Vertical circular motion experiment - feasible? I am thinking of comparing horizontal to vertical circular motion. I think I want to compare (both experimentally and mathematically) the constant tension of horizontal to the varying tension of the vertical circular motion. 
Here is a concept idea of the experiment:

It is the same as your generic high school circular motion experiment except for this time I hand spin the mass vertically instead of horizontally. 
So my questions: Is the slotted mass responsible for the centripetal force in vertical circular motion? How can I calculate the initial velocity of the mass? Given the small mass ($25\ \mathrm g$), the mass of the slotted mass ($150\ \mathrm g$), radius ($1\ \mathrm m)$ and period ($0.7$) available. 
Also is this a good experiment to do (constant tension vs varying tension)? What variables should I change instead? 
 A: The biggest problem will be making any practical measurement with the vertical plane rotation. The tension in the string will no longer be constant, as you clearly understand, but that means that the hanging slotted weight (m) will never balance the tension (well, actually it will 'balance' at two specific angles, bjut that is like saying that a stopped clock is correct twice a day). 
So during each 2Pi rotation the tension will either be greater than mg, so the weight will accelerate upwards, or will be less than mg, and the weight will accelerate downwards. Measuring the motion of a weight where it's acceleration is varying continuously will be difficult if at all practical. In fact it isn't clear to me that you will have any sort of equilibrium (as you do in the horizontal experiment) - I believe that it is likely that at any constant rotation rate the hanging mass will either drop to the floor or will accelerate upwards until it hits the 'blue' box in your diagram. 
In practice, it might be better to replace the hanging mass with a spring balance where, with care you could at least measure the maximum tension in the string as a function of rotational velocity and radius of rotation. Alternately, if you want to keep the hanging mass (or if that is all you have to use) one nice experiment is to drop the rotating mass from various heights (and with varying string length) to see at combinations of drop height and arc radius provide sufficient tension to 'just' lift the slotted weight as the rotating mass reaches the bottom of its arc. (see sketch below). Of course that makes it a very different experiment to the horizontal rotating mass experiment. 

Just calculating the dynamics of the vertical rotating system (with hanging mass) might have some fairly challenging maths involved. But I think you have the right research spirit to go a long way at whatever you try. 
A: From the diagram below, how does the newton's 2nd law equation change from top to bottom of the motion? (with mv^2, r and T). Whilst the slotted mass's weight will indicate the tension, the overall resultant force changes because of the mass of the object you are rotating is either added or taken away from the tension. 
You should have the time period for a specific number of rotations, when you measure this, you can then caculate the angular velocity. Then you should be able to move on to calculating the velocity.
Exactly, what is the scientific question you are trying to address? You should try to write in in the format 
How does x affect y when a,b and c are constant?
For example "How does the tension on a string affect the angular velocity of a rubber bung in circular motion if the radius is kept constant?"
"How does vertical circular motion of a rubber bung affect the centripetal force acting on it if the length of the string is kept constant?"
Once you have an idea of this, you can build a mathematical model, put some equations to it, take you measurements, plot them on a suitable graph and then develop a conclusion and evaluation. 
I am speaking as an A Level UK teacher. 

