At what angular speed should the Earth rotate so that a body at latitude 45° becomes weightless? If ω = √(ng/R), find n.

Question

G1 Physics · Accepted Answer

Step 1: At latitude λ the outward centrifugal acceleration component along the local vertical is ω²R cos²λ. For weightlessness, this must equal g. Step 2: At λ=45°, cos²45°=1/2, so g=ω²R/2. Step 3: ω=√(2g/R)=√(ng/R), hence n=2.