Overview
This lecture explains how motion is described relative to different reference frames, distinguishes between distance and displacement, and introduces basic calculation methods for these quantities in physics.
Motion and Reference Frames
- Motion is always described relative to a reference frame, which is the viewpoint or coordinate system used to measure position.
- Earth is commonly used as a reference frame, but moving frames (like an airplane) can also be chosen.
- A description of motion (how fast and in what direction) depends on the chosen reference frame.
- All reference frames are equally valid; no single frame is "correct."
- Galileo first formalized the idea that observations of motion depend on the observer's frame of reference.
Position, Distance, and Displacement
- An object’s position is its location relative to a reference frame, often marked as d₀ (initial) and d_f (final).
- Distance is the total length of the path traveled, regardless of direction.
- Displacement is the straight-line change in position between start and end points, including direction.
- For round trips, displacement can be zero even if distance is large.
Scalars and Vectors
- Distance is a scalar: it has magnitude only (no direction).
- Displacement is a vector: it has both magnitude and direction.
- Scalars only require a number; vectors require both a number and a direction.
Calculating Displacement and Distance
- Displacement = final position (d_f) – initial position (d₀): Δd = d_f – d₀.
- Distance is the sum of the absolute values of each segment of the path.
- Choose axes (positive/negative directions) and origins to keep calculations consistent.
Worked Example
- A cyclist rides 3 km west then 2 km east: displacement = -1 km (west), distance = 5 km.
- When calculating displacement, direction matters; for distance, only add magnitudes.
SI Units and Measurement
- SI (International System of Units) uses meters (m) as the standard for distance and displacement.
- Always convert all measurements to the same unit system before calculating.
Key Terms & Definitions
- Kinematics — the study of motion without regard to causes.
- Reference Frame — a system for specifying the location of objects.
- Position — location of an object relative to a reference frame.
- Distance — total length of path traveled; scalar.
- Displacement — straight-line change in position; vector.
- Scalar — quantity with magnitude but no direction.
- Vector — quantity with both magnitude and direction.
- Magnitude — the size or amount of a quantity.
Action Items / Next Steps
- Practice describing and calculating distance and displacement for different motion scenarios.
- Complete any assigned homework or lab activities comparing distance and displacement.
- Review example problems involving reference frames, vectors, and scalars.