Physics · Ch 4 — Laws of Motion
Centre of Gravity
Centre of Gravity
The CENTRE OF GRAVITY (c.g.) of a body is the point about which the resultant torque, due to the force of gravity acting on every part of the body, is zero -- it is, in effect, the weighted average location of the gravitational forces (weights) acting on all the individual particles of the body, exactly analogous to how the centre of mass is the weighted average of the mass distribution.
For a UNIFORM gravitational field (i.e. whenever g can be treated as constant, which is true for essentially every object encountered in daily life on Earth), the centre of gravity always coincides exactly with the centre of mass -- which is why the two terms (c.g. and c.m.) are, in common usage, often used interchangeably for everyday objects.
This coincidence gives a simple EXPERIMENTAL method for locating the c.g. (equivalently, c.m.) of a flat, laminar (leaf-like, two-dimensional) object: suspend it freely from a rigid support at one point, and hang a plumb line (a string with a small weight) from the exact same suspension point. Since a freely-hanging object at rest must have its centre of gravity directly below the suspension point (along the vertical, which is exactly the plumb line's direction), draw a line on the object along the plumb line. Repeat this from a SECOND, different suspension point on the object, drawing a second such line. These two lines, both of which must pass through the centre of gravity (since it lies vertically below the suspension point in EVERY orientation), intersect at exactly one point -- and that intersection is the object's centre of gravity (Fig 4.12). …
What this figure shows. A flat, irregularly-shaped laminar (two-dimensional, leaf-like) cardboard object is shown suspended freely from a rigid support by a pin/nail through a hole near one of its edges, hanging in its natural rest orientation; a plumb line (a string with a small weight at the bottom) also hangs from the SAME suspension point, always oriented perfectly vertically since it is in line with the force of gravity, and a straight line is drawn on the object along the plumb line's direction, from the suspension point downward across the object's face. The object is then re-hung from a DIFFERENT point (a second hole near a different edge) and the same construction is repeated, drawing a second line along the new plumb line's direction from the new suspension point. The figure shows these two drawn lines crossing at a single interior point on the object -- this intersection point is identified as the object's centre of gravity (coinciding with its centre of mass), since the line of action o …