1 A particle \(P\) moves along an arc of a circle with centre \(O\) and radius 2 m . At time \(t\) seconds, the angle POA is \(\theta\), where \(\theta = 1 - \cos 2 t\), and \(A\) is a fixed point on the arc of the circle.
- Show that the magnitude of the radial component of the acceleration of \(P\) when \(t = \frac { 1 } { 6 } \pi\) is \(6 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
\includegraphics[max width=\textwidth, alt={}, center]{2aaf3493-6509-4668-91a2-9f4708bbbb58-03_65_1573_488_324} - Find the magnitude of the transverse component of the acceleration of \(P\) when \(t = \frac { 1 } { 6 } \pi\).