06. WORK ENERGY AND POWER (HM)
Explanation:
(d) In circular motion
\(\vec{v}=\vec{w} \times \vec{r}\)
since in circular motion a body changes its direction continually and hence changes its radial vector Now, If angular velocity \(\vec{w}\) is constant then for the different radial vector \(\left(\vec{r}_{1}, \vec{r}_{2}, \vec{r}_{3}\right)\) there will be different velocity of body \(\left(i . e . \vec{v}_{1}, \vec{v}_{2}, \vec{v}_{3}\right)\) as shown in figure The centripetal acceleration of body will be to wards centre but for different position of body there will be different acceleration vector \(\left(\vec{a}_{1}, \vec{a}_{2}, \vec{a}_{3}\right)\) as shown in fig momentum is given by \(\vec{P}=m \vec{v}\)
since velocity vector is changing hence, \(\vec{P}\) will change In circular motion shown in figure \(\left|\vec{r}_{1}\right|=\left|\vec{r}_{2}\right|=\left|\vec{r}_{3}\right|=r\) (radius of circle)
\(\Rightarrow|\vec{v}|=|\vec{w}| r\)
since \(r\) and \(|\vec{w}|\) is constant therefore \(|\vec{v}|\) is constant for any position of body We know that kinectic energy \((k)\) \(k=\frac{1}{2} m|\vec{v}|^{2}\)
\(\Rightarrow\) kinectic energy \((k)\) of body will be constant