What are the reasons behind the different period in vertical and horizontal circular motion? Why does hand-spinning a small mass in a vertical circular motion produces different period if the same mass is spun in a horizontal circular motion given that the radius, slotted mass are kept the same? 
I did the following 2 experiments and collected their period with the same150g slotted mass, 1m radius.
 where I hand spin a mass (red) that is attached to the same string with the slotted mass at the other end. I spin the mass by grabbing the hollow tube (blue). Same applies to horizontal. 


Now the period that I collected is $0.8s$ for horizontal circular motion and $0.7s$ for vertical circular motion. So my question is why do they produce a different or similar period?
Is there a mathematical reason to explain why this happens? What are the reasons/physics concepts behind the different period?
 A: Probably you horizontal and vertical frequencies are similar, so the the centripetal forces are similar, but since one is a constant frequency, the other is not, so why should the effect be the same. In the vertical case the velocity at the top can be very small, the velocity at the bottom you can calculate from $v_t^2/2+4gr=v_b^2$
For the horizontal motion you should not measure the string length, but the distance of the circling mass from your tube.
A: Gravity for sure has a play in this 
Mathematically when we have to find tension in a string during vertical motion we write
T-Mg=Mv^2/r
I.e acceleration at every point is changing so time period for such motion is difficult to determine
Case 2
In horizontal circle tension solely is responsible for acceleration 
T=mv^2/r
In this time can be calculated by 
T= 2 pi/ omega
A: If you wanna go, in a given time, from a point A to a point B, then A and B will be the farthest apart if you travel directly to B with constant velocity. Just so, if you travel with constant velocity on a circle (like in the horizontal trajectory), then, for a given time, you will have traveled the biggest angle possible. If you travel sometimes faster, sometimes slower (like in the vertical circular trajectory), then the distance traveled in that same time will be less and so the vertical trajectory takes more time. So your measurements are not accurate.
Maybe this begs the question of why traveling with constant speed in a given time takes you the farthest. but similar questions about this have been asked here. This question and its answers shine a light on this topic. It's Fermat's Principle. principle.
