Ladder against a smooth wall.

A ladder on a rough floor against a smooth wall; a person climbs and the wall push, floor normal and friction needed are drawn from force and moment balance.

With μs = 0.3 at 60°, find how far up the person can climb before the ladder slips.

Taking moments about a point but forgetting the friction or wall reaction.

• 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.

Teaching this idea? Put the simulation on your own page or LMS with this code.