Question

A 5.0-kg mass is placed at (3.0, 4.0) m, and a 6.0-kg mass is placed at (3.0, -4.0) m. What is the moment of inertia of this system of masses about the y-axis?

Answer 1

Answer:

the moment of inertia of this system of masses about the y-axis is 99 kgm²

Explanation:

Given the data in the question;

mass m₁ = 5.0 kg at point ( 3.0, 4.0 )

mass m₂ = 6.0 kg at point ( 3.0, -4.0 )

Now, Moment of inertia $I$ of this system of masses about the y-axis will be;

Moment of inertia $I$ₓ = mixi²

Moment of inertia $I$ = m₁x₁² + m₂x₂²

we substitute

Moment of inertia $I$ = [ 5.0 × ( 3 )² ]  + [ 6.0 × ( 3 )² ]

Moment of inertia $I$ = [ 5.0 × 9 ]  + [ 6.0 × 9 ]

Moment of inertia $I$ = 45 + 54

Moment of inertia $I$ = 99 kgm²

Therefore, the moment of inertia of this system of masses about the y-axis is 99 kgm²