PASCO PS-2138 Goniometer - Manual (Page 12)

Goniometer Experiment
12 ®
Part 2: Tangential Velocity vs. Angular Velocity
When you rotate your forearm about the elbow, your hand does not move
in a straight line, but it always moves in a direction perpendicular to your
forearm. This direction is described as tangential.
As you rotate your arm, the magnitude of your hand’s tangential velocity
(v
T
) equals the change in the arc length traced by your hand (
∆s) divided by
the change in time (
∆t)
v
T
=
∆s ⁄ ∆t
The angular velocity (
ω) of your forearm equals the change in angle (∆θ)
divided by the change in time (
∆t).
ω = ∆θ ⁄ ∆t
In Part 1, you discovered that the relationship between arc length and angle
is s = r
θ, thus:
∆s = r ∆θ
Predict
You will use the Motion Sensor to measure the tangential velocity of your
hand, and the Goniometer to measure the angular velocity of your forearm.
Based on the above equations, write an equation predicting what you will
discover about the relationship between v
T
and
ω.
Setup
1. Connect the Goniometer and Motion Sensor to the interface (or
interfaces).
2. Place the Goniometer on your elbow so that a flexion of the joint is
measured as a positive angular displacement.