Source: University of Washington, General Physics
Tags: forces, Newton's laws, classical mechanics, inertia, F=ma, action-reaction, net force, friction, tension, normal force, gravity
Difficulty: Introductory to Intermediate | Prerequisites: Basic algebra, familiarity with vectors (direction and magnitude) is helpful but not essential.
Forces and Newton's laws sit at the foundation of classical mechanics, the branch of physics that describes how and why objects move. Everything from a ball rolling down a ramp to a satellite orbiting Earth comes back to these principles. If you have covered kinematics (describing motion with equations), this is the next layer: the "why" behind that motion. You will need these ideas in nearly every subsequent topic in the course, from energy and momentum to rotational dynamics, so getting comfortable here pays off for the rest of the term.
A force is a push or pull between objects, measured as a vector (it has both size and direction). Newton's three laws explain what happens when forces act: objects keep doing what they are doing unless a net force intervenes (first law), the net force on an object equals its mass times its acceleration (second law), and every force comes with an equal and opposite partner force on the other object (third law). Master these three statements and you can set up nearly any mechanics problem in the course.
Force
An interaction between two objects described as a vector quantity, with both magnitude (measured in newtons, N) and direction.
Think of it as any push or pull one thing exerts on another.
Contact force
A force that requires physical touching between two objects. Friction, tension, and the normal force are the main examples.
In simple terms, if the objects have to be in contact for the force to exist, it is a contact force.
Non-contact force (field force)
A force that acts across empty space without the objects touching. Gravity and electromagnetic forces are the classic cases.
In simple terms, these are the forces that "reach out" across a distance.
Normal force
The perpendicular support force a surface exerts on an object resting on it. It adjusts to match whatever is pushing the object into the surface.
Think of it as the surface pushing back so the object does not fall through.
Friction
A contact force that opposes the relative motion (or attempted motion) between two surfaces.
In simple terms, friction is what makes it harder to slide a box across a floor.
Tension
The pulling force transmitted along a rope, string, cable, or similar connector when it is pulled taut.
Think of it as the force a rope "passes along" from one end to the other.
Net force (resultant force)
The vector sum of all forces acting on a single object. It is the net force, not any individual force, that determines how the object accelerates.
In simple terms, add up every force (with direction) and that total is the net force.
Inertia
The tendency of an object to resist changes to its state of motion. More massive objects have more inertia.
Think of it as an object's "stubbornness" about changing what it is doing.
Equilibrium
The condition where the net force on an object is zero, so its velocity is constant (which includes being at rest).
In simple terms, everything balances out and the object's motion does not change.
Contact forces require the objects to touch:
Friction (opposes sliding motion)
Tension (pulling through a rope or cable)
Normal force (surface pushing back perpendicularly)
Applied force (a direct push or pull you exert)
Non-contact (field) forces act at a distance:
Gravitational force (every mass attracts every other mass)
Electromagnetic force (charges attract or repel)
Spring force (often treated as a contact force, but governed by Hooke's law: F = -kx)
An object at rest stays at rest, and an object moving at constant velocity keeps that velocity, unless acted on by a net external force.
The key word is "net": multiple forces can act, but if they cancel to zero the object's motion does not change.
This law defines what a force does, by describing what happens without one.
Example: a hockey puck on frictionless ice glides in a straight line at constant speed indefinitely.
The net force on an object equals its mass multiplied by its acceleration: ΣF = ma.
This is a vector equation. You apply it independently along each axis (typically x and y).
Larger mass means smaller acceleration for the same force. Larger force means larger acceleration for the same mass.
Practical workflow for problems:
Draw a free-body diagram showing every force on the object.
Choose coordinate axes.
Write ΣFx = max and ΣFy = may.
Solve for the unknown.
Example (block on a surface): a block of mass m on a flat table has weight mg downward and normal force N upward. If you push it horizontally with force F_applied and friction is f, then ΣFx = F_applied - f = ma.
Example (rocket): thrust T acts upward, weight mg acts downward. ΣF = T - mg = ma. If T > mg, the rocket accelerates upward.
For every force that object A exerts on object B, object B exerts a force of equal magnitude and opposite direction back on A.
These paired forces act on different objects, so they never cancel each other when you analyse a single object.
Example (spring system): two masses connected by a spring. The spring pulls mass A to the right with force F, and simultaneously pulls mass B to the left with force F. Each mass accelerates according to F = ma applied to it individually.
The third law is why you can walk: your foot pushes the ground backward, and the ground pushes you forward.
Newton's Second Law
ΣF = ma (vector form: apply component-by-component)
Weight
W = mg, where g ≈ 9.8 m/s² near Earth's surface
Hooke's Law (spring force)
F = -kx, where k is the spring constant (N/m) and x is the displacement from equilibrium
Friction (kinetic)
f_k = μ_k · N, where μ_k is the coefficient of kinetic friction and N is the normal force
Friction (static, maximum)
f_s,max = μ_s · N, where μ_s is the coefficient of static friction
Free-body diagram (FBD): draw the object as a dot, then draw one arrow per force, pointing in the correct direction and labelled. This is the single most important problem-solving tool in Newtonian mechanics.
Newton's second law is what engineers use when they calculate how much thrust a rocket engine needs to lift a given payload off the launch pad. If the thrust does not exceed the rocket's weight, it stays on the ground.
Friction and the normal force show up every time you design brakes, tyres, or conveyor belts. The coefficient of friction between two surfaces determines how much grip is available before something starts to slide.
Students often think that a moving object must have a net force acting on it. It does not. An object moving at constant velocity has zero net force (first law).
Students often confuse mass and weight. Mass (kg) is a measure of how much matter an object contains and does not change with location. Weight (N) is the gravitational force on that mass and depends on g, which varies by planet or altitude.
Students often believe the third-law reaction force cancels the action force. It does not, because the two forces act on different objects. You only add forces acting on the same object.
Students often think heavier objects fall faster. In the absence of air resistance, all objects near Earth's surface accelerate at the same g, regardless of mass.
⚠️ Free-body diagrams appear on nearly every exam. If you cannot draw one correctly and label every force, you will lose marks even when your algebra is right.
⚠️ Be ready to apply F = ma component-by-component on inclined planes, Atwood machines, and connected-block systems. These are the standard problem types.
⚠️ Know the difference between static and kinetic friction, and when to use each.
⚠️ Third-law pairs are a favourite source of conceptual (multiple-choice) questions. Remember: the two forces always act on different objects.
True or false: an object moving at constant velocity has no forces acting on it.
False. It may have many forces acting on it, but the net force is zero.
Fill in the blank: the SI unit of force is the ______, which equals 1 kg·m/s².
Newton (N).
True or false: Newton's third-law force pairs act on the same object.
False. They always act on two different objects.
Fill in the blank: F = ma is a ______ equation, meaning you must apply it along each axis separately.
Vector.
True or false: static friction has a fixed value.
False. It adjusts up to a maximum of μ_s · N, matching whatever force is trying to start the motion.
Q: A 5 kg box sits on a frictionless table. You push it with a horizontal force of 20 N. What is its acceleration?
A: ΣF = ma, so a = F/m = 20 N / 5 kg = 4 m/s².
Q: A 10 kg block rests on a surface with μ_s = 0.4. What is the maximum horizontal force you can apply before it starts to slide?
A: f_s,max = μ_s · N = μ_s · mg = 0.4 × 10 × 9.8 = 39.2 N. You must exceed 39.2 N to start the block moving.
Q: A rocket of mass 1000 kg has engines producing 15 000 N of thrust. What is its acceleration at launch?
A: Net force = T - mg = 15 000 - (1000 × 9.8) = 5 200 N upward. Acceleration = 5 200 / 1000 = 5.2 m/s² upward.
Q: You push against a wall with 50 N of force. According to Newton's third law, how much force does the wall exert on you?
A: 50 N, directed back toward you (opposite to your push). Third-law pairs are always equal in magnitude and opposite in direction.
Q: A book is at rest on a table. Identify every force acting on the book and state whether the book is in equilibrium.
A: Two forces act on the book: its weight (mg, downward) and the normal force from the table (N, upward). Because the book is at rest, N = mg and the net force is zero. The book is in equilibrium.
This connects to kinematics because F = ma is the bridge between forces and the equations of motion (x = x₀ + v₀t + ½at²). Once you know the acceleration from forces, you can predict position and velocity at any time.
This connects to work and energy because work is defined as force times displacement (W = Fd cos θ). Understanding force is a prerequisite for the energy methods you will use later in the course.
This connects to momentum because Newton's second law can also be written as F = dp/dt (force equals the rate of change of momentum), which leads directly into impulse and conservation of momentum.
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