Question

In the following figure $r_1$ and $r_2$ are $5cm$ and $30cm$ respectively. If the moment of inertia of the wheel is $5100kg-m^2$ about the axis passing through its centre and perpendicular to the plane of wheel, then what will be its angular acceleration?

Answer 1

Total clockwise direction as positive and anticlockwise as negative.

$r_1=5cm,r_2=30cm,I=5100Kg{m}^2$

$Torque=I\alpha$

$(10\times r_2)+(9\times r_2)-(12\times r_1)=I\alpha$

$(10\times 30)+(9\times 30)-(12\times 5)=5100\alpha$

$\alpha =0.1rad/r^2$