Physics
Physi Video Notes
cs Video Notes
Centre
Of Mass
Class 11ᵗʰ
, Centre of Mass Didn’t understand? Watch
the video (Click Here)
The centre of mass is defined as the point at which the mass of an object or
system can be considered to be concentrated for the purpose of analyzing its
motion.
It is the average position of all the mass in the system, weighted by the mass of
each individual part.
Mass Distribution in system of particles
Discrete Continuous Mass
Particles Distribution
Discrete Particles:
In a discrete particle system, the mass is concentrated at distinct, separate points
(particles), each with a specific mass and position.
The centre of mass is found by taking the weighted average of the positions of all
the particles in the system.
→
For a system of n discrete particles, the centre of mass R is calculated using the
formula:
Where:
mᵢ is the mass of the iᵗʰ particle,
rᵢ is the position vector of the iᵗʰ particle,
∑mᵢ is the total mass of the system.
Example: A system of three particles with masses
→ → →
m₁ , m₂ , m₃located at positions r₁, r₂ , r₃ respectively.
The centre of mass is given by :
Center of Mass of System of Two Point Masses Didn’t understand? Watch
In a two-particle system, the position of the centre of mass the video (Click Here)
depends on the masses and the positions of the two particles.
Consider a system with two particles:
→
Particle 1 has mass m₁ and is located at position r₁,
Physi Video Notes
cs Video Notes
Centre
Of Mass
Class 11ᵗʰ
, Centre of Mass Didn’t understand? Watch
the video (Click Here)
The centre of mass is defined as the point at which the mass of an object or
system can be considered to be concentrated for the purpose of analyzing its
motion.
It is the average position of all the mass in the system, weighted by the mass of
each individual part.
Mass Distribution in system of particles
Discrete Continuous Mass
Particles Distribution
Discrete Particles:
In a discrete particle system, the mass is concentrated at distinct, separate points
(particles), each with a specific mass and position.
The centre of mass is found by taking the weighted average of the positions of all
the particles in the system.
→
For a system of n discrete particles, the centre of mass R is calculated using the
formula:
Where:
mᵢ is the mass of the iᵗʰ particle,
rᵢ is the position vector of the iᵗʰ particle,
∑mᵢ is the total mass of the system.
Example: A system of three particles with masses
→ → →
m₁ , m₂ , m₃located at positions r₁, r₂ , r₃ respectively.
The centre of mass is given by :
Center of Mass of System of Two Point Masses Didn’t understand? Watch
In a two-particle system, the position of the centre of mass the video (Click Here)
depends on the masses and the positions of the two particles.
Consider a system with two particles:
→
Particle 1 has mass m₁ and is located at position r₁,
