Motion in a Plane: Identifying the Centre of Mass?

📌 CONCEPT: The Centre of Mass (COM) is the point where the entire mass of the system can be considered to be concentrated for the purpose of analysis, and it is the point where the weight of the system can be considered to act from.

📐 RULE / FORMULA: The position of the centre of mass of a system of particles is given by the formula:

x̄ = (1/m) * ∑(m_i * x_i) where m is the total mass of the system and m_i is the mass of the i-th particle, located at position x_i.

💡 WORKED EXAMPLE: Consider a system of two particles of masses 5 kg and 10 kg, placed at positions 0.5 m and 1 m respectively. Using the formula, we can calculate the position of the centre of mass as follows:

x̄ = (1/15) * (5 * 0.5 + 10 * 1) = 0.833 m

⚠️ COMMON MISTAKE: Students often forget to consider the mass of each particle in the formula, or incorrectly assume that the centre of mass lies at the geometric centre of the system.