Newton's Laws
Newton’s First Law
Newton’s First Law states that an object remains at rest or continues to move at a constant velocity unless acted upon by a resultant force. This means:
• If the resultant force is zero, a stationary object stays still and a moving object keeps moving at the same speed in the same direction.
• If there is a resultant force, the object accelerates — which means it speeds up, slows down, or changes direction.
This law applies to all objects, from cars on motorways to planets orbiting the Sun. A book on a table remains stationary because its weight (downward) is exactly balanced by the normal contact force from the table (upward). A spacecraft drifting in deep space, where there is no friction or air resistance, will continue at the same velocity forever unless a thruster fires.
Objects do not need a force to keep moving at constant velocity. A resultant force is only needed to change the speed or direction of an object.
Newton’s Second Law: F = ma
Newton’s Second Law tells us that the resultant force on an object is equal to its mass multiplied by its acceleration:
$$F = m \times a$$
Where \(F\) is force in newtons (N), \(m\) is mass in kilograms (kg), and \(a\) is acceleration in \(\text{m/s}^2\). This equation tells you two important things: a bigger force produces a bigger acceleration (if mass stays the same), and a heavier object needs a bigger force for the same acceleration. It can be rearranged to find acceleration (\(a = \frac{F}{m}\)) or mass (\(m = \frac{F}{a}\)).
Remember that \(F\) in this equation is always the resultant force, not just any single force. If a car’s engine provides 3000 N of driving force but friction and air resistance total 1000 N, the resultant force is \(3000 - 1000 = 2000 \text{ N}\) forward.
Question: A 1500 kg car experiences a resultant force of 4500 N. Calculate its acceleration.
Answer: \(a = \frac{F}{m} = \frac{4500}{1500} = 3 \text{ m/s}^2\)
You can investigate Newton’s Second Law using a trolley on a smooth track. Attach a string over a pulley to a hanging mass, which provides the force. Use light gates to measure the acceleration of the trolley. Keep the total mass of the system constant (trolley + hanging mass) and vary the force by moving masses from the trolley to the hanger. Plot a graph of force against acceleration — a straight line through the origin confirms that \(F \propto a\) at constant mass.
Weight, Mass and Gravitational Field Strength
Mass is the amount of matter in an object and is measured in kg. It does not change with location. Weight is the force of gravity acting on that mass, measured in newtons. The equation is:
$$W = m \times g$$
Where \(W\) is weight (N), \(m\) is mass (kg) and \(g\) is gravitational field strength (N/kg). On Earth, \(g = 10 \text{ N/kg}\). On the Moon, \(g \approx 1.6 \text{ N/kg}\), so a 70 kg person would weigh 700 N on Earth but only 112 N on the Moon. Their mass remains 70 kg in both locations. Weight is measured using a newton meter (spring balance), while mass is measured on a balance.
The numerical value of \(g\) at the Earth’s surface also equals the acceleration due to gravity in free fall: \(g = 10 \text{ m/s}^2\). This means that a falling object (ignoring air resistance) accelerates at \(10 \text{ m/s}^2\) regardless of its mass.
Newton’s Third Law
Newton’s Third Law states: for every action, there is an equal and opposite reaction. These action-reaction pairs act on different objects and are always the same type of force. For example:
• When you push a wall, the wall pushes back on you with an equal force (both are normal contact forces).
• When the Earth pulls you down by gravity (your weight), you pull the Earth up with the same gravitational force.
• A swimmer pushes water backwards; the water pushes the swimmer forwards.
A common mistake is to identify weight and normal contact force as a Third Law pair. They are not — both act on the same object (you). A true Third Law pair involves forces on different objects.
Newton’s Third Law pairs are equal in size, opposite in direction, the same type of force, and act on different objects.
Terminal Velocity
When a skydiver jumps from a plane, they initially accelerate because their weight is much greater than air resistance. As speed increases, air resistance increases (it depends on speed, surface area and shape). Eventually, air resistance equals weight. At this point the resultant force is zero and the skydiver reaches terminal velocity — constant speed, zero acceleration.
When the parachute opens, the surface area dramatically increases, causing air resistance to suddenly become much greater than weight. The skydiver decelerates. As they slow down, air resistance decreases until a new, lower terminal velocity is reached — slow enough for a safe landing.
Momentum is a measure of how hard it is to stop a moving object. The equation is:
$$p = m \times v$$
Where \(p\) is momentum (kg m/s), \(m\) is mass (kg), and \(v\) is velocity (m/s). In a closed system (where no external forces act), the total momentum before a collision equals the total momentum after — this is the conservation of momentum. For example, if two trolleys of equal mass collide and stick together, their combined speed will be half of the original speed of the moving trolley.
Inertia is a measure of how difficult it is to change an object’s velocity. An object with more mass has more inertia. Inertial mass is defined as the ratio of force to acceleration: \(m = \frac{F}{a}\). This is essentially Newton’s Second Law rearranged.