Mechanical problem is very likely, but if not, then I would guess dried
out electrolytic caps. Although there aren't as much cap problems in
60's turntables as in today's motheroards :-) But 40 years may be too
much for some of them..

If the motor runs on dc, and mechanics naturally have more "resistance"
on the point where it jams, it increases the load and the ripple
voltage increases on that point, and the motor doesn't get enough
effective voltage to work.

This is, however, just a kind of hypothesis, and actually an unlikely
reason if there isn't other symptoms (e.g. humming noise on output etc.)