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Nathanael

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## Main Question or Discussion Point

In introductory physics books (or at least mine) it limits the equation [itex]a_c=\frac{v^2}{r}[/itex] to the sitaution where the speed around the circular path is constant. It enforces the idea that the speed is CONSTANT.

But wouldn't the equation also apply to non-constant speeds? ([itex]a_c[/itex] would just change from being a constant to being a function of the speed)

It would be very counter-intuitive to me if this equation did not apply to variable speeds (because why does this instant in time care about the speed of the next instant in time?)

So my question is, can you also use this equation for variable speeds?

But wouldn't the equation also apply to non-constant speeds? ([itex]a_c[/itex] would just change from being a constant to being a function of the speed)

It would be very counter-intuitive to me if this equation did not apply to variable speeds (because why does this instant in time care about the speed of the next instant in time?)

So my question is, can you also use this equation for variable speeds?