Question

A wheel with an initial angular velocity ${\omega }_0$ reaches an angular velocity of $5{\omega }_0$ while it turns through an angle of $6$ rad; its angular acceleration in $radiansper{sec}^2$

• A. $\frac{{\omega }_0^2}{3}$
• B. $\frac{2}{3}{\omega }_0^2$
• C. $2{\omega }_0^2$
• D. $4{\omega }_0^2$

Answer 1

The correct option is C $2{\omega }_0^2$

Given the initial angular velocity ${\omega }_o$ rad per sec, and the final angular velocity $\omega =5{\omega }_o$ rad per sec,

We know that,

$\begin{array}{cc}{\omega }^2-{{\omega }_o}^2=2\alpha \theta & \\ \theta =6rad& \left(given\right)\\ {\left(5{\omega }_o\right)}^2-{{\omega }_o}^2=2\alpha \times 6& \\ 24{{\omega }_o}^2=2\alpha \times 6& \\ \alpha =2{{\omega }_o}^2& \end{array}$