Study Notes
The centre of mass is the point where the total mass of a system can be considered to be concentrated. It can be found for particles on a straight line, in a plane, and for various shapes like laminas and frameworks.
- Centre of mass of particles on a straight line — The point where the weighted average of the positions of particles is located. Example: For particles with masses 2 kg, 5 kg, and 3 kg at positions (3, 0), (4, 0), and (6, 0), the centre of mass is calculated using their positions and masses.
- Centre of mass of particles in a plane — The point where the weighted average of the position vectors of particles is located. Example: For particles at (x, y), (3, 2), (1, −5), and (6, 0) with a known centre of mass at (2.5, -2), x and y can be determined.
- Centre of mass of standard uniform plane laminas — The point where the mass is evenly distributed, often at the intersection of symmetry axes. Example: The centre of mass of a uniform circular disc is at its centre.
- Centre of mass of a composite lamina — Found by considering each part of the lamina as a particle at its centre of mass. Example: A disc with holes has its centre of mass calculated by considering the areas and positions of the remaining parts.
- Centre of mass of a framework — Determined by using the centre of mass of each rod or wire in the framework. Example: A framework with a semicircle and rectangle has its centre of mass found by considering the shapes' centres of mass.
Exam Tips
Key Definitions to Remember
- Centre of mass of particles on a straight line
- Centre of mass of particles in a plane
- Centre of mass of standard uniform plane laminas
- Centre of mass of a composite lamina
- Centre of mass of a framework
Common Confusions
- Confusing the centre of mass with the geometric centre
- Misunderstanding the role of symmetry in finding the centre of mass
Typical Exam Questions
- How do you find the centre of mass of particles on a straight line? Use the formula for the weighted average of positions.
- How do you determine the centre of mass of a composite lamina? Consider each part as a particle at its centre of mass and calculate the weighted average.
- What is the centre of mass of a uniform triangular lamina? It is at the intersection of the medians, called the centroid.
What Examiners Usually Test
- Ability to calculate the centre of mass for different configurations
- Understanding of how symmetry affects the centre of mass
- Problem-solving involving equilibrium of laminas and frameworks