1. The problem statement, all variables and given/known data A person enters a curve of a waterslide with velocity v. The curve is fully horizontal and has the shape of a circle segment of radius R, there is no friction and width of the curve can be neglected for calculating the centripedal force. The waterslide itself can be described as a semi circle with radius r. The question is to describe the tangential equation of motion for the angle a the person in the slide. We must than linearise this equation of motion with the small angle approx for sin and cos. 2. Relevant equations F(centripedal)=mv^2/r 3. The attempt at a solution The only forces acting are g and the normal force. Since the person is travelling in a circle of radius R with speed v there must be a centripedal force of mv^2/R (problem: the motion is not really circular since the person also has tangential movement in the slide). This centripedal force is horizontal so it cannot stem from gm -->it must come from the normal force. The horizontal component of the normal force is sin(a) N= aN=mv^2/R. The remaining force acting on the person is the vertical componenet of N and g =( mv^2/(Ra))-gm. The tangential component of this force is (mv^2/Ra)-g)sin a=(mv^2/Ra)-gm)a). This component is equal to a''mr. This gives a''=v^2/Rr-ga/r.