Understanding Inertia, Moment of Inertia, and Flywheels

Posted on Mar 23, 2025 in Physics

Inertia

Inertia is the resistance that opposes difficulty or a physical system or a social system to change.

In physics, we say that a system has more inertia when it is more difficult to change its physical state. The two most common uses in physics are mechanical inertia and thermal inertia. The first one appears in mechanics and is a measure of the difficulty to change the state of motion or repose of a body. The mechanical inertia depends on the amount of mass and the inertia tensor. The thermal inertia measures the difficulty with which a body changes its temperature when in contact with other bodies or heating. The thermal inertia depends on the amount of mass and heat capacity.

Inertial forces are called fictitious forces or apparent forces to an observer in a non-inertial reference frame.

Moment of Inertia

The moment of inertia or rotational inertia is a measure of the rotational inertia of a body. More specifically, the moment of inertia is a scalar quantity that reflects the distribution of mass of a body or system of particles rotating with the axis of rotation. The moment of inertia depends only on the geometry of the body and the position of the rotating shaft, but does not depend on the forces involved in the movement.

The moment of inertia plays a role analogous to the inertial mass in the case of uniform rectilinear motion. It is the scalar value of the angular momentum of a rigid longitudinal body.

Inertial Mass

Inertial mass is a measure of a mass’s resistance to the change in velocity in relation to an inertial reference system. In classical physics, the inertial mass of point particles is defined by the following equation, where particle one is taken as the unit (m1 = 1):

where mi is the inertial mass of the particle i and ai is the initial acceleration of particle i in the direction of particle i to particle 1 in a volume occupied only by particle i and 1, where both particles are initially at rest and at a unit distance. No external forces exert force on the particles into each other.

Flywheel

A flywheel is, in mechanics, a completely passive element that only adds to the additional inertia system allowing you to save kinetic energy. This wheel continues its movement until the inertia torque which propels it ceases. Thus, the flywheel opposes fast acceleration in a rotational movement. This allows it to reduce the angular velocity fluctuations. That is, the wheel is used to smooth the flow of energy between a power source and its load. At present, numerous lines of investigation have opened to finding new applications of flywheels. Examples of such uses are:

  • Absorb the energy of braking a vehicle, so it is reused later in its acceleration. (KERS)
  • As devices to smooth the operation of power generation facilities using wind power and photovoltaics, as well as various industrial electrical applications.
  • In electric railways that use long regenerative braking systems that feed the energy from braking back into power lines, with new materials and designs resulting in higher yields for these purposes.