Chapter 28, Problem 5Q

To determine

Would it be possible to balance sharp needle on its point.

Answer to Problem 5Q

Solution:

It is not possible to balance a needle on its point.

Explanation of Solution

To balance a needle on its point, one needs to bring into equilibrium of forces.

This involves both translational and rotational equilibrium. From diagram it is clear that the object must stay upright for extended periods of time.

We cannot simultaneously ensure that the centre of mass of the needle is vertically above the point of contact, and also that their relative velocity is zero. This is because of the Heisenberg Uncertainty Principle.

If we ensure that the points are vertical, their relative velocity may not be zero and the centre of mass will move ahead, exerting a torque that brings the needle down. If we ensure zero relative velocity, then the points may not be vertical.