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Would it be a x ds = v x dv or a • ds = v • dv for describing curvilinear motion?

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- Thread starter Iqminiclip
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- #1

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Would it be a x ds = v x dv or a • ds = v • dv for describing curvilinear motion?

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Hi sir, I was wondering why ds would be zero? Wouldn't a particle in circular motion have some sort of change in displacement over time? (e.g at 90° or so)

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Ah, I was interpreting yourHi sir, I was wondering why ds would be zero? Wouldn't a particle in circular motion have some sort of change in displacement over time? (e.g at 90° or so)

In that case the equation has to be a dot product, not a multiplication, as one cannot multiply vectors. We have an equation for each of the three dimensions:

\begin{align}

a_1\,ds_1 &= v_1\,dv_1\\

a_2\,ds_2 &= v_2\,dv_2\\

a_3\,ds_3 &= v_3\,dv_3

\end{align}

Adding them together, we can represent this as:

$$\vec a\cdot \vec {ds} = \vec v\cdot \vec {dv}$$

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