A wheel rotating at an angular speed of $20{\text{rads}}^{-1}$ , is brought to rest by a constant torque in 4s. If the M.I is $0.2\text{kg}{\text{m}}^{\text{2}}$ , the work done in first 2s is

$\alpha =?$

${\omega }_{\text{1}}=0,\text{t}=\text{us}$

${\text{w}}_1={\text{w}}_0+\alpha \text{t}$

$\text{0}=\text{20}+\alpha \left(\text{u}\right)$

$\alpha =-5{\text{rad/s}}^{\text{2}}$

${\omega }_{\text{2}}={\text{w}}_{\text{0}}+\alpha \text{t}$

$=\text{20}-5\times 2$                                       

$=10$

$\text{w}=\frac{1}{2}\times 0.2\left({10}^2-{20}^2\right)$

$=0.1\left(100-400\right)$

$=-30\text{J}$