Newton's Laws of Motion
Newton’s First Law
Newton’s first law states that an object will remain at rest or continue to move at a constant velocity unless a resultant force acts on it.
This means that if all forces on an object are balanced (resultant force = 0), the object will not change its motion. A stationary object stays still. A moving object keeps moving at the same speed in the same direction.
Inertia is the tendency of an object to resist a change in motion. The more mass an object has, the greater its inertia. This is why a heavy object is harder to push into motion or bring to a stop than a light one.
Newton’s Second Law
Newton’s second law states that the acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass:
$$F = m a$$
Where \(F\) is the resultant force in newtons (N), \(m\) is mass in kilograms (kg), and \(a\) is acceleration in m/s\(^2\).
This tells us three things: a larger force produces a greater acceleration; a larger mass requires a greater force for the same acceleration; and if the resultant force is zero, there is no acceleration.
A 1200 kg car has a driving force of 4800 N and friction of 1200 N. Calculate the acceleration.
Step 1: Resultant force = 4800 − 1200 = 3600 N
Step 2: \(a = \frac{F}{m} = \frac{3600}{1200} = 3\) m/s\(^2\)
Newton’s Third Law
Newton’s third law states that whenever two objects interact, they exert equal and opposite forces on each other. These forces act on different objects and are always the same type of force.
Newton’s third law pairs always: act on two different objects, are the same size, act in opposite directions, and are the same type of force. For example, the Earth pulls you down with gravity, and you pull the Earth up with the same gravitational force.
Students often confuse balanced forces with Newton’s third law pairs. Balanced forces act on the same object (e.g. weight and normal force on a book). Newton’s third law pairs act on different objects (e.g. the book pushes the table down, the table pushes the book up).
Another misconception: “if the forces are equal and opposite, the object can’t move.” This is wrong because the two forces act on different objects. A rocket accelerates because the rocket pushes gas backwards and the gas pushes the rocket forwards — these act on different objects.
Terminal Velocity
When an object falls through a fluid (air or water), it initially accelerates due to gravity. As its speed increases, the drag force (air resistance) increases. Eventually, the drag force equals the weight and the resultant force becomes zero.
At this point, the object reaches terminal velocity — it continues to fall at a constant speed because the forces are balanced.
When a skydiver jumps, they accelerate because weight is greater than air resistance. As speed increases, air resistance increases, so acceleration decreases. At terminal velocity (~55 m/s), forces are balanced. When the parachute opens, air resistance suddenly increases above the weight, so the skydiver decelerates. A new, lower terminal velocity (~5 m/s) is reached.