θ = ωt
where:
θ is the angular displacement in radians
ω is the angular velocity in radians per second
t is the time in seconds
The Earth completes one full rotation (2π radians) in approximately 86,400 seconds (one day). Therefore, the angular velocity of the Earth is:
ω = 2π radians / 86,400 seconds ≈ 7.27 × 10⁻⁵ radians per second
Now, we can calculate the angular displacement of the Earth in five hours, which is equivalent to 18,000 seconds:
θ = (7.27 × 10⁻⁵ radians per second) × (18,000 seconds) ≈ 1.31 radians
Therefore, the Earth rotates approximately 1.31 radians in five hours.
