Question

A constant torque of $1000Nm$ turns a wheel of moment of inertia $200kg{m}^2$ about an axis through its centre. The wheel is at rest initially. Its angular velocity after $3s$ is :

• A. $15rad{s}^{-1}$
• B. $0.6rad{s}^{-1}$
• C. $6000rad{s}^{-1}$
• D. $5rad{s}^{-1}$

Answer 1

The correct option is A $15rad{s}^{-1}$

We know that $T=I\alpha$

$1000=200\times \alpha \Rightarrow \alpha =5rad/s^2$

now we know $\omega ={\omega }_o+\alpha t$, and${\omega }_o=0$

$\omega =5\times 3=15rad{s}^{-1}$