Mass Moment of Inertia Calculator:
Enter the values of mass of an object, m(kg) and distance from the axis of rotation, r(m) to determine the value of Mass Moment of Inertia, I(kg.m2).
Mass Moment of Inertia Formula:
The mass moment of inertia (also known simply as the moment of inertia) is a physical quantity that represents how mass is distributed with respect to an axis of rotation. It is analogous to mass in linear motion, except that it quantifies resistance to angular acceleration rather than linear acceleration. The mass moment of inertia is crucial in rotational dynamics, as it determines how much torque is needed for a given angular acceleration.
The moment of inertia depends on the mass distribution of an object relative to the axis of rotation. Objects with mass distributed farther from the axis of rotation have a larger moment of inertia and thus require more torque to achieve the same angular acceleration. The shape, mass, and orientation of an object relative to the axis of rotation all influence its mass moment of inertia.
For simple shapes such as spheres, rods, disks, and cylinders, standard formulas exist for calculating their moments of inertia. However, for more complex shapes or irregular objects, the moment of inertia must be calculated using integration or approximated using various methods.
The moment of inertia plays a key role in rotational kinetic energy calculations, angular momentum, and determining how a rotating body will respond to external forces.
Mass Moment of Inertia, I(kg.m2) in kilogram metre square is equal to the product of the mass of an object, m(kg) in kilograms and the square of its distance from the axis of rotation, r(m) in metres.
Mass Moment of Inertia, I(kg.m2) = m(kg) * r2(m)
I(kg.m2) = mass moment of inertia in kilograms metres square, kg.m2.
m(kg) = mass in kilogram, kg.
r(m) = distance in metres, m.
Mass Moment of Inertia Calculation:
1.Find the mass moment of inertia of a point mass.
Given: m(kg) = 5kg, r(m) = 2m.
Mass Moment of Inertia, I(kg.m2) = m(kg) * r2(m)
I(kg.m2) = 5 * 22
I(kg.m2) = 20kg.m2.
2.Find the mass of a rotating wheel.
Given: I(kg.m2) = 90kg.m2, r(m) = 3m.
Mass Moment of Inertia, I(kg.m2) = m(kg) * r2(m)
m(kg) = I(kg.m2) / r2(m)
m(kg) = 90 / 32
m(kg) = 10kg.