If three point masses m₁, m₂, and m3 have position vectors r₁, 2, and r3 respectively, relative to some origin, then the position vector of their centre of mass relative to the origin is given by m₁r₁ + m₂ ₂ + M3 3 (m₁ + m₂ + m3) If the vectors a and b above represent the position vectors of a 2 kg point mass and a 4 kg point mass respectively (where the units of distance are considered to be subsumed within i, j, and k), calculate where a third point mass of 2 kg would need to be positioned to make the centre of mass of the system lie at the position r₂ = i+j+k.

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Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).