Question

State the expression for acceleration of the centre of mass of a system of n particles and for continuous mass distribution.

Answer 1

Let a₁, a₂,…. a_n be the accelerations of a system of point masses m₁, m₂ … m_n.

Acceleration of the centre of mass of the system is given by,

= \(\frac{resultant\,force}{total\,mass}\)

= weighted average of forces

x, y and z components of can be obtained similarly.

For continuous distribution, \(\overrightarrow{a}_{cm}\) = \(\frac{\int\,\overrightarrow{a}dm}{M}\)