suppose you stand on a bathroom scale and get a reading of 700N. in principle, would the scale read more, less, or the same if the earth did not rotate?
To determine whether the reading on the bathroom scale would be more, less, or the same if the Earth did not rotate, we need to consider the forces acting on an object when it is at rest on the Earth's surface.
When you stand on a bathroom scale, it measures the force exerted by your body weight downwards. This force is essentially the gravitational force between you and the Earth. The magnitude of this force can be calculated using the formula F = mg, where m is your mass and g is the acceleration due to gravity.
Now, let's consider the effect of the Earth's rotation on the gravitational force. The Earth's rotation produces a centrifugal force due to the circular motion. This centrifugal force is directed outward from the axis of rotation and opposes the force of gravity. It is this centrifugal force that causes a decrease in apparent weight at the equator compared to the poles.
If the Earth did not rotate, there would be no centrifugal force, and the only force acting on objects would be their weight due to gravity. Therefore, the scale would read the same as your actual weight, which in this case is 700N.
To summarize, if the Earth did not rotate, the scale reading would be the same as your actual weight because there would be no centrifugal force affecting the measurement.