Standard +0.3 This is a standard circular motion problem requiring resolution of forces (normal reaction, friction, weight) and application of F=mrω². The setup is clearly defined with given values, and the solution follows a routine method: equate vertical forces (friction = weight) and horizontal forces (normal = centripetal force), then divide to find μ. Slightly above average difficulty due to 3D force resolution and combining circular motion with friction, but still a textbook exercise with no novel insight required.
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\includegraphics[max width=\textwidth, alt={}, center]{8a7016eb-4e76-4104-aa00-fbf09e1d739a-02_560_421_258_861}
A hollow cylinder with a rough inner surface has radius 0.5 m . A particle \(P\) of mass 0.4 kg is in contact with the inner surface of the cylinder. The particle and cylinder rotate together with angular speed \(6 \mathrm { rad } \mathrm { s } ^ { - 1 }\) about the vertical axis of the cylinder, so that the particle moves in a horizontal circle (see diagram). Given that \(P\) is about to slip downwards, find the coefficient of friction between \(P\) and the surface of the cylinder.
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\includegraphics[max width=\textwidth, alt={}, center]{8a7016eb-4e76-4104-aa00-fbf09e1d739a-02_560_421_258_861}
A hollow cylinder with a rough inner surface has radius 0.5 m . A particle $P$ of mass 0.4 kg is in contact with the inner surface of the cylinder. The particle and cylinder rotate together with angular speed $6 \mathrm { rad } \mathrm { s } ^ { - 1 }$ about the vertical axis of the cylinder, so that the particle moves in a horizontal circle (see diagram). Given that $P$ is about to slip downwards, find the coefficient of friction between $P$ and the surface of the cylinder.\\
\hfill \mbox{\textit{CAIE M2 2017 Q1 [4]}}