Principle of Moments
For a rigid body in static equilibrium, the vector sum of torques is zero; in a planar problem this is equivalent to equality of total clockwise and anticlockwise moments about any selected origin.
Why this shows up in the exam
Beam balances and seesaws · Finding unknown support reactions · Locating a body's balance point
Learn the idea
Rotational equilibrium requires clockwise and anticlockwise moments about any point to balance. Rotational equilibrium requires clockwise and anticlockwise moments about any point to balance. 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: Choose the pivot that makes unknown torques disappear.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sum tau_O = 0 — Rotational-equilibrium condition about point O.
- tau = F d_perp — Moment magnitude using perpendicular distance from O to the force line.
How to approach it
- 1Draw every external force
- 2Take moments about a convenient point
- 3Also enforce force balance and check reaction directions
Common slip-ups that cost marks
- •Using the slanted distance instead of perpendicular distance
- •Balancing torques but not forces
- •Changing sign convention midway
🌟 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.