Short Question Answers

Q1. Define angular velocity . Derive v=rω ?

Ans.  Angular velocity $(\omega)$ : The rate of change of angular displacement is in known as angular velocity

$$\omega=\frac{d\theta}{dt}$$

 SI Unit: rad/s

Derivation $\underline {V=r\omega:}$As shown in the diagram Let consider a particle moving along the circular patlh and Let $r$ is radius of the circle, $ x $ is arc length, $ \theta $ is angular displacement $ V $ is linear velocity and $\omega $ is angular velocity$$x=r\theta $$Differentiating above equation with respect to time $t$. $$\begin{aligned}
&{\frac{dx}{dt}}={\frac{d(r\theta)}{dt}} \\
&V=r{\frac{d(\theta)}{dt}} \\
&V=r\omega \\
\end{aligned}$$

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