Siddhant Kolase - FOSD Unit-3

Unit-3: Centroid, Centre of Gravity and Moment of Inertia

Centroid

- A centroid is the geometric center of a shape—the point where the shape would balance if it were made of uniform material.

Centroid of simple planes

- Solid Mechanics is the branch of mechanics that deals with the behavior of solid bodies under the action of external forces, loads, and moments.

Centroid of composite sections

- Fluid Mechanics is the branch of mechanics that deals with the behavior of fluids (liquids and gases) at rest and in motion, and the forces acting on fluids and fluid systems.

Numericals on Centroid

Centre of Gravity

The centre of gravity of a body is the point through which the entire weight of the body is considered to act, irrespective of the body's orientation.

Centre of Gravity of simple solids

- Statics is the branch of Engineering Mechanics that deals with the study of rigid bodies at rest or in equilibrium under the action of forces and moments.

Centre of Gravity of compound solids

- Dynamics is the branch of Engineering Mechanics that deals with the study of rigid bodies in motion and the forces and moments associated with that motion.

First moment of area

- Kinetics is the branch of Dynamics that deals with the study of the motion of rigid bodies considering the forces and moments responsible for that motion.

Second moment of area

- Kinematics is the branch of Dynamics that deals with the motion of bodies without considering the forces and moments causing the motion.

Radius of gyration

- A rigid body is an idealized solid body in which the distance between any two points remains constant, even when external forces or moments act on it.

- A rigid body is a body that does not undergo deformation under the action of external forces.

Parallel axis theorem

The moment of inertia of a plane area about any axis is equal to the moment of inertia about a parallel axis passing through its centroid plus the product of the area and the square of the perpendicular distance between the two axes.

principal moment of inertia

A body continues to be in its state of rest or of uniform motion in a straight line unless acted upon by an external unbalanced force

Moment of inertia of simple bodies

- The rate of change of momentum of a body is directly proportional to the applied external force and takes place in the direction of that force.

Moment of inertia of composite

- For every action, there is an equal and opposite reaction.

Mass moment of inertia.

- Every two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

Questions

1. Define statics and explain the concept of a rigid body.
2. Define force and list its main characteristics with suitable examples.
3. Explain the graphical representation of a force and different force systems.
4. State and explain the law of moment and Varignon’s theorem with an example.
5. Resolve a given force into rectangular components and determine the resultant of two concurrent forces.
6. A force of 100 N acts at an angle of 30 degrees to the horizontal. Find its horizontal and vertical components.
7. State the conditions of equilibrium for a coplanar force system and explain their significance in engineering mechanics.
8. Using Lami’s theorem, determine the unknown forces acting on a particle in equilibrium under three concurrent forces.
9. Describe the different types of supports, loads, and beams used in structural mechanics with neat sketches.
10. Determine the support reactions of a simply supported beam subjected to point load and uniformly distributed load.

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