A solid cylinder of mass \(2~\text{kg}\) and radius \(4~\text{cm}\) is rotating about its axis at the rate of \(3~\text{rpm}.\) The torque required to stop after \(2\pi\) revolutions is:
The moment of the force, \(\overset{\rightarrow}{F} = 4 \hat{i} + 5 \hat{j} - 6 \hat{k}\) at point (\(2,\)\(0,\)\(-3\)) about the point (\(2,\)\(-2,\)\(-2\)) is given by:
An automobile moves on a road with a speed of \(54~\text{kmh}^{-1}.\) The radius of its wheels is \(0.45\) m and the moment of inertia of the wheel about its axis of rotation is \(3~\text{kg-m}^2.\) If the vehicle is brought to rest in \(15\) s, the magnitude of average torque transmitted by its brakes to the wheel is:

\(\mathrm{ABC}\) is an equilateral triangle with \(O\) as its centre. \(F_1,\)\(F_2,\) and \(F_3\) represent three forces acting along the sides \({AB},\)\({BC}\) and \({AC}\) respectively. If the total torque about \(O\) is zero, then the magnitude of \(F_3\) is:
A uniform rod of length \(l\) and mass \(M\) is free to rotate in a vertical plane about \(A\). The rod, initially in the horizontal position, is released. The initial angular acceleration of the rod is: (Moment of inertia of the rod about \(A\) is \(\frac{Ml^2}{3}\))
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