that force is required to sustain motion. A stopped object and one moving at steady velocity can both have zero net force. The law identifies inertial frames and is not a claim that forces never act on steadily moving objects; they can balance.

Objective: Use ΣF = ma for constant mass in an inertial frame.

For a body of approximately constant mass in an inertial frame, Newton’s second law relates net force and acceleration: ΣF = ma. Acceleration points in the direction of net force, not necessarily in the direction of current velocity. A 6 kg cart under a 12 N net force accelerates at 2 m/s² in the force direction. If mass doubles while net force stays fixed, acceleration halves in this model; if net force doubles at fixed mass, acceleration doubles. Use SI units so kg·m/s² equals N. The equation applies to the sum of external forces on one object, not to an arbitrary single force when others also act.

Objective: Combine forces before using the acceleration formula.

For one-dimensional motion, calculate signed net force first, then apply a = ΣF/m. A 10 kg sled pulled right by 35 N with 15 N friction left has net 20 N right and acceleration 2 m/s² right. The measured acceleration can also be used to infer net force from ma, but it does not identify each component force separately. A free-body diagram, chosen axis, and consistent units help avoid treating applied force as net force. In a level, nonaccelerating vertical direction, weight and normal force can balance even while horizontal forces are unbalanced. The model assumes approximately constant mass and an inertial frame.