Ferris Wheel Physics

## Question:

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.

## Answer:

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.