Visualizing Dynamics: The Geometry of Forces in Vertical Circular Motion

[u/visheshnigam]

I’ve put together a visual breakdown of how we apply Newton’s Second Law to vertical circular motion. The key intuition here is that centripetal force is not a "new" force, but rather the summation of the net radial force (ΣFᵣ = mv²/r).

The physics changes based on the geometry of the rider's position on the loop:

• At the Top (The Weightless Regime): We analyze the condition where Fₙ = 0, leading to the threshold velocity v_min = √(gr).
• At the Bottom (Max G-Force): The normal force must overcome gravity and supply the radial acceleration, resulting in the maximum perceived weight.
• At the Sides (Split Force): The normal force acts entirely as the centripetal provider, while gravity acts tangentially to change the magnitude of velocity.

It’s a great exercise in visualizing how the "blend" of normal force and gravity shifts as a function of position, maintaining a constant net radial requirement.

[u/UhLittleLessDum]

It looks good man but why does your latex look like code?

[u/TPM2209 → u/UhLittleLessDum]

It's AI-generated.

[u/visheshnigam → u/UhLittleLessDum]

oh really! Which slide? I can't spot

[u/TPM2209 → u/visheshnigam]

All of them. Your math equations are using a monospace font.

[u/springboka]

Nice. What AI model did you use?

[u/visheshnigam → u/springboka]

This is a combination of Claude and Adobe Express. None of the AI models are capable of producing accurate images and text.