Ok, so I will do my best to address each person's comment the best I can.
But, perhaps to start, I thought a visual example might be helpful to explain what I've seen before. I know there is a whole lot more going on with the physics on this example but I'm hoping the general idea will be seen. When we see gymnasts doing 'giants' on a high bar...
...it can be seen that they slow down at the top of their swing. In a thought experiment too - if one was to pump your legs hard enough on a playground swing and you could avoid having the chain becoming slack and falling down, one could swing so hard that you'd go right around. But, just beyond the minimum speed you would likely be slower at the top then speed up at the bottom. Of course, in this scenario you would need a different mechanism where the chains attach so they wouldn't wrap around.
kuruman said:
Your diagram is faulty. You show two external forces, tension T (blue) and weight W (green). OK. Then you show net force FNet in red. Not OK. The net force must be the vector sum of the blue and green arrows, reasonably drawn to scale. It is not.
For this diagram, I tried to think about the 2D vector addition and how long the Fnet would be. Though my scales are approximate I know it's not perfect. But the Fnet is supposed to be the sum of T and W is either is translated to the tip of the other.
kuruman said:
At the due North position again you show no red arrow. Why not?
I know also that I didn't draw in the Fnet for all positions of the rotating object (N, S, E, and W) But certainly these could be shown too. The only two which I'd think would
not assist or resist would be the N and S.
vanhees71 said:
I think with "vertical circular motion" you mean a pendulum.
I think vanhees71 may be onto something here, but the math is something I'd need to brush up on or learn. Apologies, I teach at the high school level and it's been awhile. :)
A.T. said:
On
this document practice problem #1talks about a ball swung in a vertical circle at 5 m/s. And on
this page if one searches for the word 'constant' it appears four times with the context being vertical circular motion and objects going at a constant speed.
Chestermiller said:
Let's see your Newton's 2nd Law equations for this.
Sorry Chestermiller, I wasn't sure what you were wanting for this. Maybe I could analyze one or two of the positions on the path to show this. I'll try to put this together.