Question

A car wheel is rotated to uniform angular acceleration about its axis. Initially its angular velocity is zero. It rotates an angle ${\theta }_1$in the first 2 s. In the next 2 s, it rotates through an additional angle ${\theta }_2$, the ratio of $\frac{{\theta }_2}{{\theta }_1}$ is

Answer 1

$\begin{array}{c}{\theta }_1=\frac{1}{2}\times {\left(2\right)}^2\\ \left({\theta }_1+{\theta }_2\right)=\frac{1}{2}\times {\left(4\right)}^2\\ \frac{{\theta }_1}{{\theta }_1+{\theta }_2}=\frac{1}{4}\\ \Rightarrow 4{\theta }_1={\theta }_1+{\theta }_2\\ \Rightarrow 3{\theta }_1={\theta }_2\\ \Rightarrow {\theta }_2=3\\ \therefore \frac{{\theta }_2}{{\theta }_1}=3\end{array}$

$\therefore$ Ans;-3