Ask Uncle Colin: how to do moments questions?

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions -- and to show off your skills at coming up with clever acronyms. Send your questions to and Uncle Colin will do what he can.

Dear Uncle Colin,

I'm struggling to make sense of questions about moments in M1. Can you help?

-- Failing Equilibrium-Related Moments... All Torque!

Hi, FERMAT! That's a bit more general than the kind of question I usually answer, but no matter!

Here’s the briefest theory of equilibrium I can come up with.


A body is in equilibrium if it is

  • in force balance (that is, the sum of all of the force vectors is zero).
  • in moment balance (that is, the signed sum of the moments is zero).

What that means in practice for you in M1 moments questions is:

  • The total of the upward forces is the same and the total of the downward forces.
  • The total of the clockwise moments about any fixed point is equal to the sum of the counterclockwise moments.


The moment of a force about a point is calculated as the (perpendicular) distance between the point and the force, multiplied by the magnitude of the force.

E.g: a force of 5N downward acting 3m to the right of a given point exerts a clockwise moment of 15Nm.

Question strategy

In terms of strategy, I recommend you...:

  • Draw a big picture. No, bigger than that.
  • Identify, draw and label all of the forces. Look out especially for reaction forces and the weight of the beam. (If it’s a uniform beam, the force acts in its centre.) If you don’t know a force’s magnitude, give it a name.
  • Set up an equation for the forces: total up = total down. Simplify, and solve if possible. Update your diagram if necessary.
  • Pick a point to take moments about. While any point will work, it’s often good to pick one where a force of unknown magnitude is acting.
  • Work out the distance from each force to the point. Again, if a distance is unknown, give it a name.
  • Set up an equation for the moments: total cw = total ccw. Simplify, and solve if possible.
  • If it’s not possible, you may need simultaneous equations; alternatively, you may need to reread the question to see if there’s something you missed.

Hope that helps, FERMAT!

-- Uncle Colin


Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.


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