• Name: Richard Flarend
• Address: Penn State Altoona 3000 Ivyside Park Altoona, PA 16601
• Phone: 814-949-5744
• Fax: 814-949-5011
• E-mail: ref7@psu.edu

Apparatus Title: Uniform Vertical Circular Motion

Abstract: A force sensor is attached onto the end of a flat bar with a counterweight on the other end. The bar is then mounted onto a rotary motion sensor so it can rotate freely in a vertical circle. A computer collects radial force and vertical position data. Students then analyze this motion and explain how/why the radial and tangential forces vary.

• Support required for apparatus: Computer (MAC). If possible the computer should have a PASCO interface with Science Workshop installed. (Sensors will be included with the apparatus.) A table suitable for mounting a table clamp onto will also be needed.
• Approximate size: 4' above table, 3' to 5' table space.
• Does this apparatus require Electrical Power? Yes
• Is this apparatus intended for use with an overhead projector? No
• Will you be present to set up your apparatus? Yes
• When do you plan to set up your apparatus? Sunday 9-11 AM
• Other support needed for the proper operation of this apparatus: None

Sketch of the apparatus:

Description:

Construction

• 1. This apparatus consist of flat aluminum stock measuring 2" x 24" x 1/8".
• 2. A 1/8" hole is drilled in the center of the flat aluminum bar allowing it to be attached to the rotary motion sensor using the 3-step pulley screw.
• 3. A 10-24 hole is drilled and tapped about 1/2" from the center hole for a small eye-hook. (The force sensor wire lead will be held by this hook to keep it from interfering with the rotation.)
• 4. Two holes are drilled and tapped (10-32) on one end of the aluminum bar so that the force sensor can be mounted to the flat bar (sensor end outward).
• 5. A 200-g slotted mass is attached to the end of the force sensor using a 6-32 screw and fender washers.
• 6. Counterweights are attached to the opposite end of the flat bar as needed to balance the bar. Note: Each counterweight is slightly different for our set of nine apparatus, so we have numbered each matching force probe, bar and counterweight, and 200 g mass.

Student Directions

• The apparatus must be tared before each set of data is collected.
• To do this, hold the bar in a horizontal position, press the tare button on the force probe and start recording data.
• CONTINUE holding the bar in the horizontal position until data begins to register on the graph.
• After the data has begun being collected, the flat bar can be spun.
• Hold the force sensor wire away from the center of the circle so that it can twist up without interfering with the motion of the bar.
• The computer collects data assuming that the inward radial direction is positive, and that the vertical is upward positive. The center of the circle is considered to be the vertical zero point.
• Collect and print data showing several cycles of radial force vs. time and vertical position vs. time for several different speeds. (Instructor visually checks to insure that student groups have data with appropriate taring and speeds.)
• For one set of data, expand the time axis so that one or two cycles for both graphs are shown in detail. Print these graphs and label positions A to H on the graphs (a label for each 45° on the circle starting at the top).
• Draw free-body diagrams for the rotating mass at each of the positions A through H. Include the following as needed in the FBDs: gravity, radial force, tangential force, and acceleration.
• Sketch the corresponding graph of tangential force vs. time for the expanded graphs. Assume that the positive tangential direction is in the forward moving direction.
• Discuss why the radial and tangential forces vary with vertical position.
• Explain the significance of why the radial force is always positive for larger rotational speeds and alternates positive/negative for smaller rotational speeds.

Sample Data