Question

A wheel starts from rest and rotates with a constant angular acceleration. It rotates by angle ${\theta }_1$ in the first second and ${\theta }_2$ in another second. Then the ratio ${\theta }_2/{\theta }_1$ is :

• A. 1
• B. 4
• C. 2
• D. 3

Answer 1

The correct option is D 3

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

${\omega }_0=Initialangularvelocity$

$\theta =angulardisplacement$

$t=time$

$\alpha =angularacceleration$

$\theta =\frac{1}{2}\alpha t^2$

$t=1sec$

${\theta }_1=\frac{1}{2}\alpha (2{)}^2=\frac{\alpha }{2}$

${\theta }_1+{\theta }_2=\frac{1}{2}\alpha (2{)}^2=2\alpha$

${\theta }_2=2\alpha -\frac{\alpha }{2}=\frac{3\alpha }{2}$

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

$\frac{{\theta }_2}{{\theta }_1}=3$