(i) An inertial frame has orthonormal coordinate basis vectors . A second frame rotates with angular velocity relative to and has coordinate basis vectors . The motion of is characterised by the equations and at the two coordinate frames coincide.
If a particle has position vector show that where and are the velocity vectors of as seen by observers fixed respectively in and .
(ii) For the remainder of this question you may assume that where and are the acceleration vectors of as seen by observers fixed respectively in and , and that is constant.
Consider again the frames and in (i). Suppose that with constant. A particle of mass moves under a force . When viewed in its position and velocity at time are and . Find the motion of the particle in the coordinates of . Show that for an observer fixed in , the particle achieves its maximum speed at time and determine that speed. [Hint: you may find it useful to consider the combination .]