Inertia and moment of inertia are different concepts, but they both deal with the resistance of a
matter to change its motion. For example, if you push the same force on two objects with different
masses, the lighter object will accelerate more than the heavier one because the latter has more
internal resistance to change its motion. This property is used to calculate the moment of inertia of
an object revolving around an axis.
Torque is the force that causes a rotational motion and moment of inertia decides how difficult it is
to change that motion. We will also be discussing rolling motion which is a combination of
translational and rotational motion. The concept behind this is that when an object rolls, the bottom
point of contact becomes stationary which leads to pure rolling without slipping.
The moment of inertia theory states that i = m * k2, where k is the radius of gyration. In the case of a
disc with a symmetric shape, k = r. This is because the radius is equally distributed in all directions.
The moment of inertia depends on the excess of rotation and mass distribution about excess of
rotations. It is classified for discrete particle and their system, and the same classification applies to
continuous and combined bodies with cavities. The moment of inertia for a discrete particle system
is identified like the center of mass analogy. It also has a spatial formula for rigid bodies. If we talk
about the moment, it can be defined as i = ∫dm * r2.
To derive the moment of inertia formula, we start by choosing a ring of radius "r" within the solid
object. The value of "r" ranges from 0 to the maximum radius of the object (represented as "R"), as
the ring can shrink to zero or expand to the full size of the object. This range defines the limits of
integration. The moment of inertia formula for a disk is "mr2", while for a solid sphere, it is also
"mr2". For a hollow sphere, the formula is different.
Next, we will discuss the perpendicular and parallel axis theorems and provide examples linking to
the respective formulas. The perpendicular axis theorem applies only to 2-D objects, while the
parallel axis theorem can be used for all rigid bodies.
matter to change its motion. For example, if you push the same force on two objects with different
masses, the lighter object will accelerate more than the heavier one because the latter has more
internal resistance to change its motion. This property is used to calculate the moment of inertia of
an object revolving around an axis.
Torque is the force that causes a rotational motion and moment of inertia decides how difficult it is
to change that motion. We will also be discussing rolling motion which is a combination of
translational and rotational motion. The concept behind this is that when an object rolls, the bottom
point of contact becomes stationary which leads to pure rolling without slipping.
The moment of inertia theory states that i = m * k2, where k is the radius of gyration. In the case of a
disc with a symmetric shape, k = r. This is because the radius is equally distributed in all directions.
The moment of inertia depends on the excess of rotation and mass distribution about excess of
rotations. It is classified for discrete particle and their system, and the same classification applies to
continuous and combined bodies with cavities. The moment of inertia for a discrete particle system
is identified like the center of mass analogy. It also has a spatial formula for rigid bodies. If we talk
about the moment, it can be defined as i = ∫dm * r2.
To derive the moment of inertia formula, we start by choosing a ring of radius "r" within the solid
object. The value of "r" ranges from 0 to the maximum radius of the object (represented as "R"), as
the ring can shrink to zero or expand to the full size of the object. This range defines the limits of
integration. The moment of inertia formula for a disk is "mr2", while for a solid sphere, it is also
"mr2". For a hollow sphere, the formula is different.
Next, we will discuss the perpendicular and parallel axis theorems and provide examples linking to
the respective formulas. The perpendicular axis theorem applies only to 2-D objects, while the
parallel axis theorem can be used for all rigid bodies.
