This might sound surprising, but bear with us… There is nothing fundamentally different between the sewing machine shown above and the large steam turbines that defined the nineteenth century. ![]() Industrial Revolution: Next Came the Steam Era ! This is due to their small size (<30cm radiuses) and slow rotation speeds (<250 rpm). While these small energy storage devices are useful in smoothing out the jerky motion of human arms and legs, they do not store very much energy, maybe around 0.01 to 0.1 Wh. Closer to home, the sewing machine below is in my in-laws’ house, and I have done my best not to break it… In medieval times, the spinning wheel started displacing hand spindles from around 1,200 AD, unlocking an order of magnitude improvement in the rate of spinning wool into yarns and threads. Flywheels were used in the manufacture of pottery in China and Mesopotamia since 6 000 BCE. The ability of rotating objects to store and smooth energy flows has been known for around 8,000 years. Rotational energy: the world’s original battery? And for more details on converting one energy unit into another, please see our overview of energy units. k = 2/5 for a solid sphere, 2/3 for a spherical shell.Īll of this is calculated for you in the data-file. k=1 for a wheel that is loaded at the rim. But generally, k=0.5 for a disc or horizontal rod. Finally k is a “shape-based scalar”, which integrates the way in which the mass is distributed across different distances from the center of rotation. Where I is moment of Inertia (kg-m2), M is the mass of the object (kg), R is the radius (m). Moment of Inertia can be captured via equations. Moment of Inertia is to rotating objects what mass is to objects that are moving in a straight line. 1 radian per second means it will take 6.3 seconds to do a full turn. ![]() It does not matter how wide the diameter is. 1 radian is 57.296°, so an angular velocity of 1 radian per second means a circular object turns by 57.296° around its axis each second. These units are admittedly a bit weirder. E = energy (Joules), I is the ‘moment of inertia’ around the axis of rotation (in kg-m2) and ω is rotational velocity (in radians per second). And α is angular acceleration, the rotund cousin of linear acceleration, a. ![]() And by extension, the kinetic energy of a rotating object E = ½ I (ω^2) where ω is rotational velocity. The same laws can be adapted for rotational acceleration, stating that F = Iα. Where E = energy (Joules), m = mass (kg) and v = velocity (meters/second). And by extension, the kinetic energy of a moving object E = ½ m(V^2). Newton’s Second Law, familiarly, tells us that F = ma, for linear acceleration a. Rotational energy: how do the mechanical physics work?
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