target="_blank" rel="nofollow" href="#ulink_5ae90f77-fc4c-5cf1-81df-7bc7308a5cff">(2.57) where all the internal forces (consisting of equal and opposite pairs) cancel out by Newton's third law, and
The term on the left‐hand side of Eq. (2.57) can be simplified by moving the time derivative outside the integral, because the total mass,
where we have
(2.59)
Thus the translational motion of the body is described by the motion of its centre of mass, as if all the mass were concentrated at that point.
Figure 2.3 A body as a collection of large number of particles of elemental mass,
The rotational kinetics of the body are described by taking moments of Eq. (2.55) about the centre of mass,
where all the internal torques cancel out (being equal and opposite pairs), resulting in only the net external torque,
A substitution of Eq. (2.61) into Eq. (2.60) yields the following equation of rotational kinetics of the body:
(2.62)
where
(2.63)
is the angular momentum of the body about its centre of mass, o. Thus a net external torque about the centre of mass of a body equals the time derivative of its angular momentum about the centre of mass.
If the body is rigid, then the distance between any two of its particles is a constant. Hence, the velocity of the elemental mass relative to
(2.64)
where
2.7 Gravity Field of a Body
The principles derived for the
(2.65)
where
(2.66)
is the total potential energy of the system,
(2.67)
is the mass of the body consisting of the last
