Classical Mechanics (Kibble & Berkshire) · Problem 1.7

Velocity, acceleration and scalar angular velocity — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · vector-geometry-centre-of-mass

Problem

A number of particles with masses

m_1, m_2, m_3, \ldots

are situated at the points with position vectors

\boldsymbol{r}_1, \boldsymbol{r}_2, \boldsymbol{r}_3, \ldots

relative to an origin

O

. The centre of mass

G

of the particles is defined to be the point of space with position vector

\boldsymbol{R} = \frac{m_1 \boldsymbol{r}_1 + m_2 \boldsymbol{r}_2 + m_3 \boldsymbol{r}_3 + \cdots}{m_1 + m_2 + m_3 + \cdots}

Show that if a different origin

O'

were used, this definition would still place

G

at the same point of space.