# Circular Acceleration

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. Show that the acceleration in constant circular motion is directed along the radius rather than along the tangent.
2. Show that centripetal acceleration is directly proportional to the radius for a rotating platform.

### MATERIALS

Bicycle wheel mounted to spin around a vertical axis, 2 Accelerometers (3-axis if available), boards to mount equipment on wheel, Interface, CPU w/ Software*

### 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 interface and accelerometers as shown in the diagrams. If possible, mount the outer accelerometer at double the radius of the inner one. For both accelerometers, the axes that are aligned with the radius should be pointing the same direction. Secure the interface with strong elastic bands. A counter weight can be used to offset the unbalanced condition with the heavy interface versus the light accelerometers.

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. COMPUTER:
• Launch Logger Pro. With a LabPro connected and the accelerometers indicated above, a graph of the three accelerations should be set up for you.
• Set up data collection for 20 seconds at a rate of 20 samples per second.
• Under Experiment, choose Remote then Setup. Follow through until the LabPro is ready to collect data.
• Disconnect the LabPro. When the right conditions are arrived at, press the [START/STOP] button to commence data collection.
• Following data collection, re-connect the LabPro to the computer and download the data.

4. CALCULATOR:
• The calculator can be mounted on the LabPro with the cradle.
• Launch Datamate. The program should recognize the accelerometers as you have them connected. If not, you will have to go through Setup to get the program to recognize the sensors.
• Set up data collection for 20 seconds at 20 samples per second (0.05 sec per sample).
• The data will be available for examination and analysis following the data run. It can be downloaded to a computer, if desired, using a TI-Graph Link.

5. Start the wheel into motion. With practice, you will be able to reach in and initiate data collection while it is rotating. Keep the wheel moving with a constant angular speed unless you wish to demonstrate the effect of speeding up or slowing down where you get acceleration along the tangent.

6. Once the data collection is complete, stop the wheel and either download or simply examine the data.

### ANALYSIS

1. Plot the graphs as shown here to examine the data you have collected
• CH1 vs Time - shows the tangential acceleration (should be approximately zero unless the wheel speeded up or slowed down)
• CH2 vs Time - shows the acceleration along the radius is large. Should be able to determine the direction as being inward.
• CH2 and CH3 vs Time - 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. If the apparatus can be changed so the wheel moves vertically without endangering the equipment, and if you can drive it at a constant speed, the effects of going in a vertical circle can be examined. This makes a good approximation of the conditions in a common carnival or amusement park ride. A counterweight is strongly recommended.

### TEACHER NOTES

1. We use the heavy wheel that we also use for gyroscope demonstrations. A metal plate is mounted on a heavier piece of particle board that has a hole conveniently located so we can tighten up the nut used to secure the axle.
1. We have used two 1/4" plywood boards that we taped to the spokes of a bicycle wheel. 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.

* CPU w/ Software = Computer, Calculator or Palm OS Device plus appropriate data collection software

Clarence Bakken
Revised 1/13/05