Ferris Wheel Physics


Hi there,

I have been trying to solve a question on the motion of passengers on a big wheel where centripetal acceleration is demonstrated.

I know that at the top and the bottom of the Ferris wheel the tension in the string is different - at the top the wheel the centripetal acceleration is in the same direction as the weight force, at the bottom the centripetal acceleration is in the opposite direction to the weight force. I know the centripetal force always points into the centre of the circle, what I don't know is :
Does the tension always point into the centre - Yes or No ?Please satisfy my curiosity.


The mental image I have of the problem is of a person sitting in one of the chairs suspended at the rim of a Ferris wheel. The wheel is rotating in the vertical plane carrying the person up one side, over the top and down the other side to the bottom at a constant angular speed w. It is correct that the centripetal acceleration is always pointed at the center of the wheel. That is the acceleration required to move the person in a circular path, as opposed to her natural tendency to move in straight lines. The other component of acceleration acting on the person is gravity which always acts downward. At the top of the wheel, assuming normal Ferris wheel behavior, the force of gravity is sufficient to curve the persons path with some left over to hold her against the seat. At the bottom of the wheel the seat must provide both sufficient force to support the person's weight and that required to curve the path. So the force of the seat on the person is maximum at the bottom of the wheel. The "tension" you speak of is the force keeping the person at a more or less fixed radius from the centre of the wheel. Unless the wheel is spinning fast enough to fling the seat to its outermost extremity, carrying the person over the top of the wheel upside down, the force is not a tension. In fact the force holding the person to the seat is the person's mass times the vector difference of centripetal and gravitational acceleration. Only at the top and bottom of the wheel does this vector difference lie along a radius of the wheel. On the sides of the wheel it points somewhat outward of down.