Write down the dimensions of velocity, force and density (which is mass per unit volume).
A vehicle moving with velocity \(v\) experiences a force \(F\), due to air resistance, given by
$$F = \frac { 1 } { 2 } C \rho ^ { \alpha } v ^ { \beta } A ^ { \gamma }$$
where \(\rho\) is the density of the air, \(A\) is the cross-sectional area of the vehicle, and \(C\) is a dimensionless quantity called the drag coefficient.
Use dimensional analysis to find \(\alpha , \beta\) and \(\gamma\).
A light rod is freely pivoted about a fixed point at one end and has a heavy weight attached to its other end. The rod with the weight attached is oscillating in a vertical plane as a simple pendulum with period 4.3 s . The maximum angle which the rod makes with the vertical is 0.08 radians. You may assume that the motion is simple harmonic.
Find the angular speed of the rod when it makes an angle of 0.05 radians with the vertical.
Find the time taken for the pendulum to swing directly from a position where the rod makes an angle of 0.05 radians on one side of the vertical to the position where the rod makes an angle of 0.05 radians on the other side of the vertical.