If Earth Suddenly Stops Rotating: Effects on the Value of g at the Equator
When considering the hypothetical scenario of Earth suddenly ceasing its rotation, the value of gravitational acceleration (g) at the equator would undergo notable changes.
1. Current Value of g
- The standard acceleration due to gravity (g) at the surface of the Earth is approximately 9.81 m/s².
2. Effect of Earth's Rotation
- Earth's rotation creates a centrifugal force that reduces the effective value of g, particularly at the equator.
- This centrifugal force counteracts gravitational pull, resulting in a slightly lower effective g.
3. Centrifugal Force Calculation
- The formula for centrifugal acceleration (a_c) at the equator is given by:
a_c = ω²R
where:
- ω = angular velocity of Earth (approximately 7.27 x 10⁻⁵ rad/s)
- R = radius of Earth (about 6,378 km or 6.378 x 10⁶ m)
- Substituting these values, the centrifugal acceleration at the equator is roughly 0.34 m/s².
4. New Value of g at the Equator
- If the Earth stops rotating, the centrifugal force disappears, and the effective value of g at the equator would increase to:
g' = g + a_c = 9.81 m/s² + 0.34 m/s² = 10.15 m/s²
5. Conclusion
- In summary, if Earth were to suddenly stop rotating, the effective value of g at the equator would increase from 9.81 m/s² to approximately 10.15 m/s², resulting in stronger gravitational effects on objects at the equator.