Uniform Circular Motion

Introduction:

In order to achieve uniform circular motion, the radius of the circle must be constant, speed of the object must be constant and there must be a constant inward acceleration. Although the velocity of the object is constantly changing, it's velocity is always tangent to the circular path it is moving on. In ordert o prevent an object from moving straight, a constant inward force is needed to move it in a circle. This centrapetal force can be determined by the equation F = 4π^2 r m f^2 where it is affected by the circle radius, object mass and revolutions of the object per second (frequency).

r

v

a

Purpose: To deterime the relationship between frequency and radius, frequency and mass, frequency and centrapetal force.

Hypothesis: If the mass of the object in motion increases, then the frequency will increase.

If the radius increases then the frequency will decrease.

If the stopper mass increases, then the frequency will increase.

Materials:

reinforced glass tube with smooth ends
strong smooth string
three one holed rubber stoppers of equal size
mass kit
masking tape
balance scale
metre stick

System diagram of the experiment

Procedure:

1. Set up the experiment like the system diagram

2. Select a 100-200g mass and attatch to the end of the string.

3. Start to spin the object at the end of the string in a horizontal circle until it is moving at a constant rate and the tape stays at the same spot under the tube, keeping radius constant.

4. Start the timer and stop it after counting 20 revolutions of the object. Record the time.

5. Repeat step 5 two more times and then find the average of the 3 runs.

6. Next, repeat steps 2-5 four more times but each time adding more mass to the end of the string.

7. Repeat steps 2-6 but keep the mass at the end of the string and radius constant and change the mass of the object that is being spun.

8. Repeat steps 2-6 but change the length of the radius.

Analysis:

When testing how frequency was affected by changing stopper mass, radius and the tension in the rope was kept constant to keep the experiment controlled. As stopper mass was increased, frequency increased also as seen by the postive linear regression in the first graph. This does not make sense as the mass is inversely proportional to frequency so there should be a downward trend.

Centripetal force was affected by the mass hanging of the string. Increasing the mass increased the tension in the string and in turn the centripetal force. There is a positive increasing trend between force and frequency because if force increases, in order to equal a greater force, frequency must increase also as it is directily proportional.

When radius was increased, frequency decreased. There was a decreasing trend because radius is inversely proportional to frequency, so if radius increased, the fraction for frequency would become smaller.

F = 4π^2 r m f^2 f = (F/4π^2 r m)^0.5