# Centripetal Force and Uniform Circular Acceleration

I am in need for some help for a lab report. The issue has happened because there is a lab of 20 students that is being led by a recently retired NASA physicist trying to lead a team of graduate student (or camel jockeys as he puts it) and the lab instructions are being botched horribly. Attached are some photos of diagrams that I have created along with data sheet that was provided in the lab. Can someone let me know if I am at least on the correct path and what the variables that I have pulled from my textbook correlate to with regard to the data sheet provided? Also, the writing and calculations on the data sheet are not my own, I am just using it to give an example of what I am confused of. Thank you.

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## Answers and Replies

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Simon Bridge
Science Advisor
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OK - I've looked at all three attachments and I have a fair idea of what is being attempted here. The best place for you to start is by describing the apparatus and how it operates using words.

i.e. it appears to be a turntable with a pendulum suspended from the edge - the pendulum bob is attached to the axle by a spring. As the turntable revolves - the bob swings away from the axle until what happens? (In terms of the tension in the string and the restoring force of the spring.)

How is the apparatus used in the experiment?
What is the aim of the experiment?

Well if you are getting at Hooke's Law and the spring's constant increasing at a linear rate until the spring cannot stretch anymore, I do not believe that that is it...

The procedure for the experiment went somewhat like:
1) Measure radius with spring disconnected to get an initial radius, then move the place marker 1/2*r away from the initial position (not shown in the pictures due to it being a benchmark stage)
2) Attach the spring between the hanging mass and the rotational shaft on one side, and on the other side attach a string, which is placed over a pulley so that you may visualize the tension force required to stretch the spring to the point [r+(1/2*r)].
*Now that I look at this, the tension force that I had of T=0.820N is incorrect as that was simple the weight, and the new tension force is T=8.24N
3) Detach the weighted string and return the mass to the initial position (spring still attached)
4) Rotate the shaft until the centripetal force is equal to that that of the radius [r+(1/2*r)]. Using a stopwatch, record the time it takes for the apparatus to rotate 50 rotations.

After this, I know that I need to calculate the rotation rate by dividing the average time by 50, then multiple the rotation rate by 2π in order to get ω. This is where I begin to get confused. I am confused in how to make a correlation in between the tension force exhibited by centripetal force and the weighted force that is measured by the benchmark at the beginning of the lab.

On a separate note, thank you for you quick response.

I forgot to answer your last two questions, although I am sure that you can probably extract that information from the procedure.
1) The apparatus is to spin the hanging weight, while a spring connects it to the rotating shaft, to measure the rotation rate after 50 revolutions.
2) The aim is supposed to display to relationship between the tension force required to stretch the spring from Xo to Xo+the displacement of the mass due to centripetal force, ultimately to find the percentage of error and circular acceleration of the mass.

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Simon Bridge
Science Advisor
Homework Helper
Well if you are getting at Hooke's Law and the spring's constant increasing at a linear rate until the spring cannot stretch anymore, I do not believe that that is it...
That's not what I'm getting at, no. I actually meant exactly what I said: you should proceed by describing the experiment in simple terms, using words (as opposed to math), and answer the questions. Which you did below:
I forgot to answer your last two questions, although I am sure that you can probably extract that information from the procedure.
1) The apparatus is to spin the hanging weight, while a spring connects it to the rotating shaft, to measure the rotation rate after 50 revolutions.
2) The aim is supposed to display to relationship between the tension force required to stretch the spring from Xo to Xo+the displacement of the mass due to centripetal force, ultimately to find the percentage of error and circular acceleration of the mass.
OK - so the answer to question 2. was
"The aim of the experiment is to verify the relationship between angular velocity and centripetal acceleration."

To do this you need two independent ways to get the centripetal acceleration.
One you get from the circular motion theory, which you are testing; and the other you get from a more reliable direct method, which has already been well established - like Newton's force law.

The method was to suspend a pendulum from a turntable.
You measure the angular speed and the radial displacement of the pendulum bob.

The radial displacement tells you the centripetal force.

To make the calculation easier - you are spinning the turntable+pendulum so a pre-chosen radial displacement has been produced. This is one where you have measure the force already ... that's what the mucking about with a spring was about.

Initially I thought you were spinning the whole thing with both string and spring attached.
Now I don't think you were supposed to do that so if you did, you have made some extra work for yourself.