How is a particle moving in circular motion accelerating but not varying speed?
When a particle moves in circular motion, the resultant centripetal force acts radially towards the centre of the circle. Since there is a force there must be an acceleration on the particle due to Newtons 2nd law. However if you were to analyse the particles movement you would observe that the time period stays constant, showing that the speed is constant. Therefore the question is, how is an acclerating particle not varying speed? The answer behind this comes from the fact that acceleration and velocity are vector quantities, meaning they have a magnitude and direction. The velocity of the particle acts in the direction of the tangent to the circle and is therefore perpendicular to the force. Due to the force and velocity being perpendicular from one another there is no work done on the particle, because the particle doesn't change energy then it cannot change speed. The change in velocity comes from the particle's velocity changing direction around the circle rather than its magnitude.
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