[The Sixth Blog] Circular Motion.

Circular motion can be observed in many instances of everyday life, such as in the blades of a ceiling fan as they spin or as a car makes a rounded turn.  However, today I will be discussing circular motion regarding something that generally can't be as commonly observed - a ferris wheel (this one was in Japan ^_^).  

There are several forces at work as the ferris wheel moves.  There is mg, which is always directed downward, F_N, which is perpendicular to the surface in contact (directed upward since people in the individual carts are sitting down...), and there is F_C, which is directed toward the center of the ferris wheel.  

Even though velocity (instantaneous velocity, tangent to circle) is unchanging, there is acceleration because the direction of motion is constantly changing.  Centripetal acceleration is equal to v²/r.

Since there is acceleration, we know that there must be some sort of unbalanced net force causing it, and that special force is known as centripetal force, which points toward the circle's center, as I have mentioned above.  At the top, F_C is equal to (mg - F_N), whereas at the bottom, it's equal to (F_N - mg).  We can also derive the equation for F_C because we know that 

F_net = ma and therefore F_C = m(v²/r).

We can even find angular values by knowing linear ones, 

ω = v/r (velocity) or α = a_T/r (acceleration). There is so much to learn from just a few values (plus all of these lovely physics equations, of course)! :]