PASCO ME-8960 DEMONSTRATION GYROSCOPE - Manual (Page 11)

7
012-05327B Demonstration Gyroscope
Experiment 1: Precession
d
φ
→
dL
→
L
→
L
top view side view
90
100
110
120
130
140
80
70
60
50
40 30
ME-8960 DEMONSTRATION GYROSCOPE
CAUTION
MAGNET
ω
mg
EQUIPMENT NEEDED
– Gyroscope (ME-8960) – meter stick
– stopwatch (SE-8702) – table clamp for pulley
– Super Pulley (ME-9450) – thread (1.5 meters)
– Pulley Mounting Rod (SA-9242) – computer (optional)
– Mass and Hanger Set (ME-9348) – Smart Pulley (optional)
– balance – Smart Pulley software (optional)
Purpose
The purpose of this experiment is to measure the precession rate of a gyroscope and com-
pare it to the theoretical value.
Theory
A torque is applied to the gyroscope by hanging a mass on the end of the shaft. This torque
causes the gyroscope to precess at a certain angular speed,
Ω
.
Assume that the gyroscope is initially balanced in the horizontal position,
θ
= 90˚. The disk
is spun at an angular speed (
ω
) and then a mass, m, is attached to the end of the gyroscope
shaft at a distance, d, from the axis of rotation. This causes a torque:
τ
= mgd. But the
torque is also equal to dL/dt, where L is the angular momentum of the disk. As shown in
Figure 1.1, for small changes in angle, d
φ
, dL = L d
φ
.
Substituting for dL in the torque equation gives
τ
= mgd = dL
dt
= L
d
φ
dt
Figure 1.1: Torque Applied to Horizontal Gyroscope
d