1. A disc, of mass \(m\) and radius \(r\), rotates about an axis through its centre, perpendicular to the plane face of the disc. The angular speed of the disc is \(\omega\).
A possible model for the kinetic energy \(E\) of the disc is $$E = k m ^ { a } r ^ { b } \omega ^ { c }$$ where \(a\), \(b\) and \(c\) are constants and \(k\) is a dimensionless constant.
Find the values of \(a , b\) and \(c\).