Final answer:
The centripetal acceleration on the Earth's equator is about one-tenth the acceleration due to gravity.
Step-by-step explanation:
The centripetal acceleration on the Earth's equator is given by the equation r² = (3.84 × 10^8 m)(2.66 × 10⁻⁶ rad/s)² = 2.72 x 10⁻³ m/s². The direction of the acceleration is towards the center of the Earth.
To compare this with the acceleration due to gravity (g = 9.8 m/s²), we can take the ratio of the two accelerations: ac/g = (2.72 x 10⁻³ m/s²) / (9.8m/s²) = 0.128. Therefore, the centripetal acceleration is about one-tenth the acceleration due to gravity.