Accurately understand Newton's three laws, the fundamental laws governing how objects move. Entrance examinations test the application of these laws and algebraic transformations of their formulas.
Basic Knowledge
First Law (law of inertia): When the net force is 0, an object at rest remains at rest, and an object in motion continues uniform linear motion.
Second Law (law of motion): The acceleration of an object is proportional to the net force and inversely proportional to its mass.F = ma (F: net force [N], m: mass [kg], a: acceleration [m/s²])
Third Law (action–reaction law): When object A exerts a force on object B, B exerts a force on A with the same magnitude and opposite direction. These two forces lie on the same straight line.
Unit of force: 1N = 1 kg·m/s². Gravitational acceleration g ≒ 9.8 m/s² (10 m/s² depending on the problem).
Weight acting on an object of mass m [kg]: W = mg
Inertia (the property of an object to maintain its current state of motion)
Net force (the vector sum of the forces acting on an object)
F = ma (the equation of motion; the most fundamental principle in entrance examinations)
Action–reaction (on the same straight line, opposite directions, equal magnitudes; acting on different objects)
Two balanced forces (acting on the same object, opposite directions, equal magnitudes; distinguish them from action–reaction)
Further Study (Background and Significance)
When using the equation of motion F = ma, it is essential to follow the procedure of selecting one object of interest and finding the net force acting on it. Even in problems involving multiple objects, they can be solved by setting up F = ma for each object.
The two forces in the third law act between different objects. Be careful: “action–reaction pairs” and “balanced-force pairs” are easily confused and are a frequently tested trap in entrance examinations.
The magnitude of inertia is proportional to mass. The heavier an object is, the harder it is to move or stop. Since mass does not change in outer space, a large force is needed to move a heavy object even under weightlessness.
F = ma is a vector equation. Resolving it into components in the x and y directions and setting up equations is a basic technique for inclined-plane and curved-motion problems.
- F = ma is a vector equation with direction
- Choose the object of interest and draw all the forces
- Action–reaction ≠ balance (different objects vs. the same object)
- If net force = 0, acceleration = 0 (uniform linear motion or rest)
- Weight W = mg (g = 9.8 m/s²)
- For inclined planes, resolve forces into parallel and perpendicular components
- N = 1 kg·m/s²
Points to Note (Common Confusions)
① Mass (kg) and weight (N) are different. Mass measures inertia, while weight is mg. ② Action–reaction acts between different objects, while balance occurs on the same object. Both consist of equal forces in opposite directions, but they are fundamentally different. ③ Do not mistake uniform motion for “no forces.” Forces may exist even when the net force is zero. ④ F = ma uses the net force. Be careful not to substitute an individual force.
Practice
- Find the acceleration when a net force of 12 N is applied to an object of mass 3.0 kg.
- Explain the difference between the “action–reaction law” and “balanced forces,” focusing on the number of objects on which the two forces act.
- What kind of motion does an object undergo when the net force is zero? Give two answers.