Difference between Center of Mass and Center of Gravity

Physics has always captivated those eager to investigate the basic forces and concepts governing the universe. Subjects like gravity, inertia, distance, and displacement provide limitless opportunities for investigation. Science as a whole investigates diverse systems, ranging from the human body and solar system to plant and animal tissues and chemicals.

Two significant concepts that frequently emerge in physics are the centre of mass and the centre of gravity. While both terms are often used interchangeably, they have distinct meanings. The centre of gravity refers to the point where the entire weight of an object can be considered to act, balancing the force of gravity. In comparison, the centre of mass is the point at which the total mass of the object is concentrated, and it represents the average location of the object's mass distribution.

What is the Center of Mass?

The center of mass is defined as the point at which the mass's relative position is calculated to be zero. The mass distribution is considered uniform around the center of mass. Because the center of mass is independent of the gravitational field (g), the body remains unaffected by changes in the gravitational field's force. 

• The center of mass is the point where an object's mass is concentrated.
• Its position doesn't change with variations in the gravitational field.
• For objects with uniform density (like spheres or cubes), the center of mass is at the center.
• For irregular objects, the center of mass is closer to the denser parts.
• The center of mass moves as if all the mass is concentrated at that point.
• If no external force acts on it, the center of mass moves in a straight line with constant speed.

What is the Center of Gravity?

The center of gravity is defined as the exact place in a body around which the instants due to gravity are regarded as zero. The center of gravity is the point at which the entire body is perfectly balanced in relation to gravity. 

• The center of gravity is the point where the entire weight of an object is considered to act.
• It is the point where the object would balance perfectly if supported at that spot.
• The center of gravity depends on the distribution of weight within the object.
• For uniform objects, the center of gravity is usually at the center.
• For irregular objects, the center of gravity is located closer to the heavier parts.
• The center of gravity is influenced by gravity, so it changes with the object's position in different gravitational fields.

Difference Between Center of Mass and Center of Gravity

Applications of Center of Mass and Center of Gravity

Center Of Mass

• The center of mass in the human body is around the lower abdomen, shifting with posture and body shape, aiding balance in athletes.
• In a bicycle, the center of mass is at the midpoint of the frame, ensuring stability when in motion.
• For aircraft design, the center of mass is carefully positioned to maintain proper balance and stability in flight.
• In space, a spacecraft’s center of mass dictates its movement and rotation, helping astronauts maneuver.
• When a ball is thrown, its center of mass follows a parabolic trajectory, aiding in analyzing its motion.

Center of Gravity

• A ladder's balance depends on its center of gravity; a higher one may cause tipping, while lowering it improves stability.
• A car's center of gravity affects handling, with higher centers (like SUVs) being more prone to tipping.
• A person's center of gravity must stay above their feet to maintain balance; if shifted too far, they will fall.
• A seesaw balances when the combined center of gravity aligns with the pivot point; uneven weight causes tilting.
• In building design, the center of gravity ensures stability, especially in tall structures during high winds or earthquakes.
• A rocket's center of gravity affects its launch stability, requiring precise alignment for controlled flight.

Solved Problems

Problem 1: Two-point masses of 3 kg and 5 kg are located at 4 m and 8 m on X-axis. Find the center of mass.

Solution:

Given,

m₁ = 3 kg

m₂ = 5 kg

x₁ = 4 m

x₂ = 8m

Using Center of mass formula,

X_cm = m₁x₁+m₂x₂/ m₁+m₂

= (3)(4) + (5)(8)/ 3 + 5

= 6.5

So, the center of mass is 6.5 m.

Problem 2: Two-point masses of 2 kg and 5 kg are located at 10 m and -5 m on Y-axis respectively. Calculate the center of mass.

Solution:

Given,

m₁ = 2 kg

m₂ = 5 kg

y₁ = 10 m

y₂ = -5 m

Using center of mass formula,

Y_cm = m₁y₁+m₂y₂/m₁+m₂

= (2)(10)+(5)(-5)/2+5

= -5/7

So, the center of mass is -5/7 m.

Problem 3: Two-point masses of 4 kg and 6 kg are located at 2 m and 5 m on the X-axis. Calculate the center of mass.

Using the center of mass formula:

Xcm​=(4)(2)+(6)(5)​/ 4+6 =8+30​/10= 38/10= 3.8 m

So, the center of mass is 3.8 m.

Problem 4 : A 10 kg object is placed at 3 m on the Y-axis. What is the center of gravity of this object?

For a single object, the center of gravity is the same as its position. Therefore, the center of gravity is 3 m.

Problem 5 :Two-point masses of 3 kg and 7 kg are located at 4 m and -2 m on the Y-axis. Calculate the center of mass.

Using the center of mass formula:

Xcm​=(3)(4)+(7)(-2)​/3+7=12-14​/10= -2/10= -0.2 m

So, the center of mass is -0.2 m.

Related Reads,

• Centre of Gravity
• Gravitational Force
• Universal Law of Gravitation