Key Concepts: Relative Motion & Reference Frames

Reference Frames

• A reference frame is a coordinate system used to measure position and motion. All motion is relative to a chosen frame.
• Inertial frame: A frame not accelerating (Newton's laws hold directly).
• Non-inertial frame: An accelerating frame where fictitious forces appear.

Relative Velocity

• The velocity of object A relative to object B: v_AB = v_A − v_B.
• If two cars move in the same direction at 60 and 40 km/h, relative velocity = 20 km/h.
• If moving toward each other, relative velocity = sum of speeds.

Applications

• River crossing: A boat's velocity relative to ground = boat velocity relative to water + water velocity relative to ground.
• Rain problems: The apparent direction of rain changes when you move.
• The Galilean velocity addition formula applies at speeds much less than the speed of light.