# Experimental set up of vertical circular motion

We are trying to do the following experiment: http://farside.ph.utexas.edu/teaching/301/lectures/node90.html.

At the moment, here is the experimental setup:

We have a rod 0.4 m long which rotates about 0.1 m from from one end and we have attached a mass at the longer end of the rod from the axis.

So, what we are basically trying out is to measure the minimum velocity required to be provided to the mass while it is resting at the bottom so that the rod completes a full circle, rather "loop the loop".

However,here are some of our objections:

1. We found the expression of initial velocity required to "loop the loop" and it was independent of mass (not really surprising). It was the same expression that was given in the website mentioned above. But in their case the rod was massless. Practically that is never possible.

So what we thought was, instead of attaching an additional mass(bob), why can't we use the rod without the mass(bob)?

(since it has a mass of its own) To resolve this issue what we did was the following:

1. What are we losing out on if we place the rod so that it rotates about the center of rotation at a point 0.1 m from the end of the rod instead of the center of rotation being the end of the rod?
• So what's the question here? You've correctly shown that the starting velocity is independent of mass (but of course the initial energy required does depend on mass)). If you have a non-massless rod and the rotation is not about the end of the rod, then the "upper" section opposes the "lower" section, so adjust your angular momentum equations accordingly. – Carl Witthoft Oct 8 '14 at 11:47
• That doesn't sound right. If you have a rod with mass, then adding a mass at the end of it should change the velocity with which you hit the (end of the) rod in order to make it loop the loop. This is because the center of mass needs enough speed to make it all the way around - and when the center of mass changes position, that means the velocity of the rod will have to change too... can you show your derivation? – Floris Oct 8 '14 at 12:45

You just have to make sure you hit the center of mass to give it a velocity you need, irrespective of the position of the pivot, whether it is at the end of the rod or 0.1m away from it. If you hit the center of mass of the rod and make it move with a velocity that is just enough for it to reach the vertical position above the pivot, that velocity will be independent of the mass of the rod.

P.S: What are you going to do about the friction present at the pivot ? If you want greater precision (if you're taking measurements), I suggest you take rods that are as long as possible and their masses as less as possible for your experiment. That would make the effect of friction on the motion of the rod minimal.

• Duuude, you can't reduce the friction! What will the students do when they need some "fudge factors" to explain why their data don't match the theory? :-) – Carl Witthoft Oct 8 '14 at 15:41
• Haha! Atleast they're taking experiments seriously. :D – Gaurav Oct 10 '14 at 4:39