Shown here are the top, base, and weight washers. The top is too light to spin in the stable volume above the base magnet; the correct weights, fitted onto the top's stem, bring the top into the stable volume. I painted the top's rim black except for a short section, to provide a light pulse to a photo transistor when the spinning top is lit with a light source.
I was trying to discover the maximum spin rate for the top - when it "flies off" over the top and off to the side of the stable volume, and the minimum rate - when it drops through the bottom of the stable volume into the base ring (where it's captured by the plastic cup on the reverse side of the plastic launch platform, to prevent damage or loss of scattered parts).
My rate 46.8 (70F) 26.6 (70F)
" 22.9 (60F no drive)
S.H.R. Paper rate 40.4 (254 rad/s) 18.1 (114 rad/s)
Well, there is the S.H.R. Paper's:
- top mass = 0.02135 kg
- rotational inertia I = 2.2x10^-6 kg m^2 (directly measured)
- transverse inertia It= 1.32x10^-6 kg m^2 (directly measured)
- It/I = .60 (calculated)
- reff = 0.0102 m (calculated)
Other quantities related to magnetic field strength were beyond my measurement means.
- Orange plastic: mass= 0.42 g, O.D.= 25.55 mm, I.D.= 6.5 mm, thick= 0.85 mm
Thick walled cylindrical tube, open at ends: mass m, height h, inner radius r, outer radius R:
Irot= m/2 * (r^2 + R^2) -- about axis through tube
Itrans = m/12 * (3 * (r^2 + R^2) + h^2) -- about axis through center of tube and perpendicular to it
I trans_at_end = Itrans + m *(h/2)^2 -- about axis at end of tube , through its central axis and perpendicular to it
- to make the tube (of mass m) solid, set inner radius r=0.
- to make the tube (of mass m) a thin shell of the outer radius, set inner radius r to the outer radius: r = R. (not used here)
Solid ball, mass M, radius r:
Iball = 2/5 * M* r^2 (not used here)
Solid hemisphere, mass m, radius r
- Ihemi_rot = 2/5 * m * r^2 -- about axis through center of base, perpendicular to base
- Ihemi_trans = Ihemi_rot -- about axis through center of base and along base
I wrote a simple VB program to add up the mass, and rotational and transverse moments of inertia for any configuration of top plus weights, by selecting the items wanted via check boxes. (Later I added the capability of determining the configuration needed to float the top based on temperature.)
(x10^-6 kg m^2) (x10^-6 kg m^2)
My unweighted top: 16.43 1.84 1.04 0.56
S.H.R. top (~68F deg): 21.35 2.20 1.32 0.60
My top for 68F deg: 19.93 2.12 1.18 0.56
My top for 27F deg: 21.35 2.21 1.23 0.56
To Be Supplied
"In 1994 Bill Hones [of Fascinations] and his father applied for a patent on a levitating top that used a square permanent magnet base, which was issued in 1995. The Levitron, made by Fascinations, has a square base magnet with a region of weaker or null magnetization in the center." (S.H.R, p287)
My Levitron base certainly appeared to contain a circular (ring) base magnet...
The magnet dimensions are:
- 110 mm outside diameter
- 58 mm inside diameter
- 20 mm thick
- If a flat plate were placed on the upright base, about 4 mm would separate the glued magnet face from the underside of the plate.
The photo shows the level bubble position after the base has been adjusted properly to float the top.
I built up a shim on one end of the CD case lid so that when the lid is positioned with the shim side down and opposite the high point on the base (marked with white tape in photo),the bubble would show level when base adjustments leave the magnetic field close to vertical. Measuring the height of the shim and the distance from it to the lip at the mark gives a correction angle of about 1.15 degrees for my base.