## Motion of Center of Mass – Class 11 | Chapter – 7 | Physics Short Notes Series PDF for NEET & JEE

Motion of Center of Mass: The motion of center of mass (COM) of an object or system can be described using the principles of Newton’s laws of motion. The motion of center of mass is related to the motion of the object or system as a whole, and can be used to analyze and predict the behavior of the object or system.

The motion of center of mass is a useful concept in physics as it allows us to simplify the analysis of the motion of complex systems, by treating them as point masses located at their center of mass. By analyzing the motion of the COM, we can understand the behavior of the object or system as a whole.

## Motion of Center of Mass

The first law of motion, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity, unless acted upon by an external force. This law can be applied to the motion of the COM of an object or system, which will remain at rest or in uniform motion unless acted upon by an external force.

The second law of motion states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. This law can be applied to the motion of the COM, which will accelerate in the direction of the net external force acting on the object or system. The acceleration of the COM is directly proportional to the force acting on the object or system, and inversely proportional to its mass.

The third law of motion states that for every action, there is an equal and opposite reaction. This law can be applied to the motion of the COM, which will experience an equal and opposite force to any force applied to the object or system. This means that the COM will move in response to external forces, but will also exert an equal and opposite force on the environment.

## Applications of Motion of Center of Mass

The concept of the center of mass (COM) and its motion has many applications in physics and engineering. Some of the key applications of the motion of center of mass include:

• Stability analysis: The motion of the COM is used to analyze the stability of objects and systems. An object or system is in stable equilibrium when the COM is at its lowest point. For example, the design of buildings, bridges, and other structures must take into account the location of the COM to ensure that they are stable.
• Projectile motion: The motion of the COM is used to analyze the trajectory of a projectile. By considering the motion of the COM, we can determine the point where the projectile will land and how far it will travel.
• Vehicle dynamics: The motion of the COM is used to analyze the stability and handling of vehicles, such as cars and airplanes. By considering the motion of the COM, we can determine the effects of external forces on the vehicle, such as wind resistance, and adjust the design accordingly.
• Spacecraft dynamics: The motion of the COM is used to analyze the stability and control of spacecraft in space. By considering the motion of the COM, we can determine the effects of external forces on the spacecraft, such as gravitational forces from other objects, and adjust the trajectory accordingly.
• Biomechanics: The motion of the COM is used to analyze the motion of living organisms, such as humans and animals. By considering the motion of the COM, we can determine how forces are distributed throughout the body during movement, and adjust training and rehabilitation programs accordingly.

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