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 colin@flyingcoloursmaths.co.uk 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.

Equilibrium

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.

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

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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