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Last time we arrived at a general formula to compute the kinetic energy, KE, contained within the totality of a spinning flywheel made up of numerous parts. Today we’ll discuss the terms in that formula, which encompasses a phenomenon of flywheels known as moment of inertia.
Moment of Inertia in a Flywheel
The kinetic energy formula we’ve been working with is, again, KE = ½ × Σ[m × r2] × ω2 (1) The bracketed part of this equation makes reference to spinning flywheels comprised of one or more parts, and that’s what we’ll be focusing on today. The symbol Σ is the Greek letter sigma, standard engineering shorthand notation used to represent the sum of all terms and mathematical operations contained within the brackets. Our illustration shows we have five parts to consider: a hub, three spokes and a rim, and label them A, B, C, D, and E respectively. Each part has its own mass, m, and is a unique distance, r, from the flywheel’s center of rotation. The flywheel’s angular velocity is represented by ω. For our flywheel of parts A through E our expanded equation becomes, Σ[m × r2] = [mA × rA2] + [mB × rB2] + [mC × rC2] + [mD × rD2] + [mE × rE2] (2) Equation (2) represents the sum total of moments of inertia contained within our flywheel. It’s a numerical representation of the flywheel’s degree of resistance to changes in motion. The more mass a flywheel has, the greater its moment of inertia. When at rest this greater moment of inertia means it will take more effort to return it to motion. But once in motion the flywheel’s greater moment of inertia will make it harder to stop. That’s because there’s a lot of kinetic energy stored within its spinning mass, and the heavier a flywheel is, the more kinetic energy it contains. In fact, for any given angular velocity ω, a large and heavy flywheel stores more kinetic energy than a smaller, lighter flywheel. But there’s more to a flywheel’s moment of inertia than just mass. What’s really important is how that mass is distributed. We’ll get into that next time when we discuss torque. Copyright 2017 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |
