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A static balance (sometimes called a force balance [2] [3]) occurs when the inertial axis of a rotating mass is displaced from and parallel to the axis of rotation.Static unbalances can occur more frequently in disk-shaped rotors because the thin geometric profile of the disk allows for an uneven distribution of mass with an inertial axis that is nearly parallel to the axis of rotation.
The moment of inertia depends on how mass is distributed around an axis of rotation, and will vary depending on the chosen axis. For a point-like mass, the moment of inertia about some axis is given by , where is the distance of the point from the axis, and is the mass. For an extended rigid body, the moment of inertia is just the sum of all ...
The moments of inertia of a mass have units of dimension ML 2 ([mass] × [length] 2). It should not be confused with the second moment of area, which has units of dimension L 4 ([length] 4) and is used in beam calculations. The mass moment of inertia is often also known as the rotational inertia, and sometimes as the angular mass.
For free-floating (unattached) objects, the axis of rotation is commonly around its center of mass. Note the close relationship between the result for rotational energy and the energy held by linear (or translational) motion: E translational = 1 2 m v 2 {\displaystyle E_{\text{translational}}={\tfrac {1}{2}}mv^{2}}
It also depends on the distribution of the mass: distributing the mass further from the center of rotation increases the moment of inertia by a greater degree. For a single particle of mass m {\displaystyle m} a distance r {\displaystyle r} from the axis of rotation, the moment of inertia is given by I = m r 2 . {\displaystyle I=mr^{2}.}
A less tedious means of achieving dynamic balance requires just four measurements. 1) initial imbalance reading 2) an imbalance reading with a test mass attached on a reference point 3) The test mass moved to 120 degrees ahead and the imbalance again noted. 4) The test mass finally moved to 120 degrees behind the reference point.
The comptometer-type calculator was the first machine to receive an all-electronic calculator engine in 1961 (the ANITA mark VII released by Sumlock comptometer of the UK). In 1890 W. T. Odhner got the rights to manufacture his calculator back from Königsberger & C , which had held them since it was first patented in 1878, but had not really ...
Cavendish's result provided additional evidence for a planetary core made of metal, an idea first proposed by Charles Hutton based on his analysis of the 1774 Schiehallion experiment. [18] Cavendish's result of 5.4 g·cm −3 , 23% bigger than Hutton's, is close to 80% of the density of liquid iron , and 80% higher than the density of the Earth ...