Question

A circular disc is rotating about its own axis at constant angular acceleration. If its angular velocity increases from $210rpm$ to $420rpm$ during $21$ rotations then the angular acceleration of disc is :

• A. $5.5rad/s^2$
• B. $11rad/s^2$
• C. $16.5rad/s^2$
• D. $22rad/s^2$

Answer 1

The correct option is A $5.5rad/s^2$

${\omega }_2^2-{\omega }_1^2=2\alpha \theta$

${\omega }_1=210rpm=210\times \frac{2\pi }{60}=7\pi rad/s^2$

${\omega }_2=420rpm=420\times \frac{2\pi }{60}=14\pi rad/s^2$

$\theta =21rotations=21\times 2\pi =42\pi$

$\Rightarrow {\omega }_2^2-{\omega }_1^2=2\alpha \theta$

$(14\pi {)}^2-(7\pi {)}^2=2\alpha \left(42\pi \right)$

$4\left(7\pi \right)-7\pi =2\alpha \left(6\right)$

$21\pi =12\alpha$

$\alpha =\frac{21\pi }{12}=5.5rad/s^2$