Physics
Circular Motion and Rotational Mechanics
Centrifugal Force in Rotating Frames
Class 11
⚡ Quick Summary
When you're looking at things from a spinning viewpoint (like being on a merry-go-round), it seems like there's a force pushing things outward. That's the centrifugal force. It's not a real force in the usual sense, but we use it to make Newton's laws work in these spinning situations.
F_centrifugal = mω²r, where m is mass, ω is angular speed, and r is the radius of the circular path.
- Centrifugal force arises when describing motion from a non-inertial, rotating frame of reference.
- It's a pseudo force used to apply Newton's laws in such frames.
- The centrifugal force acts radially outwards from the axis of rotation.
Effect of Earth's Rotation on Apparent Weight
Class 11
⚡ Quick Summary
Because the Earth is spinning, your weight isn't exactly what it would be if the Earth stood still. The spinning creates a slight outward force that makes you weigh a tiny bit less. Also, what we consider 'vertical' (like a hanging string) isn't perfectly pointing to the center of the Earth because of this spin!
g' = √(g² - ω²R sin²θ (2g - ω²R)), where g' is apparent gravity, g is true gravity, ω is Earth's angular speed, R is Earth's radius, and θ is colatitude.
tan α = (ω²R sinθ cosθ) / (g - ω²R sin²θ), where α is the angle between the true and apparent vertical.
- Earth's rotation causes an apparent reduction in weight.
- The effect is greatest at the equator and diminishes towards the poles.
- The direction of apparent gravity (g') differs slightly from the true gravitational acceleration (g).
- A plumb line aligns with the apparent vertical, perpendicular to the surface of still water.