Question

a) What is the slope and y-intercept of the following equation, for moment of inertia?

I_s = Mh² + (I_cm + I_table)

b) What are other ways of measuring the mass of a ring other than using moment of inertia

Answer 1

here,

The parallel axis theorem provides a useful way to calculate the moment of inertia I about an arbitrary axis.

The theorem states that I = Icm + Mh2,
where ,
Icm is the moment of inertia of the object relative to an axis that passes through the center of mass and is parallel to the axis of interest,

M is the total mass of the object

h is the perpendicular distance between the two axes

From the given equation :

Is = M*h^2 + Icm + Itable
Slope will be : h
Intercept : Icm + Itable

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Part b :

The moment of inertia can also be calculated by using, A trifilar pendulum in which a platform supported by three wires designed to oscillate in torsion around its vertical centroidal axis.

The period of oscillation of the trifilar pendulum yields the moment of inertia of the system.