Centre of gravity — A/L Combined Mathematics

What must I remember about Centre of gravity?

• Center of Gravity (C.G.) Definition: The single point G through which the resultant gravitational force (total weight W = Mg) acts in all orientations of the body.
• Equivalence of C.M. and C.G.: In a uniform gravitational field where gravitational acceleration g is constant across the entire body, the Center of Gravity G coincides exactly with the Center of Mass.
• Experimental determination: Plumb line method — suspend body freely from different points; the vertical plumb lines dropped from the suspension points intersect at the Center of Gravity.
• Distinction in non-uniform gravitational fields: For colossal astronomical bodies (e.g., Moon or space elevators), g varies with position, causing the Center of Gravity to diverge slightly from Center of Mass.
• Potential Energy connection: The gravitational potential energy of a rigid body in a uniform field is U = M * g * hG, where hG is the vertical elevation of its Center of Gravity above reference datum.

Test yourself (1 minute)

1. Rigid body weight representation

   In equilibrium problems, the distributed gravitational forces on all particles are replaced by a SINGLE downward force W = Mg acting vertically through G.

2. Support point alignment

   A body supported at a single point or pivot can only remain in equilibrium if the vertical line through the support point passes directly through G.

3. Work done against gravity

   Work done in tilting, raising, or turning a body of mass M equals M * g * ΔhG, where ΔhG is the vertical change in height of its Center of Gravity.

Practise Centre of gravity questions today

Source: NIE G.C.E. (A/L) Combined Mathematics Resource Book - Applied Mathematics, Unit 5

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Where does Centre of gravity fit in the syllabus?

Year 2 · Term 2