I'm going to consider the situations of standing on the North Pole or standing on the equator in terms of ones velocity and momentum.
Starting with North Pole (and pretending there is no 'wobble' of the Earth as it rotates on it's axis), we are not actually moving in any direction at all; all of our motion is in the form of rotation around a stationary point. We have 'circular motion', but no linear velocity. Our momentum is all of the 'angular' kind, and none of the linear. There are no centrifugal or centripetal forces acting on us, giving tendancy to fly of in a linear pathway in any direction. The momentum we have all acts to keep us spinning on the spot (as it were) until brought to rest by friction.
Standing at the equator thngs are somewhat different - and the same. If I'm thinking right, our motion can be broken down into two elements - linear and rotational. In the case of our rotational motion, it is effectively exactly the same as if we were standing on the Pole; we execute a single 360 degree turn in any twenty four hour period and thus our angular momentum must be equal to that if we were standing on the Pole. In respect of our velocity, however, things are different. Where at the Pole we had no linear velocity (we did have angular however) on the equator we do), but as velocity is a vector (ie it has both direction and magnitude) our velocity is constantly changing. I believe that any form of change in velocity is thought of in terms of acceleration or deceleration, and if memory serves me, in the case of standing on the equator we would be considered to be in a constant state of acceleration toward the central point at which the motion was proceeding around, ie the centre of the Earth. So in moving from the Pole to the equator we essentially go from a linear velocity of zero to that of (at any instant) about one thousand miles per hour (the approximate circumference of the Earth divided by the number of hours it takes to perform one revolution) gaining the instantaneous pinpoint linear momentum given by our mass times our (linear) velocity at the point we happen to take the measurement along the way. Our angular velocity and momentum however remains unchanged at all times.
Presumably this increase in momentum and velocity as we move out from Pole to Equator is 'bought' from the work that has to be done in increasing our distance from the center of gravity of the Earth: effectively buying potential energy as we do so. No - something is wrong here; that potential energy would have to be 'swoppable' with kinetic energy,...... so where is the energy of the linear velocity/momentum bought from? It can't be the angular momentum because this stays exactly the same at equator as t pole.
And here, my friends, is the point where ratiocination grinds to a standstill for me.....
If you can take it further I'd be interested to see it done!
Edit; I think the energy of your linear acceleration/momentum must be 'bought' from the ever so slight shift in the mass of the Earth away from the central axis of spin toward the equator that your move would cause. By extrapolation of this idea, I reckon that in moving from the Pole to the equator, you probably cause the Earth to slow down in respect of it's spin, ever so slightly - something in the manner of a ballet dancer raising her arms while spinning and thereby slowing down her spin rate in co doing?