Newton's Laws of Motion
Master the three fundamental laws that describe how forces and motion are related -- the cornerstone of classical mechanics.
Newton's Three Laws
Sir Isaac Newton published his three laws of motion in 1687 in Principia Mathematica. Together, they describe the relationship between a body and the forces acting upon it, and the body's resulting motion.
First Law (Law of Inertia)
An object at rest stays at rest, and an object in motion stays in motion with the same velocity, unless acted upon by a net external force.
If ΣF = 0, then a = 0 (velocity is constant).
Second Law (F = ma)
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
ΣF = ma (net force = mass × acceleration)
Third Law (Action-Reaction)
For every action force, there is an equal and opposite reaction force. These forces act on different objects.
FA on B = -FB on A
Important: The action and reaction forces in Newton's Third Law act on different objects. They never cancel each other out because they are not applied to the same body.
Free Body Diagrams
A free body diagram (FBD) is a simplified representation showing all the forces acting on a single object. The object is drawn as a dot or simple shape, and each force is represented by an arrow showing its direction and relative magnitude.
Example: Block on a Surface
Common Forces
- Weight (W) = mg, always acts downward
- Normal force (FN) -- perpendicular to surface
- Friction (f) -- opposes relative motion
- Tension (T) -- along a rope or string
Steps for FBD
- 1. Identify the object of interest
- 2. Draw the object as a dot or box
- 3. Identify ALL forces acting on it
- 4. Draw force arrows from the object
Net Force and Applications
The net force (ΣF) is the vector sum of all forces acting on an object. It determines the acceleration via Newton's Second Law. Forces are often resolved into perpendicular components (typically horizontal and vertical).
Calculating Net Force
Step 1: Draw the free body diagram
Step 2: Choose a coordinate system
Usually horizontal (x) and vertical (y)
Step 3: Resolve forces into components
Fx = F cos θ, Fy = F sin θ
Step 4: Apply ΣF = ma
ΣFx = max and ΣFy = may
Equilibrium
When the net force on an object is zero (ΣF = 0), the object is in equilibrium. This means it either remains at rest or continues at constant velocity (Newton's First Law). Equilibrium does NOT necessarily mean the object is stationary.
Key Vocabulary
Inertia
The tendency of an object to resist changes in its state of motion. An object with more mass has more inertia.
Net Force
The vector sum of all forces acting on an object, also written as ΣF. Determines the object's acceleration.
Normal Force
The perpendicular contact force exerted by a surface on an object resting on it, preventing the object from passing through.
Equilibrium
The state where the net force on an object is zero, resulting in zero acceleration (constant velocity or at rest).
Worked Examples
A 5.0 kg box is pushed with a horizontal force of 20 N across a frictionless surface. Find its acceleration.
Known: m = 5.0 kg, F = 20 N, friction = 0
Using Newton's Second Law: ΣF = ma
a = ΣF / m = 20 / 5.0 = 4.0 m s-2
A 60 kg person stands on scales in a lift accelerating upward at 2.0 m s-2. What is the normal force (apparent weight)?
Known: m = 60 kg, a = 2.0 m s-2 (upward), g = 9.8 m s-2
Vertical: ΣFy = ma → FN - mg = ma
FN = m(g + a) = 60(9.8 + 2.0) = 60 × 11.8 = 708 N
Identify the Newton's Third Law force pair when you push a wall with 50 N.
Action: Your hand pushes the wall with 50 N to the right.
Reaction: The wall pushes your hand with 50 N to the left.
Note: Same magnitude, opposite direction, and each force acts on a different object (hand vs wall). They are NOT drawn on the same free body diagram.
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Newton's First Law is sometimes called the law of:
Question 2
A net force of 30 N acts on a 10 kg object. What is the acceleration?
Question 3
According to Newton's Third Law, when you push a wall, the wall pushes back on you with a force that is:
Question 4
An object moving at constant velocity has:
Question 5
If the same force is applied to a 2 kg block and a 4 kg block, how do their accelerations compare?
Key Concepts Summary
- ●Newton's First Law: An object maintains its velocity unless a net external force acts on it.
- ●Newton's Second Law: ΣF = ma -- net force equals mass times acceleration.
- ●Newton's Third Law: Forces always come in equal and opposite pairs acting on different objects.
- ●Free body diagrams show all forces acting on a single object and are essential for solving force problems.
- ●When ΣF = 0, the object is in equilibrium (at rest or constant velocity).