ZhixuPhysics | Start with a force diagram
Many mechanics errors begin before the calculation: which object is being studied, which forces act on it, and which direction is positive? A clear model turns Newton’s second law into a reasoning tool.
Choose one object
Isolate the object and identify the interactions with its surroundings. Earth exerts weight, a surface may exert a normal force and friction, and a rope may exert tension. Include forces acting on the chosen object, not the forces it exerts on other objects.
Give each force a source and direction
Weight normally points vertically down, a normal force is perpendicular to a surface, and tension follows a rope. Friction opposes relative motion or the tendency for relative motion at the contact; it need not oppose motion relative to the ground. Label each arrow and any known magnitude.
Net force determines acceleration
For constant mass in an inertial frame, ΣF = ma. An object moving right may accelerate left while slowing down. If the net force is zero, acceleration is zero: the object may be at rest or moving in a straight line at constant velocity.
Worked example: a horizontal push
A 2 kg object on a horizontal surface has an 8 N push to the right and 2 N friction to the left. Assume no vertical acceleration and no additional forces, so normal force and weight balance. Taking right as positive gives a horizontal net force of 8 − 2 = 6 N. Thus a = 6/2 = 3 m/s² to the right. This is acceleration, not velocity.
Check signs, units and force pairs
Use newtons for force, kilograms for mass and m/s² for acceleration. A negative result indicates the direction opposite your chosen positive axis. Action–reaction pairs act on different objects, so they cannot cancel within the force equation for a single object. Match every term to the diagram.
Try it yourself
For the same 2 kg object, make the rightward push 2 N while leftward friction remains 2 N. What is its acceleration? Must its velocity be zero?
Show reasoning and answer
The horizontal net force and acceleration are both zero. Its velocity need not be zero: a moving object may continue at constant velocity. Zero acceleration and zero velocity are different conditions.
Use the method in your next study session
Use five steps: object, forces, coordinates, equation and checks. Explain the signs with a diagram before substituting numbers.
These guides explain general subject foundations for learning and revision. They are not official examination syllabuses or questions. Refer to the relevant official institutions for examination requirements.