Question
Define a uniform circular motion. For uniform circular motion, prove that:
Linear velocity $\text{v}=\text{r}\omega.$
Linear velocity $\text{v}=\text{r}\omega.$
✓
Answer
If the speed of the particle in circular path remains constant, the motion is uniform circular motion. We know, the arc length x covered with an angular displacement $\theta$ is $\text{x}=\text{r}\theta.$ Differentiating, $\frac{\text{dx}}{\text{dt}}=\text{r}\frac{\text{d}\theta}{\text{dt}}$ $\because$ r is constant, $\therefore\ \text{v}=\text{r}\omega.$
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