🧠 SemiSimTech Intuition Lab
Conservation Law Intuition
Projectile sticks to a pivoted rod: why energy and linear momentum fail, while angular momentum works.
Core Theme
Choosing the right conservation law
Main Conflict
Energy vs momentum vs angular momentum
Key Condition
External force ≠ external torque
Learning Goal
Physical judgment before formulas
🧩 Big Picture
This lab is built around a classic physics trap: a projectile hits and sticks to a rod that can rotate about a fixed pivot.
Three familiar methods can be attempted, but only one is valid.
The purpose is not just to compute angular speed. The real purpose is to learn how to decide
which conservation law is allowed by the physical constraints.
Energy fails
Linear momentum fails
Angular momentum works
System boundary thinking
🧠 Main Puzzle
Why do different methods give different answers?
If we use energy conservation, we get a larger angular speed because it assumes no kinetic energy is lost.
But the projectile sticks to the rod, so the collision is inelastic.
Energy intuition:
energy is not protected when sticking, deformation, heat, or sound are produced.
Why is angular momentum special here?
The pivot can give a large external force, so linear momentum is not conserved.
But that force acts at the pivot, so its torque about the pivot is zero.
Angular momentum intuition:
choose the pivot as the reference point, and the pivot force has no lever arm.
🎛️ Interactive Lab
Adjust the rod/projectile parameters and compare three possible answers. The correct answer comes from angular momentum about the pivot.
1) Conservation law check
Energy
Not conserved
Projectile sticks → inelastic collision → kinetic energy is lost.
Linear Momentum
Not conserved
The pivot provides external impulse during impact.
Angular Momentum
Conserved about pivot
Pivot force has zero lever arm, so torque about pivot is zero.
Decision rule:
conservation laws are chosen by constraints. Ask: external force? external torque? energy loss?
🧮 Formula Summary
Correct method
Use angular momentum about the pivot:
Lbefore = m v r
Ifinal = (1/12) M d² + m r²
ω = m v r / Ifinal
where r = d/2 because the projectile hits the rod end and the pivot is at the center.
Wrong but useful methods
Energy gives an upper bound because it assumes no energy loss.
Linear momentum is not valid because the fixed pivot prevents free translation.
Wrong answers are useful when they reveal which assumption was broken.
🚀 Final Insight
The real lesson:
Do not choose a conservation law because it is familiar. Choose it because the system boundary and external interactions allow it.
In this problem, the collision destroys mechanical energy and the pivot destroys linear momentum conservation.
But the pivot does not create torque about itself, so angular momentum about the pivot survives.