Centre of Gravity and Stability
The centre of gravity is the point through which the resultant gravitational force acts; in a uniform gravitational field it coincides with the centre of mass, while stability requires its vertical projection to remain inside the support base.
Why this shows up in the exam
Balancing irregular bodies · Testing whether a body topples · Analysing rolling polygons and suspended bodies
Learn the idea
The centre of gravity is where the resultant gravitational force may be considered to act. The centre of gravity is where the resultant gravitational force may be considered to act. Start from a clear axis, origin, body, and reference frame; the geometry and constraints then decide which rotational law is safe to use.
🧠 Memory hook: The weight line must land inside the support.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- tau_weight = r_cg cross M g — Torque of weight about a chosen point in a uniform field.
- stable if projection of CG lies inside base — Geometric stability condition for a supported body.
How to approach it
- 1Locate the centre of gravity using symmetry or moments
- 2Draw its vertical line through the support
- 3Compare gravitational potential energy for nearby orientations
Common slip-ups that cost marks
- •Assuming centre of gravity always equals geometric centre
- •Ignoring the chosen pivot in the weight torque
- •Calling neutral equilibrium stable without an energy check
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
Masses 1 kg and 3 kg lie at x = 0 and x = 4 m. Find the x-coordinate of their centre of mass.
More from Motion of System of Particles and Rigid Body
Conservation of momentum and angular momentum
The total linear and angular momentum of a system remains constant in the absence of external forces or torques, including during collisions and rotational motion.
Moment of inertia and radius of gyration
Moment of inertia quantifies how mass is distributed with respect to an axis of rotation, and the radius of gyration is a measure related to this distribution.
Torque and rotational equilibrium
Torque is the rotational analogue of force, causing angular acceleration, and equilibrium occurs when the net torque on a body is zero.
Center of mass: definition and calculation
The center of mass is the point representing the mean position of the mass in a system, and can be calculated for discrete particles or continuous bodies.
Rotational kinematics and dynamics
Rotational kinematics describes the motion of rotating bodies, while dynamics relates torque, angular acceleration, and rotational kinetic energy.
Centre of Mass of Discrete Particles
For discrete particles, the centre-of-mass position is the vector sum of each mass times its position divided by total mass; this point governs translation even when the particles move relative to one another.