Question

One of the objects used in this lab is a heavy ring. If this ring will be approximated as a hoop, what error is introduced?

a) Overestimation of inertia
b) Underestimation of inertia
c) No error is introduced
d) Changes in gravitational force

Answer 1

Approximating a heavy ring as a hoop introduces an underestimation of inertia because the mass distribution is different, leading to a lower actual moment of inertia for the solid ring as compared to the hoop.

Step-by-step explanation:

This is because a hoop has all its mass distributed on the outer edge, which results in a higher moment of inertia than if the mass were distributed across the entire volume of the object, such as in a solid ring. So, when a heavy ring is approximated as a hoop, it is assumed that all the mass is at a greater radius from the axis of rotation than it actually is, leading to an underestimation of its inertia. Considering the equation for the moment of inertia of a thin hoop (I = mr², where m is the mass and r is the radius), and comparing it with that of a solid cylinder (I = 1/2mr²), it becomes clear that the inertia of a hoop would be greater than that of a ring with the same mass and radius, because the mass in the hoop is concentrated further from the axis.