Question 2 - A-Level Maths

A particle P of mass 0.6 kg is connected to a fixed point by a light inextensible string of length 2.8 m . The particle P moves in a horizontal circle as a conical pendulum, with the string making a constant angle of \(55 ^ { \circ }\) with the vertical.
1. Find the tension in the string.
2. Find the speed of P .
A turntable has a rough horizontal surface, and it can rotate about a vertical axis through its centre O . While the turntable is stationary, a small object Q of mass 0.5 kg is placed on the turntable at a distance of 1.4 m from O . The turntable then begins to rotate, with a constant angular acceleration of \(1.12 \mathrm { rad } \mathrm { s } ^ { - 2 }\). Let \(\omega \mathrm { rad } \mathrm { s } ^ { - 1 }\) be the angular speed of the turntable. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5bb02383-91c0-4454-aaea-0bd6af6ba325-3_517_522_870_769} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure}
1. Given that Q does not slip, find the components \(F _ { 1 }\) and \(F _ { 2 }\) of the frictional force acting on Q perpendicular and parallel to QO (see Fig. 2). Give your answers in terms of \(\omega\) where appropriate. The coefficient of friction between Q and the turntable is 0.65 .
2. Find the value of \(\omega\) when Q is about to slip.
3. Find the angle which the frictional force makes with QO when Q is about to slip.