Using Moments with Equilibrium (Edexcel IAL Maths)

Using Moments - Equilibrium

Spec point — 6.1

Using moments with equilibrium

What is the resultant moment for a body in equilibrium?

• If a rigid body is in equilibrium then:

  • The resultant force is 0 N
  • The resultant moment about any point is 0 N m

• The sum of the magnitudes of the clockwise moments equals the sum of the magnitudes of the anti-clockwise moments

How do I use F = ma and moments to solve equilibrium problems?

• Step 1: Identify all forces and perpendicular distances from the pivot

• Step 2: Use the fact that the resultant force is 0 N to form an equation

• Step 3: Use the fact that the resultant moment about any point is 0 N m to form equations

  • If there is an unknown force you can choose a pivot that is on the line of action of that force – this will mean that the moment of that force is 0 N m

• Step 4: Solve the equations

Worked Example A light rod AB of length 10 m is held in equilibrium by three forces: 50 N, T₁ N and T₂ N.

T₁ N acts vertically upwards at A, 50 N acts vertically downwards 6 m away from A and T₂ N acts vertically upwards 2 m away from B as shown in the diagram.

Find the values of T₁ and T₂.

Answer:

Exam Hint

• If you see a force diagram that involves distances then you can be fairly sure that moments will be involved! A clear diagram showing all the distances is key.
• If you pick a pivot and form a moment equation which involves more than one unknown, try choosing another pivot to form simultaneous equations.
• Pick your pivot wisely as unknown and unwanted forces can be eliminated from the equation by choosing the point to be on the line of action of a force.