1. What is Center of Gravity ?
A point may be found out in a body, through which the resultant of all such parallel forces act. The point, through which the whole weight of the body acts is known as Center of Gravity (Briefly C.G). Each body has only one CG and its location in the body is depends upon the shape of the body.
We can find the center of gravity or centroid by the following methods.
- By Geometrical consideration
- By Moment
- By Graphical Method
Centroid: Any plane figures don’t have mass. it only has area. Center of the plane figure is known as centroid. You have understood the difference between C.G and Centroid.
Axis of Reference: Center of Gravity of a body always calculated with reference to some axis. For plane figure we can assume axis are X-X and Y-Y, in this case the C.G of the Axis X-X is x and along Y-Y axis y.
Table of Contents
2. Geometrical Consideration:
1. We can find the C.G point in a rectangle and square where two diagonal intersect each other.
Reference to Fig. 4.1 Rectangle AC and BD intersecting each other at point O. Point O is the C.G of the figure, we can locate the C.G point from base BC at AB/2 or DC/2. Similarly, from base DC location of the C.G will be at BC/2 or AD/2.
2. We can find the C.G point in a Triangle where three median intersects each other.
Reference to Fig. 4.1 Equilateral triangle ABC has three medians from vertex A, C and B intersecting each other at point O. Hence, point O is the C.G of the figure, we can locate the C.G point from base AB at height of triangle(H)/2. The system of finding the C.G of the other Triangle will remain same, but the calculation will change depend on the Triangle.
3. We can find the C.G point in a Trapezium ABCD at the height of the figure.
Reference to Fig. 4.1 Trapezium ABCD has a height, it is the shortest distance between the two sides AB and CD. The location of the C.G will be at H(AB+2CD)/3(AB+CD)
By Moment:
An object has a body mass M, now we need to find out its Center of Gravity. Let’s assume (Ref. Fig. 4.4) there are 2 different point has mass M1 and M2 at a distance from the C.G line X1 and X2 respectively.
3. Center of Gravity of Common Bodies
| Body | Position of C.G. |
|---|---|
| Uniform Rod | Midpoint |
| Rectangle | Intersection of diagonals |
| Square | Intersection of diagonals |
| Circle | Centre |
| Sphere | Centre |
| Cube | Geometrical centre |
| Cylinder | Midpoint on axis |
| Cone | One-fourth of height from base |
| Hemisphere (Solid) | (3r/8) from the flat face |
| Semicircular Lamina | ( 4R/3pi) from diameter |
4. Mathematical Formula
For discrete particles,
Where:
- โ = Weight of each particle
- โ = Coordinates of each particle
For continuous bodies,
Factors Affecting Center of Gravity
- Shape of the object
- Density distribution
- Addition or removal of material
- Position of attached components
5. Methods to Determine Center of Gravity
1. Symmetry Method
Used for regular objects.
Example:
- Circle โ Centre
- Rectangle โ Centre
2. Suspension Method
Used for irregular lamina.
Procedure:
- Suspend the object from one point.
- Draw the vertical line using a plumb bob.
- Repeat from another suspension point.
- The intersection of the two lines is the C.G.
3. Composite Body Method
The body is divided into simple shapes, and the centroid formula is applied.
6. Stability and Center of Gravity
Stable Equilibrium
- Low C.G.
- Wide base.
- Difficult to overturn.
Example:
- Passenger bus
- Heavy crane
Unstable Equilibrium
- High C.G.
- Narrow base.
- Easily tips over.
Example:
- Pencil standing vertically
Neutral Equilibrium
The C.G. remains at the same height after displacement.
Example:
- Ball on a flat surface
7. Engineering Applications
Automobile Engineering
- Lower C.G. improves cornering and reduces rollover risk.
Cranes
- Counterweights are used to keep the C.G. within the base.
Aircraft
- Proper C.G. is essential for stable flight.
Ships
- The C.G. affects stability and prevents capsizing.
Construction
- Heavy structural members are lifted considering their C.G. to avoid rotation during lifting.
8. Example Problem
A beam carries two loads:
- 200 N at 2 m
- 400 N at 5 m
Find the center of gravity.
Solution
Answer: The center of gravity is 4 m from the reference point.
9. Difference Between Center of Gravity and Center of Mass
| Center of Gravity | Center of Mass |
|---|---|
| Depends on gravity | Independent of gravity |
| Point where weight acts | Point where mass is concentrated |
| Changes if gravity changes | Remains unchanged |
| Same as center of mass in uniform gravity | Fundamental property of mass |
Key Points to Remember
- Center of gravity is the point through which the total weight acts.
- For symmetrical bodies, the C.G. lies at the geometric center.
- A lower C.G. provides greater stability.
- In a uniform gravitational field, the center of gravity and center of mass are identical.
- Engineers use C.G. calculations in design, lifting, transportation, and structural analysis.
Frequently Asked Questions (FAQs)
1. What is the center of gravity?
It is the point through which the entire weight of a body acts vertically downward.
2. Is the center of gravity always inside the object?
No. For some shapes (such as a ring or boomerang), it can lie outside the material.
3. What is the difference between center of gravity and centroid?
The centroid is the geometric center of an area, while the center of gravity is the point where the body’s weight acts.
4. Why is the center of gravity important in engineering?
It is essential for ensuring stability, safe lifting, proper balancing, and efficient design of structures and machines.
5. Can the center of gravity change?
Yes. It changes if the mass distribution changes, such as when a load is added, removed, or shifted.