# Relationships/formulae relating to spinning disc

#### shinwarrior

Joined Apr 1, 2019
3
I am doing a project, but am struggling to find relationships or formulae between my dependent variables (angular velocity, displacement, acceleration of the disc and kinetic energy of the system) and my independent variables (falling masses and then the number of winds) or any other relationships that can occur. Below is a picture of my setup. It works by winding the disc, and then releasing it to unwind. The disc has two holes which the strings go through.

Thank you.

#### WBahn

Joined Mar 31, 2012
27,410
Since this is Homework Help, you need to show your best attempt to get as far as you can. That gives us a framework to help you move a bit further.

It will also help to know what your level of math is? Do you understand basic calculus, for example?

#### shinwarrior

Joined Apr 1, 2019
3
Since this is Homework Help, you need to show your best attempt to get as far as you can. That gives us a framework to help you move a bit further.

It will also help to know what your level of math is? Do you understand basic calculus, for example?
I do have a basic understanding of calculus (high-school level). I have searched online and understand the basic rotational movement equations that link together the angular displacement with angular velocity. I do not know how to approach how the masses falling off both sides impacts the rotational movement of the disc, and how the number of winds of the disc also effect its rotational movement.

#### WBahn

Joined Mar 31, 2012
27,410
I do have a basic understanding of calculus (high-school level). I have searched online and understand the basic rotational movement equations that link together the angular displacement with angular velocity. I do not know how to approach how the masses falling off both sides impacts the rotational movement of the disc, and how the number of winds of the disc also effect its rotational movement.
Do you have enough information to relate the number of turns to the height of the masses?

What are the types of energy that you can think of for this system?

You have a certain amount of energy in the system. If you assume that the system is lossless, then that energy is a constant.

#### RBR1317

Joined Nov 13, 2010
704
Can we assume this is a photo of the system in its zero-energy state? How do you measure the displacement of the weights from the zero state? Do you measure the rotational speed of the disc, or is that to be calculated?

#### shinwarrior

Joined Apr 1, 2019
3
Can we assume this is a photo of the system in its zero-energy state? How do you measure the displacement of the weights from the zero state? Do you measure the rotational speed of the disc, or is that to be calculated?
So the photo is the system at zero-state energy. I am going to measure the rotational speed of the disc by recording with a camera, but I was wondering whether it would be possible to calculate the angular velocity in order to match my experimental data with theoretical data?

#### WBahn

Joined Mar 31, 2012
27,410
So the photo is the system at zero-state energy. I am going to measure the rotational speed of the disc by recording with a camera, but I was wondering whether it would be possible to calculate the angular velocity in order to match my experimental data with theoretical data?
It would probably be easiest to estimate the angular velocity as the angular displacement between frames divided by the frame period.

Most other methods you might use would be doing the same basic thing, but probably averaging it over a period of time longer than you can tolerate for what you are doing.

#### WBahn

Joined Mar 31, 2012
27,410
So the photo is the system at zero-state energy. I am going to measure the rotational speed of the disc by recording with a camera, but I was wondering whether it would be possible to calculate the angular velocity in order to match my experimental data with theoretical data?
I've got a couple of concerns here. First, how much does the height of the disk itself change as the strings wind and unwind? Second, how many turns does it take to raise the weights an appreciable amount? Third, how linear is the relationship between number of turns and weight height. Fourth, how much energy is going to be lost in the friction of the twisted strings as they rotate and unwind?

Okay, more than a couple.

#### wayneh

Joined Sep 9, 2010
17,175
I've got a couple of concerns here. First, how much does the height of the disk itself change as the strings wind and unwind? Second, how many turns does it take to raise the weights an appreciable amount? Third, how linear is the relationship between number of turns and weight height. Fourth, how much energy is going to be lost in the friction of the twisted strings as they rotate and unwind?

Okay, more than a couple.
I don't think 2 and 3 matter, if this is supposed to be about energy conversion. What will matter is the mass of the disk and of course the weights. Measuring the damping that occurs - after the weights have fallen as far they can and unwound the strings, and then rewinds and raises the weights - should give an estimate of the overall losses.

#### WBahn

Joined Mar 31, 2012
27,410
I don't think 2 and 3 matter, if this is supposed to be about energy conversion. What will matter is the mass of the disk and of course the weights. Measuring the damping that occurs - after the weights have fallen as far they can and unwound the strings, and then rewinds and raises the weights - should give an estimate of the overall losses.
You may be right. If you are setting up the equations of motion they would matter because they are what tie the position of the weights to the position of the disk. But if you aren't looking to find the results as a function of time, you can probably get away with out that link.