pivot on something
to rotate on something; to spin around, centered on something. This part spins around and pivots on this little red spot, which is what they call a jewel. If the lever will not pivot on the bar, it needs some lubrication.
pivot onor pivot around
1. To rotate or spin around while remaining centered on some point: The chair pivots on a steel post.
2. To depend on something or someone for success or failure: This business deal pivots on whether or not we are willing to change the name of our product.
3. To develop from a central idea: The plot of the show pivots on the effects of drug addiction.