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4 through 6 the tension T and the angular acceleration α may be eliminated. The angular and linear accelerations are related by įrom Eq. Τ f is the retarding torque due to all frictional forces, primarily in the pulley and the main bearing. The net torque on the rotating shaft is therefore 3 to calculate the linear acceleration of the falling weight. The falling weight covers a distance y in t seconds, so
![how to find moment of inertia of a circle how to find moment of inertia of a circle](https://i.stack.imgur.com/jfgTl.png)
Weights (W) are placed on the hanger and allowed to fall a measured distance. A string is wrapped around the vertical shaft, run over the pulley (H) to a weight The rotation is produced in a manner that allows measurement of the acceleration of
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You will also check these results against calculations madeīy use of the textbook formulae for moments of inertia of simple shapes. Measure the moment of inertia of weight distributions placed on this arm, with respect Placed on this arm at various radii, and secured with wing nuts. Horizontal arm attaches to the top of the shaft. The apparatus has a vertical shaft (D) rotating on high quality ball bearings (B). You will need to consult this table, and you will also need to be able to apply the Textbooks have tables showing moments of inertia of bodies of simple geometric shape. Infinitesimal point masses and integrating over the entire volume of the mass. The moment of inertia of a distributed mass is found by subdividing the body into Where m is the mass and r is the perpendicular distance measured from the axis to the The moment of inertia of a localized or "point" mass about an axis is Where τ is the applied torque, I is the body's moment of inertia, and α is its angular acceleration. The body will cause an angular acceleration of the body given by Of inertia lies in its effect on the body's dynamical behavior. It is determined by the body's mass distribution about that axis. The moment of inertia of a body is the measure of its rotational inertia about an axis. Welch rotation apparatus with ball-bearing shaft. Method and to verify the equation I = mr 2 for moment of (2) To measure the moment of inertia of various mass distributions by a dynamical (1) To demonstrate the application of energy and momentum principles to a rotating