Answer to Question 2 

A motor takes a current I, and the armature is placed in a magnetic field for flux density B. The armature has N turns and is of length l and width w, rotating at a frequency f. Show that the equations P = Fv and P = tw are consistent. What is the final relationship between power and angular velocity? 

Using P = Fv: F = NBIl v = 2p × w/2 × f = 2pwf P = NBIl × 2pwf
Since A = wl, we can write: P = BANI × 2pf Since w = 2pf, we can write: P = BANIw 
Using P = tw t = BANI By definition: w = 2pf We can combine the two to give: P = BANIw 
The two results are the same, so each relationship is consistent with the other. The final relationship is P = BANIw or P = 2pBANIf 