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Equilibrium of a rigid body
Beginner
Net force and net torque both zero.
ΣF=0, Στ=0Static equilibrium needs both ΣF = 0 and Στ = 0. Taking moments about a clever point removes unknown forces.
A 6 m ladder leaning on a wall: use torque about the base.
Don't forget the weight acts at the centre of mass.
In more detail
A rigid body is in equilibrium when both the net force and the net torque are zero. These conditions allow the forces on structures and levers to be calculated.
Real-world uses
- Architects check that beams and trusses are in equilibrium under loads.
- A seesaw balances when the torques from each side are equal.
- A ladder leaning on a wall is in equilibrium when the forces and torques from the floor and wall balance its weight.
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Frequently asked questions
Can a body be in translational equilibrium but not rotational?
Yes. It can have zero net force and still rotate if there is a net torque.
Which point should I take torques about?
Any point. Choose one that eliminates unknown forces to simplify the algebra.
Why must I check torque as well as force?
A body can have zero net force and still rotate, so both conditions are needed for full equilibrium.
Related topics in Rotational Motion
Rotational kinematics · Torque · Lever arm and moment · Centre of mass of shapes · Centre of gravity · Stability and toppling