Free Fall
Overview
Free fall is a special case of UAM where the only acceleration is g = 9.81 m/s² downward (on Earth). In the absence of air resistance, all objects fall with the same acceleration regardless of mass. At the top of the trajectory, velocity = 0 but acceleration = g still acts downward.
Galileo's insight: all objects fall equally
In the absence of air resistance, ALL objects — regardless of mass — fall with the same gravitational acceleration g = 9.81 m/s² near Earth's surface. This was demonstrated by Galileo dropping objects from the Tower of Pisa. The reason: although a heavier object has greater gravitational force, it also has greater inertia (resistance to acceleration), and these exactly cancel — so a = F/m = mg/m = g, independent of mass.
Free fall as a special case of UAM
Free fall is UAM with a = g = 9.81 m/s² directed downward. For an object thrown upward with speed u: it decelerates at 9.81 m/s² on the way up, momentarily stops at the top (v = 0), then accelerates downward at 9.81 m/s². The time to reach the top = u/g. At the top, velocity is zero but acceleration is still g downward — the object is still in free fall. It returns to the launch height with the same speed u (no energy loss).
- ⚠Setting a = 0 at the top of the trajectory — acceleration is always g downward throughout
- ⚠Not considering sign when substituting g — if up is positive, use a = −9.81 m/s²
- ⚠Forgetting that the object returns to launch height with the same speed (symmetry of free fall)