Gyroscopic precession
A fast-spinning top doesn't fall over — it circles around instead.
When a fast-spinning gyroscope is supported at only one end, the torque of gravity about the pivot does not make it fall over; instead it keeps turning the direction of the angular momentum around in the horizontal plane. This is precession. From dL/dt = M, the precession angular velocity is Ω = mgd/(Iω): the faster the spin, the slower the precession. For a uniform disk I = ½mR², so the mass cancels between numerator and denominator.
Precession vs. spin angular velocity
Ω is inversely proportional to ω and independent of the disk's mass.
Think about it
What happens to the precession if you double the gyroscope's spin rate?
The precession angular velocity halves and the precession period doubles. Ω is inversely proportional to the spin angular velocity ω; note also that Ω stays the same when you change the disk's mass.
Model assumptionsGyroscopic approximation ω ≫ Ω · uniform disk, radius 10 cm · nutation and friction ignored
Data log
Set the parameters and click “Record data”. Record several rows with different parameters to plot their relationship and fit a straight line; pause and record at different times to study how a reading changes with time.