Center of Gravity

4 Key excerpts on "Center of Gravity"

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  eBook - PDF

  Conceptual Dynamics

  • Richard C. Hill, Kirstie Plantenberg(Authors)
  • 2013(Publication Date)
  • SDC Publications

    (Publisher)

  The weight force (W) is applied at the Center of Gravity/mass of the body when drawing its free-body diagram. Since rigid bodies have size, a force applied to a body may generate a moment causing the body to rotate. Moments and Center of Gravity/mass are important concepts that must be understood when applying Newtonian mechanics to analyze the motion of a rigid body. We will devote some time reviewing centers of gravity/mass, mass moments of inertia, calculating moments and the rotational kinematic relationships. Conceptual Dynamics Kinetics: Chapter 6 – Rigid Body Newtonian Mechanics 6 - 4 6.2) CENTER OF MASS / GRAVITY The Center of Gravity of a body in many instances coincides with its mass center, but they do not share the same definition. The mass center is the mean location of all the mass in a given body or system. The Center of Gravity, usually denoted as G, is the mean location of the gravitational force acting on the body. This is the point where you apply the mg force in your free-body diagram. You can also think of the Center of Gravity as a balancing point. If you balance an object on your finger, you are balancing it at its Center of Gravity. The Center of Gravity and mass center are different concepts as illustrated by their definitions; however, in a uniform gravitational field they coincide. Therefore, they are often used interchangeably. Another concept that may get confused for the Center of Gravity is the centroid. The centroid of a body is the center of its volume. If the body has a uniform density, its centroid coincides with its center of mass. However, if the body is a composite or has varying density, its center of mass and its centroid may be in different locations. How do the concepts of center of mass and Center of Gravity differ? When do they coincide? Why do we need to know where the Center of Gravity of a body is located? How do the concepts of centroid (center of volume) and center of mass differ? When do they coincide?

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  Available until 29 Nov |Learn more

  Aircraft Design

  A Systems Engineering Approach

  • Mohammad H. Sadraey, Peter Belobaba, Jonathan Cooper, Roy Langton, Allan Seabridge, 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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  eBook - PDF

  Engineering Mechanics

  Problems and Solutions

  • Arshad Noor Siddiquee, Zahid A. Khan, Pankul Goel(Authors)
  • 2018(Publication Date)
  • Cambridge University Press

    (Publisher)

  Chapter 7 Centroid and Centre of Gravity 7.1 Introduction So far we have dealt with the point loads or concentrated loads which do not exist practically. Generally loads are distributed over a line, surface area or total volume of a body. Some examples of load distributions are weight of a body, uniformly distributed load, uniformly varying load, etc. To apply the conditions of equilibrium, such distributive forces are replaced by equivalent resultant force R which acts at a certain coordinates and produces the same effect as produces by distributive forces. These certain coordinates are the point of application and termed as centroid or centre of gravity, G. It is characterized as centroid for line, surface area or volume and centre of gravity, G remains unaltered if body is rotated. The centroid or centre of gravity is very useful to determine the stability of fast moving vehicles like truck, ship, etc. during turning. These vehicles are supposed to topple if the height of centre of gravity is not close to their bottom portion. Apart this, it also plays a vital role to conduct sports events, stability of dams and safe lifting of heavy loads by cranes, etc. 7.2 Centre of Gravity, Centroid of Line, Plane Area and Volume A body can be treated as a collection of very large numbers of particles of infinitesimal size. Each particle has its own weight which acts at certain coordinates. The weight of each particle acts vertically downwards towards the centre of the earth. Thus the weight of all particles represents a non-coplanar parallel force system. This force system can be replaced by their single resultant force which is nothing but weight, whose coordinates can be determined by using Varignon’s theorem. Consider a body of weight W consisting of n Particles of individual weights w 1 , w 2 , w 3 ... w n whose coordinates are (x 1 , y 1 ), (x 2 , y 2 ), and (x 3 , y 3 ), ...... (x n , y n ), respectively, from reference axis as shown in Fig.

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  eBook - ePub

  An Elementary Treatise on Theoretical Mechanics

  • Sir James H. Jeans(Author)
  • 2013(Publication Date)
  • Dover Publications

    (Publisher)

  Oxy . Thus

  The line of action of the resultant force of gravity is the vertical line through the centroid of the particles.

  For this reason the centroid of a number of points, weighted according to the masses of the particles which occupy these points, is called the Center of Gravity of the particles. The effect of gravity acting on a rigid body is, as we have now seen, represented by a single force acting vertically downwards through the Center of Gravity of the body, the amount of the force being equal to the total weight of the body. The action of gravity is, accordingly, the same as if the whole mass of the body were concentrated in a single particle placed at the Center of Gravity.

  87 . It is clear that if we suspend a rigid body or system of bodies by a string, the Center of Gravity must be vertically below the string. For all the forces acting on the system reduce to two, — the tension of the string and the weight acting at the Center of Gravity, — and in equilibrium these two must act along the same line.

  In the same way it will be seen that if a body is placed on a point in such a way as to balance in equilibrium on this point, then the Center of Gravity must be vertically above the point.

  88 . A few simple instances of the position of the Center of Gravity have been mentioned in § 77. These were as follows:

  (a ) the Center of Gravity of a uniform rod is at its middle point;

  (b ) the Center of Gravity of a uniform circular disk, circular ring, or sphere is at the center;

  (c ) the Center of Gravity of a cube or parallelepiped is at the center (i.e. the intersection of the diagonals).

  89

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