A particle $P$, with mass $0.4\,\text{kg}$, travels at constant speed round a horizontal circle on the smooth inside of a fixed hollow hemisphere of radius $0.5\,\text{m}$ and centre $O$ (see diagram).
(i)[2]
With the particle speed at $4\,\text{m s}^{-1}$ and the angular speed at $10\,\text{rad s}^{-1}$, calculate the angle between $OP$ and the vertical.
(ii(a))[2]
If instead the magnitude of the force exerted on $P$ by the hemisphere is $6\,\text{N}$, calculate the angle between $OP$ and the vertical.
(ii(b))[3]
If instead the magnitude of the force exerted on $P$ by the hemisphere is $6\,\text{N}$, calculate the angular speed of $P$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies $4 = 10r$” …