Unit iii properties of surfaces and solids
- 1. Unit- 3(Properties of Surfaces and Solids) 2marks 1. Define centroid. The centroid is defined as the point at which the total area of plane figures namely rectangle, square, triangle circle etc. It is assumed to be concentrated. 2. Define centre gravity. The centre of gravity of a body may be defined as the point through which the entire weight of the body acts. Denoted by CG or G 3. State Pappus-Guldinus theorem for finding surface area. It states that “The area of surface of revolution is equal to the product of the length of the generating curve and the distance travelled by the centroid of the generating curve while generating that surface”. 4. State Pappus-Guldinus theorem for finding volume. It states that “the volume of a body of revolution is obtained from the product of the generating area and the distance travelled by the centroid of the area, while the body is being generated”. 4. Define moment of inertia. A quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation 5. Define radius of gyration. Radius of gyration is defined about an axis. The elemental parts of an area are concentrated at a radius from an axis such that the area moment of inertia about the same axis is same. 6. What is polar moment of inertia? The area moment of inertia about an axis perpendicular to the plane of an area is called polar moment of inertia. Ip= Ixx + Iyy
- 2. 7. When will the product of inertia will be zero? The product of inertia of a symmetrical area about one or two axes of symmetry must be zero. 8. Define parallel axis theorem. The theorem of parallel axis states that the moment of inertia of a body about an axis parallel to an axis passing through the centre of mass is equal to the sum of the moment of inertia of body about an axis passing through centre of mass and product of mass and square of the distance between the two axes. Io= Ic+ mh2 9. Define perpendicular axis theorem. This theorem states that the moment of inertia of a planar body about an axis perpendicular to its plane is equal to the sum of its moments of inertia about two perpendicular axes concurrent with the perpendicular axis and lying in the plane of the body. Ioz= Iox + Ioy 10. Define mass moment of inertia. The property which measures the resistance of a body to angular acceleration is the mass moment of inertia of the body. The larger the Mass Moment of Inertia the smaller the angular acceleration about that axis for a given torque. Note: Simple Problems may asked by using formulas or formulas may asked for simple sections.