Question

You are designing an experiment to determine the rotational inertia of a large spherically shaped object around its center.

Your experimental data shows that the mass of the object is distributed radially and you determine that the radius of the object as a function of its mass is given by the equation r = km2 , where k = 3 m/kg2 .

Determine the correct expression for the rotational inertia of the object.

Answer 1

The rotational inertia of a spherically shaped object around its center is given by the equation:

I = (2/5)mr2

where I is the rotational inertia, m is the mass, and r is the radius.

In this case, the radius of the object is given by the equation r = km2, where k = 3 m/kg2. Substituting this equation into the expression for I, we get:

I = (2/5)m(km2)2
I = (2/5)m(k2m4)
I = (2/5)m(3^2)m4
I = (2/5)(9m2)m4
I = 18m6 / 5

Therefore, the correct expression for the rotational inertia of the object is I = 18m6 / 5.