No, if you stood at one end of Earth's axis, you would not spin rapidly in place. The Earth's axis of rotation is an imaginary line that runs through the North and South Poles. When the Earth rotates, it spins around this axis, completing one full rotation in approximately 24 hours.
If you were standing at one of the poles, you would be located directly on the axis of rotation. This means that you would not experience any spinning motion at that point. Instead, you would essentially be rotating with the Earth, moving in a circle around the axis while remaining in the same position relative to the axis itself.
However, it's worth noting that the Earth's axis is not perfectly vertical. It has a slight tilt, which causes the changing seasons and variations in daylight hours throughout the year. Nonetheless, if you were standing precisely at one of the poles, you would not spin rapidly in place.