PASCO PS-2138 Goniometer - Manual (Page 15)

Model No. PS-2138 Experiment
15 ®
Part 3: Centripetal and Tangential Accelerations
When your forearm rotates about your elbow the velocity of your hand is
entirely in the tangential direction, but the acceleration is not. There are
two components to the acceleration of your hand: tangential (perpendicular
to your forearm), and centripetal (parallel to your forearm.) You will use
the Acceleration Sensor to measure both components.
The magnitude of tangential acceleration (a
T
) is equal to the change in
magnitude of tangential velocity (
∆v
T
) divided by the change in time (
∆t).
a
T
=
∆v
T
⁄ ∆t
The angular acceleration (
α) of your forearm equals the change in angular
velocity (
∆ω) divided by the change in time (∆t).
α = ∆ω ⁄ ∆t
In Part 2, you discovered that the relationship between tangential velocity
and angular velocity is v
T
= r
ω, thus:
∆v
T
= r
∆ω
Predict
You will use the Acceleration Sensor to measure the tangential acceleration
of your hand, and the Goniometer to measure the angular acceleration of
your forearm. Based on the above equations, write an equation predicting
what you will discover about the relationship between a
T
and
α.
Setup
1. Connect the Goniometer and Acceleration Sensor to the interface (or
interfaces).
2. Set the sample rates of both sensors to 20 Hz.
3. Place the Goniometer on your elbow so that a flexion of the joint is
measured as a positive angular displacement.