The rotation of the Earth does indeed create a centrifugal force, but its effect on countering gravity is relatively small compared to the gravitational force itself.
The centrifugal force is an apparent force that arises due to the rotation of a reference frame. It acts in the outward direction and is proportional to the square of the rotational speed and the distance from the axis of rotation.
At the equator, where the rotational speed of the Earth is highest, the centrifugal force does counteract a portion of the gravitational force. However, it's important to note that the gravitational force is still significantly stronger.
To quantify this, we can use some basic calculations. The rotational speed of the Earth at the equator is approximately 1670 kilometers per hour (or about 1037 mph). The gravitational acceleration on the Earth's surface is approximately 9.8 meters per second squared (m/s²).
The centrifugal force at the equator can be calculated using the formula: F = m * ω² * r, where F is the centrifugal force, m is the mass of the object, ω is the angular velocity (in radians per second), and r is the distance from the axis of rotation.
Assuming a person with a mass of 70 kilograms standing at the equator, the centrifugal force can be calculated as follows:
F = 70 kg * (1670 m/h * 1000 m/km * (2π rad/360°) / 3600 s/h)² * 6378 km ≈ 198.9 Newtons
Comparatively, the gravitational force acting on the person can be calculated using the formula: F = m * g, where g is the acceleration due to gravity.
F = 70 kg * 9.8 m/s² = 686 Newtons
As you can see, the centrifugal force of the Earth's rotation is much smaller than the gravitational force. If the Earth were to suddenly stop spinning, the reduction in the centrifugal force would have a negligible effect on the overall weight of objects on Earth. So, in practical terms, we would not weigh significantly more if the Earth stopped spinning.