Episode 203: Turning effects

Many students will recall the principle of moments from earlier work. The application of moments to situations beyond the simple ‘see-saw’ examples met earlier in the school career can cause some students difficulty. It is important to ensure that each step in the argument leading to an application of moments to general equilibrium situations is made as clear as possible.

Summary

  • Discussion: Moments and turning effects (10 minutes)
  • Student experiment: Weighing a broom/laboratory stand (10 minutes)
  • Student experiment: Centre of gravity of a student (5 minutes)
  • Discussion: Conditions for equilibrium (5 minutes)
  • Student experiment: Forces on a bridge (15 minutes)
  • Worked example: The bookshelf (10 minutes)
  • Student questions: Moments (15 minutes)

Discussion: Moments and turning effects
Your students will have come across these concepts already but their understanding may be shaky. It is therefore worthwhile to clearly define a moment and a couple thus:

Diagrams of a moment and a couple

It is also sensible to remind students of the equilibrium condition for moments (zero net moment about any point) before considering the first activity.

Couple acting on a wheel

Student experiment: Weighing a broom/laboratory stand
Episode 203-1: Using the centre of gravity to find the mass of a broom (Word, 28 KB)

If you have insufficient brooms to go around you can use a lab stand with a weight of a few newtons hanging from it. (Take care that feet don’t get injured by dropping weights.) This has the advantage of allowing all the students to have a go at the experiment and allowing for some useful comparison of results. For example, did all the students get the same result? If not, why not? To what degree of precision should the result be quoted?

The students will need to know the importance of the centre of gravity. Once this is established the experiment becomes fairly simple, but a little more interesting than see-saws.

Student experiment: Centre of gravity of a student
Find the position of the centre of gravity of a student. This reverses the process of the preceding activity.

Looking for centre of gravity - student on the plank

You need to be a little sensitive about who you choose for the student – you can always volunteer yourself. This activity can be adapted to work for Action Men and Barbie dolls!

Episode 203-2: Centre of gravity of a student (Word, 40 KB)

Discussion: Conditions for equilibrium
Careful questioning will encourage the students to formulate the conditions for equilibrium. They will readily state that the sum of the turning effects must be zero (or words to that effect such as: clockwise moments = anticlockwise moments) but they may need to be reminded that the resultant force must also be zero.

Student experiment: Forces on a bridge
This exercise gives practice in combining the two sets of equilibrium conditions. It can become as complex as required. The metre rule must be horizontal if possible (never that easy). There is a degree of practical difficulty which gives students an opportunity to develop practical skills, but some may need help.

The results will not match up particularly well (especially with lighter weights or weights far from the centre of gravity). Use this as an opportunity for discussion but emphasize the usefulness of the mathematical approach.

Episode 203-3: Forces on a bridge (Word, 74 KB)

Worked example: The bookshelf

Episode 203-4: Worked example (Word, 26 KB)

This is a standard example and links equilibrium conditions with resolved forces. This link is not obvious to all students – it is advisable to proceed with care! A non-mathematical class may lose confidence in the previous work if they are confused by this ‘synoptic’ question across Episodes 1 – 3. Check carefully whether the specification you are following requires this before proceeding and choose further examples with care.

However, mathematically-inclined post-16 level students will enjoy such examples and should be encouraged to tackle them.

Student questions: Moments
Various situations requiring the ideas of moments are used. You may wish to set extra questions to more able students

Episode 203-5: Moments questions (Word, 146 KB)

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Episode 203: Turning effects (Word, 271 KB)