# Circular Acceleration - CBL

When an object is in uniform circular motion, there is a net force and resulting acceleration involved because this is a non-inertial frame of reference. Textbooks demonstrate that the acceleration and the resulting net force is directed radially inward, having a value

ac = v2/R

Any acceleration along the tangent (perpendicular to the radius) occurs only while speeding up or slowing down. If the circular motion is uniform, the speed is constant, there is no tangential acceleration.

### OBJECTIVES

1. Use a CBL to show that the acceleration in constant circular motion is directed inward rather than along the tangent.
2. Determine that the acceleration is directly proportional to the radius for a platform which is rotating.

### MATERIALS

 Bicycle wheel mounted so it spinsaround a vertical axis Boards to mount equipment onto bicycle wheel (2) 3-axis Accelerometers TI Graphing Calculator (3) DIN-CBL Adapters CBL Velcro fasteners GRTAM96.82P program DOWNLOAD.82P program

### PRELIMINARY QUESTIONS

1. If one travels in a circular path at a constant speed, he/she feels a force. In which direction does this force appear to be directed? Explain.

2. If one travels in a circular path at a constant speed, what is his/her acceleration in their direction of motion? Explain. What is their direction of motion at any time?

### PROCEDURE

1. Mount the CBL and accelerometers as shown in the diagrams. For both accelerometers, the axes that are aligned with the radius should be pointing the same direction, with outward being recommended.
2. Connect the tangential direction of the outer accelerometer to CH1. Connect the radial direction of the outer accelerometer to CH2. Connect the radial direction of the inner accelerometer to CH3.
3. Run the program GRTAM96. Choose 3-AXIS from the choice of accelerometers. Choose PRACTICE from the menu, which gathers 90 data points, 0.1 second apart.
4. Once the program has loaded up the CBL, and it says "READY", disconnect the TI-82 from the CBL.
5. Start the wheel into motion. With practice, you will be able to reach in and press the TRIGGER button on the CBL. This initiates the data collection, which will continue for 9 seconds.
6. Once the data collection is complete, stop the wheel and re-connect the TI-92 to the CBL. Press [ON] on the TI-82 to halt the program, choosing QUIT at the prompt. Run the program DOWNLOAD.
7. DOWNLOAD will ask several questions. You have collected data from 3 channels, and you have recorded time.

### ANALYSIS

1. Once DOWNLOAD has finished, only a matter of a second or two, you will have the following data to work with:
1. L1 = Time
L2 = Tangential Acceleration
2. Plot the graphs as shown here to examine the data you have collected
1. L1 vs L2 - shows the tangential acceleration (should be approximately zero)
L1 vs L3 - shows the acceleration along the radius is large
L1 vs L3 and L4 - shows the relationship between radius and acceleration

### EXTENSIONS

1. If one uses two accelerometers in a CBL case, mounted along the length and width of the case, the procedure above can be repeated with the experimenter holding the case at arm's length and spinning. This doesn't yield the radial dependence of the acceleration, but shows the tangential vs the radial very clearly.
2. The data can be downloaded into Graphical Analysis (Vernier) and plotted using a computer. This makes it convenient for printing out the results.

### TEACHER NOTES

1. We have used two 1/4" plywood boards that we taped to the spokes of a bicycle wheel. Actually, we used the heavy wheel used for gyroscope demonstrations.
2. We have also mounted velcro pads on one side to accept the velcro pads we place on the bottom of the 3-axis accelerometers. This makes for convenient mounting, and we use this technique throughout our labs.

Clarence Bakken
Gunn High School
1998