Lesson 7 of 13 · 6 min
Equilibrium of a rigid body
NCERT §6.8
Ananya tries to open a stubborn bottle of lemonade at the juice stall. She grips the lid with her thumb on one side and her fingers on the other and twists. The lid turns but stays in place over the bottle.
The lesson in notes
In short
A rigid body is in mechanical equilibrium when neither its linear momentum nor its angular momentum changes: it has no linear and no angular acceleration.
Translational equilibrium: ΣF = 0. Rotational equilibrium: Στ = 0. Each is three scalar equations, six conditions in all.
If all the forces lie in one plane, three conditions are enough: force components add to zero along two perpendicular directions in the plane, and torques about an axis perpendicular to the plane add to zero.
If ΣF = 0, the total torque is the same about every point, so the origin for torques can be chosen freely.
Partial equilibrium is possible. Two equal parallel forces in the same direction at the ends of a light rod: zero net torque about the centre but a net force. Equal and opposite forces at the two ends: zero net force but a net torque.
A couple is a pair of equal and opposite forces with different lines of action. It produces rotation without translation. Turning a bottle lid and a compass needle in the earth's magnetic field (not pointing north–south) are examples.
The moment of a couple is AB × F, where AB joins the points of application; it does not depend on the point about which moments are taken.
A particle can only be in translational equilibrium; the forces on it act at one point, so they are concurrent.