How does radius affect frequency in uniform circular motion?

[Tannerbobanner]

I am writing a lab report on the effect of the radius of a string on the frequency of rotation on an object in horizontal uniform circular motion.

My hypothesis is:
If the radius of the string from the origin of rotation increases, then the frequency will decrease because frequency has an inverse relationship to the radius.

I have gathered the following results from the experiment and comparing it to the theoretical this is the graph.

I am trying to write a conclusion explaining why my hypothesis remained true other than the relationship between them in the equation:

So my question is, does anyone know about centripetal force and may be able to help me explain my results other than this relationship. If you want a copy of my lab let me know.

 

[berkeman]

Welcome to the PF.

How was the object constrained to move in a circle? Was it on a frictionless flat surface? How was the circular motion started and maintained? How was the length of the string changed (like was it pulled down through a hole in the center of the frictionless table?

It seems like there is something else that can influence the speed of rotation, even with the same string length. After all, you can spin a ball around on a string at various speeds without changing the length of the string. It seems like you would need to define how the mass got to that spinning speed somehow, no?

 

[Tannerbobanner]

Welcome to the PF.

How was the object constrained to move in a circle? Was it on a frictionless flat surface? How was the circular motion started and maintained? How was the length of the string changed (like was it pulled down through a hole in the center of the frictionless table?

It seems like there is something else that can influence the speed of rotation, even with the same string length. After all, you can spin a ball around on a string at various speeds without changing the length of the string. It seems like you would need to define how the mass got to that spinning speed somehow, no?

Here is a link to my lab: https://files.fm/u/v347hgn5#/
Basically, A rubber stopper was connected to a string, which ran through a glass tube that I would hold on to and the tension came from a mass hanging below and I would swing it and count revolutions for trials.

 

[ZapperZ]

I am writing a lab report on the effect of the radius of a string on the frequency of rotation on an object in horizontal uniform circular motion.

My hypothesis is:
If the radius of the string from the origin of rotation increases, then the frequency will decrease because frequency has an inverse relationship to the radius.

I have gathered the following results from the experiment and comparing it to the theoretical this is the graph.
View attachment 223774
I am trying to write a conclusion explaining why my hypothesis remained true other than the relationship between them in the equation:
View attachment 223775
So my question is, does anyone know about centripetal force and may be able to help me explain my results other than this relationship. If you want a copy of my lab let me know.

Did you do a circular motion experiment similar to this:

https://www.thephysicsaviary.com/Physics/Programs/Labs/ClassicCircularForceLab/index.html

Zz.

 

[berkeman]

Here is a link to my lab: https://files.fm/u/v347hgn5#/

Could you save it as a PDF? Many folks are reluctant to download a DOCX file. Once it is in PDF format, you can use the Upload button at the lower right to Upload it to the PF as an attachment to your post. Thanks.

 

[Tannerbobanner]

Did you do a circular motion experiment similar to this:

https://www.thephysicsaviary.com/Physics/Programs/Labs/ClassicCircularForceLab/index.html

Zz.

Exactly, however the mass swinging was constant at 0.03kg and the mass below was constant with 0.2kg and I changed the radius of the string.

 

[Tannerbobanner]

Here it is, note: background information was not required as it is due two days after it was assigned, aka tommorow :)

 

[ZapperZ]

You need to show that you know how to draw the free-body diagram of the system, and then to write down the forces involved.

Zz.

 

[Tannerbobanner]

You need to show that you know how to draw the free-body diagram of the system, and then to write down the forces involved.

Zz.

Could you elaborate a little bit, and where would the proper place to put a diagram be in a lab formatted like so?

 

[ZapperZ]

Could you elaborate a little bit, and where would the proper place to put a diagram be in a lab formatted like so?

I don't know. I'm not addressing your lab report. I'm addressing your understanding of the physics. You asked for the explanation of your result. I'm not sure if you know how that equation came about, and why you'd even make a linear fit to the data.

Zz.

 

[Tannerbobanner]

I don't know. I'm not addressing your lab report. I'm addressing your understanding of the physics. You asked for the explanation of your result. I'm not sure if you know how that equation came about, and why you'd even make a linear fit to the data.

Zz.

I understandthe F_g of the mass hanging below the glass tube is the centripetal force and the glass tube is acting as a pully, what I don't understand is how if an object is closer to it's origin of rotation why it spins faster or why more velocity is required etc...

 

[berkeman]

Are you familiar with the equations of uniform circular motion? How is the centripetal force related to angular velocity?

 

[ZapperZ]

I understandthe F_g of the mass hanging below the glass tube is the centripetal force and the glass tube is acting as a pully, what I don't understand is how if an object is closer to it's origin of rotation why it spins faster or why more velocity is required etc...

Actually, in the equation that you typed, the hanging mass is F_T.

The frequency f is not proportional to 1/r, but rather 1/√r. Look again at that equation.

If you want to do a curve fit to your data, you should fit it to such a function, i.e. something of the form k/√r, where k is the fitting parameter.

If you don't know how to do that in Excel (it appears that you are using that based just looking at your graph), then you can do a linear curve fit, but you have to plot f² versus 1/r instead.

Zz.

 

[Tannerbobanner]

Are you familiar with the equations of uniform circular motion? How is the centripetal force related to angular velocity?

I'm aware of the three centripetal force/acceleration equations and everything that comes before that in physics.

 

[Tannerbobanner]

Actually, in the equation that you typed, the hanging mass is F_T.

The frequency f is not proportional to 1/r, but rather 1/√r. Look again at that equation.

If you want to do a curve fit to your data, you should fit it to such a function, i.e. something of the form k/√r, where k is the fitting parameter.

If you don't know how to do that in Excel (it appears that you are using that based just looking at your graph), then you can do a linear curve fit, but you have to plot f² versus 1/r instead.

Zz.

That was an error on my part, your correct it is 1/√r.

 

[Tannerbobanner]

I really just need a basic explanation of why this trend persists not from a numerical point of view but a scientific point of view, why when it's closer it's faster and why when it's further it's slower so I can then compare the experimental data to the theoretical data and reference my percentage error. That's what I'm trying to do in the last two paragraphs of my lab, however, I cannot find a way of wording it in reference to my hypothesis and then the data independently. That is what I need help with.

 

[berkeman]

I'm aware of the three centripetal force/acceleration equations

Write those out, and look for the relationship between the string radius and the angular speed, given the same tension in the string...

 

[Tannerbobanner]

Write those out, and look for the relationship between the string radius and the angular speed, given the same tension in the string...

Agh, I have to go study for calculus tommorow, thanks for the help. If you think of anything let me know