1. The problem statement, all variables and given/known data An amusement park ride consists of a ring of radius A from which hang ropes of length l with seats for the riders as shown in Figure I. When the ring is rotating at a constant angular velocity, omega, each rope forms a constant angle, theta, with the vertical as shown in Figure II. Let the mass of each rider be m and neglect friction, air resistance, and the mass of the ring, ropes, and seats. (A picture is given here on page five: www.swcp.com/~gants/calendars/ap%20physics/sept%20docs/(A)%20Newton's%20LawsC.doc) Determine the minimum work that the motor that powers the ride would have to perform to bring the system from rest to the constant rotating condition of Figure II. Express your answer in terms of m, g, l, theta, and the speed v of each rider. 2. Relevant equations Work=change in kinetic energy work=force*displacement force=m*a(centripetal) 3. The attempt at a solution I know that the force causing centripetal motion is tension. F(net, x) = m*a(centripetal) = T * sin (theta) F(net, y) = T*cos(theta) - m*g T = m*g*sec(theta) force = m*a(centripetal) = m*g*tan(theta) displacement = L * sin(theta) W = force*displacement = (m*g*tan(theta))*(l*sin(theta)) delta(KE)=1/2*m*(v(final))^2-1/2*m*(v(initial))^2, since v(initial)=0, W = delta(KE) = 1/2*m*(v(final))^2 So I have two separate equations for work. Have I done something incorrectly?