3 The kinetic energy, \(E\), of a compound pendulum is given by
$$E = \frac { 1 } { 2 } I \omega ^ { 2 }$$
where \(\omega\) is the angular speed and \(I\) is a quantity called the moment of inertia.
3
- Show that for this formula to be dimensionally consistent then \(I\) must have dimensions \(M L ^ { 2 }\), where \(M\) represents mass and \(L\) represents length.
[0pt]
[2 marks]
3 - The time, \(T\), taken for one complete swing of a pendulum is thought to depend on its moment of inertia, \(I\), its weight, \(W\), and the distance, \(h\), of the centre of mass of the pendulum from the point of suspension.
The formula being proposed is
$$T = k I ^ { \alpha } W ^ { \beta } h ^ { \gamma }$$
where \(k\) is a dimensionless constant.
Determine the values of \(\alpha , \beta\) and \(\gamma\).