Question

A pencil is just balanced at its tip, what is its state of equilibrium? Give answer
with reason.

Answer 1

. To balance perfectly, the pencil would have to be perfectly upright and perfectly still. The uncertainty principle limits how well you can do both at the same time.

Momentum and position form a conjugate pair. ΔxΔp≥ℏΔxΔp≥ℏ.

Angular momentum and angular position form one too. ΔLΔΘ≥ℏΔLΔΘ≥ℏ

This doesn't guarantee that angular momentum and angular position will be non-zero. It is an uncertainty - The actual values can be anything, including 0.

But it does prevent you from arranging them both so the pencil stays upright. Furthermore, if you ask what the probability of finding both values very close to 0, you find that it is very small. In the limit, infinitely improbable.

If it turns out that L=Θ=ℏ−−√L=Θ=ℏ, and you plug in reasonable values for the mass and length of the pencil, you will find it falls over in a few seconds.

Answer 2

Answer:. To balance perfectly, the pencil would have to be perfectly upright and perfectly still. The uncertainty principle limits how well you can do both at the same time.

Momentum and position form a conjugate pair. ΔxΔp≥ℏΔxΔp≥ℏ.

Angular momentum and angular position form one too. ΔLΔΘ≥ℏΔLΔΘ≥ℏ

This doesn't guarantee that angular momentum and angular position will be non-zero. It is an uncertainty - The actual values can be anything, including 0.

But it does prevent you from arranging them both so the pencil stays upright. Furthermore, if you ask what the probability of finding both values very close to 0, you find that it is very small. In the limit, infinitely improbable.

If it turns out that L=Θ=ℏ−−√L=Θ=ℏ, and you plug in reasonable values for the mass and length of the pencil, you will find it falls over in a few seconds.

Explanation: