Question

A wheel I axis $=3kg{m}^2$ $\tau =6Nm$. Find work done by $\tau$ in $t=20sec?$(Starting from rest)

Answer 1

W.d$=(\tau \times \theta )$
$\tau =I\frac{dw}{dt}$
$6=3\frac{d}{dt}$
$2=\frac{dw}{dt}$
${\int }_{t=0}^{t=20}2dt={\int }_{w=0}^{w}dw$
$w=2t$
$w=\frac{d\theta }{dt}$
${\int }_{w=0}^{w=wt}wdt={\int }_{\theta =0}^{\theta }d\theta$
${\int }_{t=0}^{t=20}2tdt=\theta$
$\frac{t^2}{2}=\theta$
$\theta =100$
W.D$=6\times 100$
$=600J$