Motion Relative to Earth

Motion Relative to Earth (Rotating Frame)

Earth is a non-inertial (rotating) frame, so we add fictitious forces to apply Newton's laws.

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1. Centrifugal Force (affects g)

• Cause: Earth's rotation (every object, moving or not).
• Direction: Radially outward from the axis.
• Effect on g:

$$g^{\mathrm{\prime }}=g-{\omega }^{2}R{\cos }^2\lambda$$

2. Coriolis Force (affects moving objects)

• Cause: Motion relative to rotating Earth.
• Formula: ${\vec{F}}_{cor}=-2m(\vec{\omega }\times \vec{v})$
• Direction: Perpendicular to motion; does no work (changes direction only).
• Deflection: Right in N. Hemisphere, Left in S. Hemisphere.
• Examples: Cyclones, ocean currents, trade winds, Foucault pendulum, projectile drift.