1 A particle \(P\) is moving in a circle of radius 2 m . At time \(t\) seconds, its velocity is \(( t - 1 ) ^ { 2 } \mathrm {~m} \mathrm {~s} ^ { - 1 }\). At a particular time \(T\) seconds, where \(T > 0\), the magnitude of the radial component of the acceleration of \(P\) is \(8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). Find the magnitude of the transverse component of the acceleration of \(P\) at this instant.
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A uniform square lamina \(A B C D\) of side \(4 a\) and weight \(W\) rests in a vertical plane with the edge \(A B\) inclined at an angle \(\theta\) to the horizontal, where \(\tan \theta = \frac { 1 } { 3 }\). The vertex \(B\) is in contact with a rough horizontal surface for which the coefficient of friction is \(\mu\). The lamina is supported by a smooth peg at the point \(E\) on \(A B\), where \(B E = 3 a\) (see diagram).
- Find expressions in terms of \(W\) for the normal reaction forces at \(E\) and \(B\).
- Given that the lamina is about to slip, find the value of \(\mu\).