2.
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\caption{Figure 1}
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A hockey stick is modelled as a uniform rod \(O A\) of length \(14 r\) joined to a uniform semicircular arc \(A B\) of diameter \(2 r\), as shown in Figure 1. The rod and the arc lie in the same plane and are made of the same material.
- Find, in terms of \(\pi\) and \(r\), the distance of the centre of mass of the hockey stick from the line \(A B\).
The hockey stick is freely suspended from \(O\) and hangs in equilibrium.
Given that the centre of mass of the hockey stick is a distance \(\frac { \pi r } { ( 14 + \pi ) }\) from \(O A\), - find, in degrees to 3 significant figures, the angle between \(O A\) and the vertical.
[0pt]
[Question 2 Continued]