The Tower Clock: Designed and Made for the University of Chicago by the Chicago Manual Training School of the University of Chicago

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1903 - 57 Seiten
 

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Seite 27 - It is the least possible when the axis passes through the centre of gravity. To find the moment of inertia of a body, referred to a given axis, divide the body into small parts of regular figure. Multiply the weight of each part by the square of the distance of its centre of gravity from the axis.
Seite 26 - ... the center of gyration is the point at which the whole weight of the body may be considered as concentrated, the angular velocity remaining the same.
Seite 27 - ... above, the moment of inertia about an axis through its center of gravity may be found by taking the sums of the moments of inertia of each component part about an axis through its own center of gravity parallel to the axis of the compound section, and the sums of products of the area of each component part by the square of the distance of its center of gravity from the axis of the compound section. Having thus obtained the moment of inertia of the compound section, the section modulus may be...
Seite 26 - ... of each elementary particle by the square of its distance from the axis; hence, the moment of inertia of the same body varies according to the position of the axis. It has its minimum value when the axis passes through the center of gravity.
Seite 29 - ... which will be the same as if the whole mass were concentrated at that point. This point is called the center of oscillation. The distance between the center of oscillation and the point of suspension is called the radius of oscillation. CENTER OF PERCUSSION. If a body oscillates about an axis, then the point at which, if a blow is struck by the body, the percussive action is the same as if the whole mass of the body were concentrated at that point, is called the center of percussion. This point...
Seite 27 - ... axis. The sum of the products is the moment of inertia. The value of the moment of inertia thus obtained \yill be more nearly exact, the smaller and more numerous the parts into which the body is divided.
Seite 28 - To find the radius of gyration divide the body into a considerable number of equal small parts— the more numerous the more nearly exact is the result, — then take the mean of all the squares of the distances of the parts from the axis of revolution, and find the square root of the mean square. Or, if the moment of inertia is known, divide it by the weight and extract the square root.
Seite 26 - C, so that it thus increases with the weight of the beam, and the distance of the center of gravity from the point of suspension.
Seite 25 - Vtf+h*, it is sometimes called the principal radius of gyration. 319. PROP. If a body oscillate about a fixed horizontal axis not passing through its center of gravity, there is a point in the right line, drawn from the center of gravity perpendicular to the axis, whose motion is the same as it would be if the whole mass were collected at that point and allowed to vibrate as a pendulum about the fixed axis. Let the horizontal axis be perpendicular to...
Seite 28 - CENTER AND RADIUS OF GYRATION THE CENTER OF GYRATION with reference to an axis is that point at which the entire weight of a body may be concentrated without changing its moment of inertia.

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