![]() This axis will be the reference to measure the desired moment of inertia. The form to proceed consists of placing an object, whose moment of inertia will be determined, over the platform, in a way that both mass centers coincide in a vertical axis. One way to measure this physical property for a certain object is by using a mechanical system made from a homogeneous circular platform, horizontally suspended by three vertical strings equidistantly placed on the platform’s border. ![]() This concept idea is used for motor, robot’s moving parts, and mechanism’s dynamic design, among other applications. The relevance of obtaining the moment of inertia of a mechanical system’s mobile components is associated with the component’s capability to make slow or abrupt rotations. We can estimate the moment of inertia for the entire area as the sum of the moments of inertia of the segments, written as I x = a i y i 2 1 n ! where n = the total number of segments, and i = the number of each segment (from 1 to n), or: The centroid of segment #1 is 7 cm from the x-x axis y 1 = 7 cm () the centroid of segment #2 is 5 cm from the x-x axis y 2 = 5 cm () and so on. We can divide the beam into 8 equal segments 2 cm deep, 5 cm wide, so that each segment has an area a = 2 cm ! 5 cm = 10 cm 2. This beam has a depth of 16 cm and a width of 5 cm. The " x " and " y " in I x and I y refer to the neutral axis. We can calculate the moment of inertia about the vertical y-y neutral axis: I y = a ! x () ! x = ax 2. If we divide the total area into many little areas, then the moment of inertia of the entire cross-section is the sum of the moments of inertia of all of the little areas. In Strength of Materials, " second moment of area " is usually abbreviated " moment of inertia ". The second moment of this area is I x = a ! y () ! y = ay 2. ![]() Take a small area " a " within the cross-section at a distance " y " from the x-x neutral axis of the beam. The horizontal neutral axis of this beam is the x-x axis in the drawing. Consider a beam with a rectangular cross-section. For example, in Statics, a force acting on a wrench handle produces a torque, or moment, about the axis of a bolt: M = P ! L. In physics and engineering mechanics, moment is the product of a quantity and the distance from that quantity to a given point or axis. Definition In everyday speech, the word " moment " refers to a short amount of time. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |