Tippe Top
The tippe top is a truncated sphere with a short stem. When spun fast enough, it flips upside-down and spins on its stem — apparently converting kinetic energy into gravitational potential energy. Friction with the surface is the key.
The Inversion Mechanism
Why does it flip? When a tippe top tilts, friction at the contact point produces a torque. For a fast-spinning top, gyroscopic precession means this torque causes the spin axis to rise rather than fall — the top "wants" to stand upright, but since it started near upright, "upright" for the inverted configuration means stem-down.
Energy paradox resolved: The total energy (kinetic + potential) actually decreases — friction dissipates energy. Although the center of mass rises (gaining potential energy), the spin slows enough that net energy is lost to heat. The Jellett integral of motion is key: J = I·ω·cos θ − Ma·R·ψ̇·sin²θ is approximately conserved.
Adjust friction (must be nonzero to invert), eccentricity (how far the CoM is from the center), and initial spin (must exceed a threshold). The right panel shows tilt angle θ (cyan) and spin ω (gold) over time.