Rotating coordinate system we define the vector F(t) = F_s(t)x + F_y (t) y + F_s(t)z. Let the coordinate system of the unit vectors x, y, z rotate with an instantaneous angular velocity Ω, so that dx/dt = Ωyz – Ω_zy, etc. 

(a) Show that dF/dt = (dF/dt)_R + Ω x F, where (dF/dt)_n is the time derivative of F as viewed in the rotating frame R.

(b) Show that (7) may be written (dM/dt)_R = γM x (Ba + Ω/γ). This is the equation of motion of M in a rotating coordinate system. The transformation to a rotating system is extraordinarily useful; it is exploited widely in the literature. 

(c) Let Ω = – γB₀z; thus in the rotating frame there is no static magnetic field. Still in the rotating frame we now apply a dc pulse B₁x for a time t. If the magnetization is initially along 9, find an expression for the pulse length t such that the magnetization will be directed along – z at the end of the pulse. (Neglect relaxation effects.) 

(d) Describe this pulse as viewed from the laboratory frame of reference.