Force
Forces and Motion

Don't abuse the equals sign

Teaching Guidance for 14-16 Supporting Physics Teaching

An assertion of equality

Good mathematical habits can help you to think tidily, and not lead your students off down the wrong tracks.

As we've suggested you present it (following the development through the SPT: Forces topic, and the SPT: Motion topic), this kind of statement represents an empirical statement about the world.

forcemass = acceleration

The quantities on the left hand side are found (by experiment) to be equal to the quantities on the right hand side. There's nothing voluntary about it: this is the way the world is.

You might want to (and perhaps should) debate the empirical status of Newton's second law with colleagues (what experiments could you do to show that it is false?), but you do need to present a coherent line of reasoning to students, and we think the position taken here is plausible, intelligible and fruitful.

Some would argue for:

force = mass × acceleration. We don't think that's all that helpful in learning to use the relationship.

Teacher Tip: Use the = to mean that the left hand and right hand sides of a relationship are equal, rather than as an act of assignment (let's make this equal to that). So always, implicitly (by aligning the = in multiple line calculations) or explicitly (by always writing things out in full), ensure this balance by having a left and right hand side.

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