Centre of mass
Forces in Action - OCR A-Level Physics
Key Definition
Centre of mass
The single point where the entire mass of an object can be considered to act. For a uniform object, it is at the geometric centre.
The single point where the entire mass of an object can be considered to act. For a uniform object, it is at the geometric centre.
Key Definition
Centre of gravity
The single point where the entire weight of an object can be considered to act. In a uniform gravitational field, it coincides with the centre of mass.
The single point where the entire weight of an object can be considered to act. In a uniform gravitational field, it coincides with the centre of mass.
- The conditions for static equilibriumA state in which the resultant force AND the resultant moment on an object are both zero.: (1) the resultant force in any direction is zero, AND (2) the resultant moment about any point is zero
- An object topples when the line of action of its weight falls outside its base of support
- A lower centre of gravityThe single point at which the entire weight of an object can be considered to act. and wider base make an object more stable
- To find the centre of gravityThe single point at which the entire weight of an object can be considered to act. of an irregular lamina: suspend it from two or more points, draw plumb lines, and find where they intersect
Examiner Tips and Tricks
- When solving equilibriumA state in which the resultant force AND the resultant moment on an object are both zero. problems, you can take moments about ANY point.
- Choosing the point where an unknown force acts eliminates that force from the moment equation, simplifying the calculation.
$$\text{Equilibrium:}\quad \sum F = 0 \quad \text{and} \quad \sum M = 0$$
Common Mistake
LOW
Students often: treat centre of mass and centre of gravity as always identical.
Instead: they coincide only in a uniform gravitational field. In a non-uniform field (e.g. a very tall object near a planet), the centre of gravity sits slightly closer to the source of the field than the centre of mass.
Instead: they coincide only in a uniform gravitational field. In a non-uniform field (e.g. a very tall object near a planet), the centre of gravity sits slightly closer to the source of the field than the centre of mass.
Diagram pending
Irregular lamina suspended from a pin, with a plumb line drawn vertically through the pin. Repeat from a second pin position; the centre of gravity is where the two plumb lines cross.
Will be replaced with a GeoGebra SVG in stream 2.