Moment of Inertia
Newton’s Second Law of Motion states that force is equivalent to the mass of the object multiplied by its acceleration. However, this equation is different for an object that rotates. In rotation, force is replaced with torque, acceleration is replaced with rotational acceleration, and mass is replaced with the moment of inertia. Newton’s Second Law of Rotation states that torque is equivalent to the moment of inertia multiplied by rotational acceleration. The object’s mass, radius,and inertia constant
determine the moment of inertia.
The mass and radius of a flywheel can easily be determined by weighing and measuring. However, the inertia constant of a flywheel is dependent on the shape
.
Flywheels are usually one of two shapes: a ring with spokes or a solid disk. A ring with spokes most clearly resembles a wheel, while a solid disk looks like a CD with out a hole in the middle.
Since flywheels usually only come in these two shapes we will only be concerned with two values of inertia constant
.
The inertia constant for a ring is 1.0 and the inertia constant for a disk is 0.5. The difference in the inertia constants is due to the fact that all of the mass in a ring is concentrated at its circumference, while the mass of a disk is evenly distributed from the center to the outside.
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