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# lecture9 - Lecture 9 Circular Motion Today we’ll discuss...

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Unformatted text preview: Lecture 9 Circular Motion Today we’ll discuss motion along a curved path. First, let’s consider the simple case of uniform circular motion. 1 Uniform Circular Motion • Earlier in the class, we discussed uniform motion and pointed out that both the magni- tude and direction of the velocity stay constant in this case. But, what about situations where the direction of the motion changes in time? • A simple case is that of an object moving in a circular path with constant speed. This is called “uniform circular motion”. • In this case, since the direction of the velocity is changing, the momentum is not constant. • Consider a particle moving in a circle at constant speed. Let’s find the direction of the acceleration vector: – DRAW two velocity vectors – The change in velocity is given by the difference vectorv ( t )- vectorv ( t + Δ t ). DRAW – This is an isosceles triangle since velocity is constant. As delta theta goes to zero, base angles must go to 90 degrees since angles must sum to 180 degrees. Hence vector Δ v ⊥ vectorv in this limit. Acceleration points inwards towards the center of the circle. – Can also draw position vectors which gives a similar triangle. So | Δ vectorv | v = | Δ vector r | r Divide both sides by Δ t and rearrange: Δ vectorv Δ...
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lecture9 - Lecture 9 Circular Motion Today we’ll discuss...

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