- Name: Richard Flarend
- Address: Penn State Altoona 3000 Ivyside Park Altoona,
- Phone: 814-949-5744
- Fax: 814-949-5011
- E-mail: firstname.lastname@example.org
Introductory Laboratory Apparatus
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
- 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'
- Does this apparatus require Electrical Power? Yes
- Is this apparatus intended for use with an overhead
- Will you be present to set up your apparatus? Yes
- When do you plan to set up your apparatus? Sunday
- Other support needed for the proper operation of this
Sketch of the apparatus:
- 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.
- The apparatus must be tared before each set of data is
- 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
- 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
- Explain the significance of why the radial force is always
positive for larger rotational speeds and alternates positive/negative
for smaller rotational speeds.