Physics Meets Pop: Calculating the Energy to Literally Stop the World

When Modern English sang "I'll stop the world and melt with you" in their 1982 hit, they likely didn't anticipate physicists taking the claim literally. Yet, decades later, astronomer Phil Plait used the lyric as a springboard to explore a fundamental question: How much energy would it actually take to stop Earth's rotation? Dr. Drang, building on Plait's SciAm article, provides a deep dive into the underlying physics—centering on the crucial concept of the mass moment of inertia.

Unlike the area moments of inertia familiar to structural engineers, mass moments of inertia govern rotational dynamics for physical bodies. The rotational kinetic energy (KE) of Earth is given by:

KE = (1/2) * I * ω²

Where:

• I = Mass moment of inertia (kg·m²)
• ω = Angular velocity (radians/second)

Dr. Drang starts with a simplified model: Earth as a uniform density sphere. Using NASA's archived data:

• Mass (M) = 5.9722 × 10²⁴ kg
• Mean radius (R) = 6371 km = 6.371 × 10⁶ m

The moment of inertia for a uniform sphere is:

I_uniform = (2/5) * M * R² ≈ 9.69 × 10³⁷ kg·m²

Earth's sidereal rotation period (23.9345 hours) yields ω = 7.292 × 10⁻⁵ rad/s. Plugging in:

KE_uniform ≈ 2.58 × 10²⁹ joules

This exceeds Plait's cited value of 2 × 10²⁹ J. Why the discrepancy? Earth isn't uniform. Its core is denser than its crust, concentrating mass toward the center and reducing I. Citing geophysicist Kurt Lambeck's precise measurement:

I_actual = 0.3307 * M * R² ≈ 8.02 × 10³⁷ kg·m²

Recalculating with this value:

KE_actual ≈ 2.13 × 10²⁹ joules

This aligns closely with Plait's figure. The ~20% difference between models underscores how planetary density gradients dramatically impact rotational energy calculations—a critical consideration in astrophysics and spacecraft trajectory modeling.

While Plait also explored stopping Earth's orbital motion (leading to a fiery plunge into the Sun), Dr. Drang sidesteps this scenario, noting the song implies melting with a lover, not incinerating the entire planet. The analysis ultimately highlights how pop culture can frame complex physics concepts, revealing the delicate interplay between simplified models and real-world geophysical complexity.

Source: Dr. Drang - "There’s Nothing You and I Won’t Do"