Centrifugal Force vs. Centripetal Acceleration: And How to Calculate Them

What’s the Difference?

Centripetal acceleration is the real force that acts inward, toward the center of a circle. It’s what keeps a rotating object moving in a circle.

Centrifugal force is what you feel when you’re rotating and it feels like something is pushing you outward, away from the center. But it’s actually inertia: your body wants to move in a straight line, and the centripetal force is pulling you inward to keep you moving in a curve.

Why It Matters for Artificial Gravity

When we talk about artificial gravity (especially using spin) we’re talking about centripetal acceleration. We simulate gravity by rotating something fast enough that it feels like weight is pressing outward.

To do that, we need to calculate:

How fast to spin
How far from the center
What effective G-force is produced

The Key Equations

$ a = r \cdot \omega^2 $

or alternatively:

$ a = \frac{v^2}{r} $

Where:

$a$ = acceleration in m/s²
$r$ = radius from center in meters
$\omega$ = angular velocity in radians/sec
$v$ = tangential velocity in m/s

A Worked Example (Like Ours)

Let’s say we want to simulate 2G at a radius of 0.5 meters.

We want $ a = 2g = 2 \cdot 9.81 = 19.62 , m/s^2$

Using:

$ a = r \cdot \omega^2 \quad \Rightarrow \quad \omega = \sqrt{\frac{a}{r}} = \sqrt{\frac{19.62}{0.5}} \approx 6.26 , rad/s $

Convert to RPM (rotations per minute):

$ \text{RPM} = \frac{\omega}{2 \cdot \pi} \times 60 \approx \frac{6.26}{6.283} \times 60 \approx 59.7 , RPM $

So to simulate 2G at 0.5 meters, we’d need ~60 RPM.

This is exactly the kind of math we used to plan Spark Gravity’s first test rig.

Common Misconceptions

❌ “Centrifugal force is fake.”
✅ It’s a useful concept in a rotating frame, but the real force is centripetal.
❌ “You can’t simulate gravity with spin.”
✅ You absolutely can. It’s how every sci-fi space station works, and we’re testing it on Earth.
❌ “Faster is better.”
✅ Not always. Higher RPM can cause nausea or mechanical stress. Radius matters too.

How Spark Gravity Uses This

We’re using these equations every day as we build out Earth-based prototypes to simulate gravity levels from 1G to 2+G.

Right now, we’re testing a phone in a spinning bucket to measure G-force using simple tools. Next up: Arduino sensors, motors, and programmable profiles.

Understanding the relationship between radius, speed, and gravity is core infrastructure for our future orbit labs.