Circular Motion: Advanced — Gravity Turn MCQ

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Advanced — Gravity TurnHardQuestion 30679

Question

At the equator, what angular velocity would make g_eff = 0 (objects become weightless)? (g = 9.8 m/s², R_Earth = 6.4×10⁶ m)

A
1.24×10⁻³ rad/s
Correct
B
7.27×10⁻⁵ rad/s
C
0.00124 rad/s
D
0.0124 rad/s

Correct answer

1.24×10⁻³ rad/s

Explanation

g_eff = 0: g = ω²R → ω = √(g/R) = √(9.8/6.4×10⁶) = √(1.53×10⁻⁶) ≈ 1.24×10⁻³ rad/s. Compare with Earth's actual ω = 7.27×10⁻⁵ rad/s — Earth would need to spin ~17× faster!

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