Answer
Horizontal static frictional force causes centripetal acceleration.
Work Step by Step
Three forces acting on the child are the downward force of gravity (i.e., weight), the normal force up from the saddle, and a horizontal static frictional force from the seat. It is the last force that provides the centripetal acceleration for the child.
There might be other forces that can provide a horizontal component, such as contact forces between the child’s legs and the horse’s flank, or the child’s hands and the vertical pole. These can also contribute to providing the child’s centripetal force.
