a rod rotating about one end in a magnetic field has emf across its ends. but a rod rotating about its own axis has no emf.
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To measure the EMF between the axial point and the metallic circumference we have to take a certain point on the circumference. Now, draw a line each from the axial point and the chosen point on the circumference. Join them and connect a galvanometer in parallel. Observe carefully here, w.r.t the point on the circumference, as the rod moves, the area under the circuit changes. So, according to EMI, there is an induced EMF. The change in area is relative. According to you the area was constant because you didn't consider any circuit.
chlorineradicle:
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Because there is no flux change in the rod
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