Might one fall out of a basket swing? My nieces like being pushed high in a basket swing. My sister-in-law worries they will fall out.
Assuming I don't push them above horizontal, that I don't catch the basket and stop it mid-swing, and that they don't deliberately abandon ship, might they fall out?
I suspect not, because the same forces act on the "riders" as on the basket - that is, gravity acting downwards and tension in the ropes acting towards the pivot.  At any given position, whatever tendency the "riders" have to move in a given direction (including falling out when the basket is at its highest point), the basket will match.
Is that basically correct, or do I need to work on my physics as well as my child-care?
(This won't apply above horizontal, since both basket and occupant call fall, with occupant now beneath the basket.)
This is a basket swing:

Edit:
The basket is a large "part of a sphere" (don't know what that's called - shaped like a huge contact lens) - the diameter must be considerably more than a meter, and it easily accommodates two children with only the occasional foot protruding. Riding position is lying in the basket so CoG while inward of the basket, is only half-a-child-thickness inward.  It doesn't have a small "seat" like a normal swing, which one might topple off.
 A: For swing arcs of less than about +/- 60 degrees you ought to be OK, but beware of going higher. The extreme case, of course, occurs for a full 180 degree arc, and Mythbusters has that one covered. However, as you exceed 90 degrees peak, keep in mind that your daughter's center of gravity is radially inwards of the basket seat. When she starts back down, if you're using a flexible swing chain she will tend to fall, then when tension is restored to the chain she will be on the wrong side of seat. 
If she's holding onto the chain (as she will) and leans back during the climbing portion of the swing, she will tend to torque the chain between her hand and the seat, causing the outer portion of the chain to exceed horizontal at the top of the arc even for arcs of less than 90 degrees, and this will have the same effect. 
So, yeah, be a bit careful. Look especially for the condition where she experiences a "jerk" as she starts back down, and don't go any higher.
No matter how much she pleads.
