Why Review Newtonian Mechanics?

Before studying rigid body mechanics, it is important to review the basic principles of Newtonian mechanics.

So far, we have mainly treated objects as particles, focusing on how forces affect their motion from one place to another.

Rigid body mechanics builds on these ideas by introducing rotation as well as translation.

Everything you learned about forces still applies—but now we must also consider where the force acts.

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Newton's Three Laws of Motion

Newton's Laws form the foundation of classical mechanics.

They explain how forces affect the motion of objects, whether they move in straight lines or rotate.

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Newton's First Law (Law of Inertia)

An object remains at rest or continues moving with constant velocity unless acted upon by a net external force.

This means:

• Objects at rest stay at rest.
• Moving objects continue moving at constant speed in a straight line.
• Motion only changes when a net force acts.

Examples:

• A hockey puck sliding on smooth ice.
• A book resting on a table.
• A spacecraft coasting through space.

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Newton's Second Law

Newton's Second Law explains how forces produce acceleration.

It states:

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

The mathematical relationship is:

$F_{\text{net}} = ma$Fnet​=ma

where:

• F = net force (N)
• m = mass (kg)
• a = acceleration (m/s²)

This is one of the most important equations in physics.

It allows us to predict how objects respond to applied forces.

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Newton's Third Law

Newton's Third Law states:

For every action force, there is an equal and opposite reaction force.

Whenever one object exerts a force on another:

• The second object exerts an equal force back.
• The forces act on different objects.
• The forces occur simultaneously.

Examples include:

• Walking.
• Swimming.
• Rocket launches.
• Birds flying.

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The Relationship Between Force and Motion

Force does not produce motion.

Force produces changes in motion.

Specifically:

• A net force causes acceleration.
• No net force means constant velocity.

For example:

A car travelling at constant speed on a level highway has:

• Driving force forward.
• Air resistance and friction backward.

If these forces are balanced:

• Net force = 0
• Acceleration = 0

The car continues moving at constant speed.

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Balanced and Unbalanced Forces

Balanced Forces

When forces cancel:

• Net force = 0
• No acceleration occurs.

The object may:

• Remain at rest.
• Continue moving at constant velocity.

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Unbalanced Forces

When forces do not cancel:

• Net force ≠ 0
• The object accelerates.

The acceleration is always in the direction of the net force.

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Free-Body Diagrams

A free-body diagram (FBD) is a simple drawing that shows all the forces acting on an object.

Common forces include:

• Weight
• Normal force
• Friction
• Tension
• Applied force
• Air resistance

Drawing a clear free-body diagram is often the first step in solving mechanics problems.

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Solving Force Problems

A systematic approach helps solve mechanics problems.

Step 1

Draw a free-body diagram.

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Step 2

Identify all forces.

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Step 3

Find the net force.

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Step 4

Apply:

$F_{\text{net}} = ma$Fnet​=ma

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Step 5

Calculate the unknown quantity.

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Worked Example

A 5 kg box is pushed across a frictionless floor by a force of 20 N.

Find its acceleration.

Step 1

Known values:

Mass = 5 kg

Force = 20 N

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Step 2

Apply Newton's Second Law.

$F=ma$F=ma

Rearrange:

$a=\frac{F}{m}$a=mF​

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Step 3

Substitute.

$a=\frac{20}{5}$a=520​$a=4\text{ m/s}^2$a=4 m/s2

Answer

The box accelerates at:

$\boxed{4\text{ m/s}^2}$4 m/s2​

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From Translation to Rotation

Everything learned so far describes translational motion.

Rigid body mechanics asks a new question:

What happens if a force is applied away from an object's centre?

Instead of producing only translation, the force may also produce rotation.

For example:

Pushing a door near its hinges is difficult.

Pushing near the handle causes the door to rotate easily.

The force may be the same—but its point of application changes the result.

This introduces a new concept:

Torque.

Torque is the rotational equivalent of force and will be studied in the following lessons.

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Comparing Linear and Rotational Mechanics

Many ideas in rotational mechanics are direct extensions of Newtonian mechanics.

Understanding linear motion makes learning rotational motion much easier.

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Why Newtonian Mechanics is Still Important

Even when studying rotating objects:

• Newton's Laws still apply.
• Forces still produce acceleration.
• Free-body diagrams are still essential.
• Conservation laws still hold.

Rigid body mechanics extends Newtonian mechanics rather than replacing it.

The main difference is that we now consider how forces act at different locations on an object.

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Real-World Applications

Newtonian mechanics forms the basis of:

• Vehicle design.
• Building construction.
• Robotics.
• Sports biomechanics.
• Aircraft engineering.
• Spacecraft design.
• Mechanical engineering.

Rigid body mechanics builds directly upon these same principles.

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Key Terms

Newtonian Mechanics — The branch of physics based on Newton's Laws of Motion.

Net Force — The vector sum of all forces acting on an object.

Free-Body Diagram (FBD) — A diagram showing all external forces acting on an object.

Balanced Forces — Forces that produce zero net force.

Unbalanced Forces — Forces that produce a non-zero net force and cause acceleration.

Torque — The turning effect of a force about an axis of rotation.

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Key Takeaways

• Newton's Three Laws describe how forces influence motion.
• A net force causes acceleration according to Newton's Second Law.
• Balanced forces produce constant velocity, while unbalanced forces change an object's motion.
• Free-body diagrams are an essential problem-solving tool.
• Rigid body mechanics extends Newtonian mechanics by introducing rotation in addition to translation.
• Torque plays the same role in rotational motion that force plays in translational motion.

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Suggested Images

Suggested placement:

1. After "Newton's Three Laws of Motion" – Infographic summarizing Newton's First, Second, and Third Laws.
2. After "Free-Body Diagrams" – A simple free-body diagram of a box on a horizontal surface showing weight, normal force, and an applied force.
3. After the "Worked Example" – Illustration of a box accelerating across a frictionless surface under an applied force.
4. After "From Translation to Rotation" – Comparison of pushing a door near the hinge versus near the handle to introduce the concept of torque.