🌀 The Motion of the System of Particles and Rigid Body
Learn centre of mass, rigid body motion, rotational motion, torque, moment of inertia and angular momentum through animations, calculators, quiz and FAQ.
📌 Learning Map
🎯 Learning Objectives
- Understand system of particles.
- Define centre of mass.
- Differentiate translational and rotational motion.
- Understand torque, moment of inertia and angular momentum.
📊 Learning Outcomes
- Explains centre of mass clearly.
- Identifies rigid body motion.
- Uses torque and moment of inertia formulas.
- Solves basic rotational motion numericals.
🧩 Competencies
- Conceptual Understanding
- Mathematical Reasoning
- Problem Solving
- Diagram Interpretation
🌈 5W-1H + 1U
🔴 What: This topic studies motion of many particles and bodies whose shape does not change.
🟠Why: It helps explain rotation, balance, rolling, spinning and motion of extended bodies.
🟡 When: It is used when an object cannot be treated as a single point particle.
🟢 Where: Used in wheels, doors, gears, planets, machines, sports and engineering systems.
🔵 Who: Students, physicists, engineers, mechanics and designers use these concepts.
🟣 How: Motion is studied using centre of mass, torque, moment of inertia and angular momentum.
⚫ 1U: A rigid body can have both translational and rotational motion at the same time.
🎯 Centre of Mass
The centre of mass is the point where the entire mass of a system may be considered to be concentrated for studying translational motion.
Animated System of Particles
m
m
m
m
CM
The red point represents the centre of mass of the particle system. It behaves like the balance point of the system.
Xcm = (m₁x₁ + m₂x₂) ÷ (m₁ + m₂)
Total external force = M × acceleration of CM
🌀 Rigid Body Rotation
Animated Rotating Rigid Body
Axis
In rotational motion, every particle of the rigid body moves in a circle around the axis of rotation.
Torque Opens a Door
➡
Torque is the turning effect of force. A force applied farther from the hinge produces greater torque.
| Quantity | Meaning | Formula |
|---|---|---|
| Torque | Turning effect of force | τ = rF sinθ |
| Moment of Inertia | Rotational analogue of mass | I = Σmr² |
| Angular Momentum | Rotational momentum | L = Iω |
| Rotational Kinetic Energy | Energy due to rotation | K = ½Iω² |
🧮 Interactive Calculators
Centre of Mass
Xcm = (m₁x₁ + m₂x₂) ÷ (m₁ + m₂)
Torque
Ï„ = Force × Perpendicular distance
Angular Momentum
L = Iω
Rotational Kinetic Energy
K = ½Iω²
✅ Rigid Body Motion Quiz
🧠HOTS Questions
1. Why is centre of mass useful?
It allows the motion of a system of particles to be studied as if the whole mass were concentrated at one point.
2. Why is a door handle placed far from the hinge?
Placing the handle far from the hinge increases the perpendicular distance, producing greater torque for the same force.
3. Why does a figure skater spin faster when arms are pulled in?
Pulling arms in reduces moment of inertia, so angular velocity increases to conserve angular momentum.
4. Can a body rotate and translate at the same time?
Yes. A rolling wheel both translates forward and rotates about its axis.
5. Why is moment of inertia important?
Moment of inertia tells how difficult it is to change the rotational motion of a body.
