Balancing Moments

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This is a basic physics GCSE tutorial reviewing how to balance moments.

What does it mean to balance moments?

As discussed in the previous tutorial, the turning effect of a force (i.e. its moment) can act in two directions – clockwise and anticlockwise. When there is more than one applied force, there will be more than one moment exerted on the object. The balance between their magnitude and direction determines which way the object turns / rotates, if at all.

In the case of a seesaw, balanced turning forces result in the seesaw being horizontal (as below).

How do we check if moments balance?

There are three steps needed to check if moments acting on an object such as a seesaw balance.

Step 1: Calculate the moment sum acting in one direction (e.g. clockwise).
Step 2: Calculate the moment sum acting in the other direction (e.g. anticlockwise).
Step 3: Compare the two. If they are the same, the object will balance. If not, compare the two sums and determine what direction the object will turn.

Let's work through an example

On the right hand side of a playground seesaw we have a force of 520 N acting downwards at a distance of 2.8 m from the pivot. On the left hand side we have a force of 350 N acting downwards at a distance of 1.4 m from the pivot. Our task is to determine which way the seesaw will turn, if at all.

To do this, let's follow the steps above.

Step 1: Calculate moment sum acting in the clockwise direction (i.e. as a result of object B).
M = f x d
M = +520 N x 2.8 m
M = +1456 N or 1456 Nm clockwise

Step 2: Calculate the moment sum acting in the anticlockwise direction (i.e. as a result of object A).
M = f x d
M = -350 N x 1.4 m
M = -490 N or 490 Nm anticlockwise

Step 3: Compare the two values and determine what direction the object will turn, if at all (as above).
There are 1456 Nm acting in the clockwise direction, and 480 Nm acting in the anticlockwise direction. As 1456 Nm is greater than 480 Nm, the object will turn in the clockwise direction.

How do we make the seesaw balance?

For the seesaw to balance, the moments acting on either side need to be of the same magnitude .

In order for the moments in the above seesaw to balance, you have two options. You can either make changes to the left hand side (to A), or the right hand side (to B). Let's leave A exactly where it is, and move B - either closer or further away from the pivot. Let's calculate exactly where we need to move B to.

So, in order for the seesaw to balance, we simply need to move B to a distance of 0.94 m from the pivot.

Now it's your turn

Redo the above calculation, but leave B exactly where it was (2.4 m from the pivot) and move A. What distance does A need to be from the pivot in order for the seesaw to balance? Once you've got your answer, hover your mouse over the below "Answer" image to get the answer.

Does it matter if moments balance?

As we know, when the turning forces on an object don't balance, the object turns. Objects like seesaws rely on fluctuating unbalanced forces to work properly (with the people on them pushing up and off the ground to alter the moments).

Other objects require the turning forces to be balanced, otherwise there can be significant danger to anyone present. For example, an unbalanced crane could topple over and cause significant damage. Consequently, a counterbalance can be used to balance the moments and thus the crane. (Hint: hover over the image below to see where the counterweight is).

In addition to using moments for fun (e.g. with seesaws), turning forces can also be very useful. Learn how in the next tutorial