Centre of Mass
The center of mass is the point in a system or object where its mass can be considered to be concentrated. It is the average position of all the mass in the system, and it behaves as if all the mass is concentrated at that point. In a uniform gravitational field, the center of mass is also the point where the force of gravity can be considered to act.
3 Key excerpts on "Centre of Mass"
eBook - ePubBasic Engineering Mechanics Explained, Volume 1
Principles and Static Forces
- Gregory Pastoll, Gregory Pastoll(Authors)
- 2019(Publication Date)
- Gregory Pastoll(Publisher)
...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...
eBook - ePub- 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/m 3. 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 of a body is the point in or near the body through which the resultant attraction of the earth acts for all orientations of the body...
eBook - ePub- Bertrand Russell(Author)
- 2009(Publication Date)
- Routledge(Publisher)
...The mass as measured by an observer who is in motion relative to the body in question is a relative quantity, and has no physical significance as a property of the body. The ‘proper mass’ is a genuine property of the body, not dependent upon the observer; but it, also, is not strictly constant. As we shall see shortly, the notion of mass becomes absorbed into the notion of energy; it represents, so to speak, the energy which the body expends internally, as opposed to that which it displays to the outer world. Conservation of mass, conservation of momentum, and conservation of energy were the great principles of classical mechanics. Let us next consider conservation of momentum. The momentum of a body in a given direction is its velocity in that direction multiplied by its mass. Thus a heavy body moving slowly may have the same momentum as a light body moving fast. When a number of bodies interact in any way, for instance by collisions, or by mutual gravitation, so long as no outside influences come in, the total momentum of all the bodies in any direction remains unchanged. This law remains true in the theory of relativity. For different observers, the mass will be different, but so will the velocity; these two differences neutralise each other, and it turns out that the principle still remains true. The momentum of a body is different in different directions. The ordinary way of measuring it is to take the velocity in a given direction (as measured by the observer) and multiply it by the mass (as measured by the observer). Now the velocity in a given direction is the distance travelled in that direction in unit time. Suppose we take instead the distance travelled in that direction while the body moves through unit ‘interval’...
