= Centre of mass after removing material
{title2=$\mathbf R=(M_0\mathbf R_0-M_c\mathbf R_c)/(M_0-M_c)$}
Suppose a body of <mass> $M_0$ has <centre of mass> $\mathbf R_0$, and material of <mass> $M_c<M_0$ with <centre of mass> $\mathbf R_c$ is removed. Additivity of the first <mass> moment gives the remaining <centre of mass>
$$
\mathbf R=\frac{M_0\mathbf R_0-M_c\mathbf R_c}{M_0-M_c}.
$$
When the original <centre of mass> is at the origin, the remaining <centre of mass> points opposite the removed material's first <mass> moment. For a constrained <rigid body> rotating about a fixed axis, this displaced <centre of mass> undergoes <centripetal acceleration> even if the applied axial <torque> is zero.
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