Unit 1 Review: Galileo, Falling Objects, and the Tower That (Probably) Never Happened

Most people have heard the story: Galileo Galilei climbed the Leaning Tower of Pisa, dropped two cannonballs of different weights, and watched them hit the ground at the same instant — proving Aristotle wrong about heavier objects falling faster. It's a great story. There's just no real evidence it happened. No record exists of Galileo describing this experiment himself, and the only source is a biography written by his former assistant, decades after Galileo had died, with no contemporary witnesses backing it up. It's the kind of legend that sticks around because it sounds like something a bold, contrarian genius would do.

The real story is less dramatic, but genuinely clever. Around 1600, Galileo wanted to study how falling objects speed up — but true free fall happens too fast to time accurately with the clocks available in his era; an object dropped from a reasonable height hits the ground in well under a second. So instead of dropping something straight down, he rolled a bronze ball down a long, grooved wooden incline. Tilting the ramp "dilutes" gravity's effect, stretching the same falling motion out over several seconds instead of a fraction of one — slow enough to actually measure with the tools he had.

For a stopwatch, Galileo used a water clock: a large vessel of water with a small spout at the bottom, timed by weighing how much water drained out during each run. Rolling the ball down the same incline over and over, marking how far it traveled in equal time intervals, he found a pattern that took real insight to spot: the distance covered isn't proportional to time — it's proportional to time squared. Double the time the ball rolls, and it travels four times as far, not twice as far. That relationship, $\Delta x \propto t^2$, is the seed of the actual equations used to describe accelerating motion today.

Whether or not the tower drop ever happened, the incline experiment is the real, well-documented foundation of the physics that follows — a reminder that good experimental design (finding a way to actually measure something) often matters more than a dramatic gesture.

Videos

This was a review and history day — no new video assigned. For a refresher tying together everything reviewed, see Motion Graphs - AP Physics 1: Unit 1 Review Supplement (Flipping Physics).

Practice Problems

A self-check review covering the first nine lessons of this unit — one question per topic:

1. Distance vs. Displacement: A hiker walks 5 km east, then 2 km west. Find the total distance traveled and the displacement (with direction).
2. Vectors vs. Scalars: Label each quantity as a vector or a scalar: (a) "12 m/s" (b) "12 m/s north" (c) "30 minutes" (d) "3 km southeast"
3. Average Velocity and Average Speed: A cyclist rides 20 km north in 1 hour, then rides 20 km south back to the start in 1 hour. Find the average speed and average velocity for the entire trip. Explain why they're different.
4. Acceleration: A skater slows from 6 m/s to 2 m/s in 4 seconds. Find the acceleration. Is it positive or negative — and does that mean the skater is speeding up or slowing down? Explain.
5. Position-Time Graphs: Sketch a position-time graph for this story: a student walks away from their locker at a steady pace for 10 seconds, stops and talks to a friend for 5 seconds, then walks back to their locker twice as fast as before.
6. Velocity-Time Graphs: A car's velocity increases steadily from 0 to 12 m/s over 6 seconds, then stays constant at 12 m/s for the next 4 seconds. Find (a) the acceleration during the first 6 seconds and (b) the displacement during the last 4 seconds.