# A sphere of coefficient of linear expansion a, mass m and radius r is spinning about an axis through its diameter with an angular velocity w when it is heated such that is temprature increases by delta t. what is angular velocity?

Norman Manchu
151 Points
4 years ago
With the use of conservation of angular momentum-
I1w1=I2w2 where I represents moment of inertia and w represents angular velocity hence
${\color{Orchid} \frac{2mr^{2}}{5}w}=\frac{2m(r(1+\alpha\Delta \Theta ) ^{2}}{5}(wfinal)=\frac{2m(r^{2}(1+2\alpha\Delta \Theta )}{5}(w')(extension)$

Equate purple equation with the last most extended form and you'll get wfinal=w|{1+2(alpha)(∆t)}