Video Analysis

Every kinematics graph so far has come from an equation or simulation. To begin applying these concepts IRL, you can record a video and perform a simple analysis of motion.

A video is a sequence of still frames taken at a known rate, so the frame number is a clock. Mark the same object on frame 0, frame 3, frame 6, and you have positions at known times. The resulting table of $[x, t]$ values is exactly what we need to give a precise physical description.

Analysis Steps

1. Scale. Drag across your known length, then type that length in meters. Every position is derived from this conversion, so it is worth getting right. You can always change it later and every point you have already marked will rescale.
2. Origin. Click where $x = 0$, $y = 0$ should sit. Moving the origin shifts your positions and leaves the velocities alone, because a velocity is a difference of positions.
3. Axis tilt. For a cart on a ramp, drag along the slope. The measured $x$ then runs along the incline and $y$ runs perpendicular to it, which is the coordinate choice that makes an inclined-plane problem easy.
4. Frame rate. The analysis tool attempts to select the correct conversion between frame number and elapsed time. If your camera says otherwise, type the real value.
5. Mark. Click the object; the video advances by a selected number of frames and waits for the next click. Pick a feature you can find every time. This could be the center of a ball or the front edge of a cart.

Velocity values are not measured directly. The two components are computed from your marked positions by comparing each point to its neighbours, which is why the first and last points have no velocity listed: there is no neighbor on one side.

Acceleration values are not computed, as small errors in position would be amplified greatly. Instead, I suggest performing a linear fit to the velocity vs. time graph or a quadratic fit to the position vs. time graph.

Copy for spreadsheet puts the table on the clipboard tab-separated, which pastes into Google Sheets or Excel as proper columns. Download CSV saves the same table as a file. Either way you can take the data somewhere else and do your own fitting.