Rigid-Body Static Equilibrium and Supports
Static equilibrium of a rigid body requires simultaneous translational and rotational equilibrium, so all external force components sum to zero and the total torque about any point is zero.
Why this shows up in the exam
Hinged rods and ladders · Loads carried by shoulders or supports · Finding cable tensions and contact reactions
Learn the idea
A rigid body is static only when both net external force and net external torque vanish. A rigid body is static only when both net external force and net external torque vanish. 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: No slide and no spin: balance force and torque.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sum F_x = 0 and sum F_y = 0 — Planar translational-equilibrium equations.
- sum tau_O = 0 — Planar rotational-equilibrium equation about convenient O.
How to approach it
- 1Isolate the complete rigid body
- 2Resolve every external force
- 3Take moments about a point that removes unknown reactions
Common slip-ups that cost marks
- •Using only torque balance
- •Assuming a hinge reaction direction
- •Including internal forces in the external free-body diagram
🌟 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.