A rough horizontal disc turns about a fixed vertical axis that goes through its centre. A particle $P$ of mass $0.2\,\text{kg}$ stays in contact with the surface and, without slipping, moves with the disc at a distance of $0.5\,\text{m}$ from the axis. The largest speed of $P$ for which this motion can occur is $1.5\,\text{m s}^{-1}$.
(i)[2]
Calculate the coefficient of friction for the disc and $P$.
(ii)[5]
Find the greatest and least values of $\omega$ for which this motion is possible.
(iii)[2]
Calculate the value of $\omega$ at which the disc exerts no frictional force on $P$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies Newton’s second law with centripetal acceleration: $\dfrac{0.2\times1.5^2}{0.5}=F_r$” …