You want to use a scroll view. Specifically you want a hidden scroll view where you attach the pan gesture recogniser from the scroll view to your custom menu view. Then you implement the delegate methods of the scroll view to redraw your menu. This WWDC video has a good overview of the process. The benefit of this approach is that you get true iOS style acceleration and deceleration for free. You don't need to worry about finger position or speed, only the content offset of the scroll view.
Unless you want to spin your finger round in a circle with the menu items. That's a different ball game...
In theory, the same approach as above can be used for spinning your finger in a circle. You would need to ensure that directionalLockEnabled
was set to NO on the scroll view. The problem is that the calculations to determine the rotation of your menu view are a lot more complex. Probably you would want to be modal and check if the scroll view is dragging
in the callbacks. If it is dragging you would use the touches on the pan gesture to find the exact finger location to set the rotation. You'd also want to maintain data on the instantaneous direction of finger movement so that when the touch is released... If it isn't dragging then you use the scroll view content offset to apply the deceleration effect on the rotation (using the scroll direction just before the touch was released to know how to use the content offset changes).