Question

A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first two seconds it rotates through angle ${\theta }_1$. In the next two seconds it rotates through angle ${\theta }_2$. What is the ratio ${\theta }_2/{\theta }_1$?

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

Answer: (B)

$3$

lets say uniform angular acceleration$=\alpha$

and ${\omega }_0=0$

$\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$

$\Rightarrow {\theta }_1=0+\frac{1}{2}\alpha 2^2=2\alpha$ .........$\left(I\right)$

and lets say angular velocity changes to ${\omega }^{\prime }$

${\omega }^{\prime }={\omega }_0+\alpha t\Rightarrow {\omega }^{\prime }=0+\alpha \times 2\Rightarrow {\omega }^{\prime }=2\alpha$

now ${\theta }_2={\omega }^{\prime }t+\frac{1}{2}\alpha t^2=\left(2\alpha \right)2+\frac{1}{2}\alpha 2^2=6\alpha$ .........$\left(II\right)$

$\frac{{\theta }_2}{{\theta }_1}=\frac{6\alpha }{2\alpha }=3$