Physics

Center of Gravity

The center of gravity is the point in an object or system where its weight is considered to act. It is the average location of the weight distribution and is the point where the force of gravity can be considered to act. Understanding the center of gravity is important for analyzing the stability and equilibrium of objects and systems.

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3 Key excerpts on "Center of Gravity"

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  • Basic Engineering Mechanics Explained, Volume 1
    eBook - ePub

    Basic Engineering Mechanics Explained, Volume 1

    Principles and Static Forces

    • Gregory Pastoll, Gregory Pastoll(Authors)
    • 2019(Publication Date)
    • Gregory Pastoll
      (Publisher)
    The centre of gravity of a rigid object does not change position within the object. Once you have established the location of that point, you can always support the weight of the object by a single upward force whose line of action passes through this point, irrespective of the orientation of the object.
    Centre of mass: It turns out that the point we call the centre of gravity is also the same point through which inertial forces act, when an object is being accelerated. In analysing situations where acceleration occurs, this point is referred to as the centre of mass.
    If one needs to apply a force to impart linear acceleration or deceleration to an object, the force should be applied such that its line of action passes through the centre of mass of the object. Otherwise, the force will cause the object to rotate, as well as to change position.
    Which term to use: It makes no difference whether one uses the term ‘centre of mass’, or ‘centre of gravity’, because both terms describe the same point in the space within the boundaries of a given rigid object. In this chapter we will refer to this point as the centre of gravity, abbreviated CG. We lean towards this usage because the method of determining the location of such a point relies on a consideration of gravitational forces in a situation of static equilibrium.
    The importance of knowing the location of the CG of an object Knowing the location of the centre of gravity of an object or assembly of objects is vital in applications like the following:
    • Reducing the likelihood of a vehicle overturning when taking a curve in the road.
    • Knowing where to attach support points on an object being raised by a crane.
    • Maintaining the stability of a small boat when changing position in the boat.
    • Placing the load correctly in a ship or aircraft.
    • Determining the inertial forces on a moving machine part.
    • Ensuring the stability of a suspended item like a pulley running on a rope.
    Rules for locating the CG of an object 1. The location of the centre of gravity of a given rigid object is fixed and would only change if the object were to be deformed, or have material added or removed.
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  • Principles of Structure
    eBook - ePub

    Principles of Structure

    • Ken Wyatt, Richard Hough(Authors)
    • 2013(Publication Date)
    • CRC Press
      (Publisher)
    8    Properties of Area
    CENTRE OF GRAVITY
    As stated in paragraph 8.1, the Centre of Gravity is the point where the entire weight of the object appears to be concentrated. This is the principle that underlies the method of computation in Example 8.1 . It also provides a convenient experimental method for finding the C.G. If the body is suspended from any point, it will rotate until the C.G. is vertically beneath the point of support. (Can you explain why this is so?) By suspending the body several times from different points, and drawing the vertical through each point of support, the C.G. may be found.
    EXAMPLE 8.1
    The metal plate shown is 10 mm thick and has a density of 8000 kg/m3 . What is the location of the centre of gravity?
    Weight of section 1
    =   0.080   ×   0.060   × ​ 0.010   ×   8   ×  
    10 3
      × 10   (N/kg)
    =3 .84   N
    Weight of section 2
    =   0.120   ×   0.020   × ​ 0.010   ×   8   ×  
    10 3
      × 10   (N/kg)
    =1 .92   N
    Weight of section 3
    =   0.160   ×   0.120   × ​ 0.010   ×   8   ×  
    10 3
      × 10   (N/kg)
    =5 .76   N
    ∴   Resultant   =   3.84   +   1.92   +   5.76
    =   11.52   N
    Take moments about A:
    ∴   R   ×   X   =   3.84   ×   30   +   1.92   ×   120   +   5.76   ×   210
    ∴   X   =  
    1555 11.52
      =   135
    i.e. the C.G. is on the horizontal axis of symmetry, 135 mm from L.H. end.
    CONTENT OF CHAPTER 8
    The behaviour of many structural components depends to a large extent upon their cross-sectional shapes. The amount of deflection of a beam under load, the load that a long column can safely carry, the stability of a retaining wall against overturning — these are just some of the important consequences of the shape of structural cross-sections. In this chapter, we will bring together these attributes of shape and area, so that they can be related to one another.
    Concepts introduced include centre of gravity, centroid, second moment of area, and section modulus.

    8.1    CENTRE OF GRAVITY

    The centre of gravity
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  • Aircraft Design
    eBook - ePub

    Aircraft Design

    A Systems Engineering Approach

    • Mohammad H. Sadraey, Peter Belobaba, Jonathan Cooper, Roy Langton, Allan Seabridge(Authors)
    • 2012(Publication Date)
    • Wiley
      (Publisher)
    The aircraft Center of Gravity is the cornerstone for aircraft stability, controllability, and trim analysis, as well as handling qualities evaluation. All the analyses and evaluations are aimed at determining airworthiness aspects of the aircraft. In addition, the aircraft cg is the center of the coordinate axis system that all calculations are based on. All non-aerodynamic moments are measured with respect to the aircraft cg. Therefore, aircraft cg determination is a vital task in the aircraft design process. The main objective of aircraft weight distribution is to achieve an ideal cg location and ideal cg range. By definition, the Center of Gravity is the point at which an aircraft would balance when suspended. Its distance from the reference datum is determined by dividing the total moment by the total weight of the aircraft.
    The center of mass or Center of Gravity of a complex system is the mean location of all the mass in the system. The term center of mass is often used interchangeably with Center of Gravity, but they are physically different concepts. They happen to coincide in a uniform gravitational field, but where gravity is not uniform the Center of Gravity refers to the mean location of the gravitational force acting on an object. For a rigid body, the position of the center of mass is fixed in relation to the body. The center of mass of a body does not often coincide with its geometric center. In the case of a movable distribution of masses in a compound, such as the passengers from a transport aircraft, the position of the center of mass is a point in space among them that may not correspond to the position of any individual mass. The application of the Center of Gravity often allows the use of simplified (e.g., linear) governing equations of motion to analyze the movement of a dynamic system. The Center of Gravity is also a convenient reference point for many other calculations in dynamics, such as the mass moment of inertia. In many applications, such as aircraft design, components can be replaced by point mass located at their centers of gravity for the purposes of analysis.
    The distance between the forward and aft Center of Gravity (or center of mass) limits is called the Center of Gravity range or limit along the x
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