Important Derivations for Class 11 Physics Chapter 5 Laws of Motion

Important Derivations for Class 11 Physics Chapter 5 Laws of Motion

Here we are providing important derivations for Class 11 Physics Chapter 5 Laws of Motion.

Derivation 1:

Derivation of First Law of Motion from Newton’s Second Law

To derive the First Law of Motion (Law of Inertia) from Newton’s Second Law of Motion (F = ma), we consider a particle that is at rest or moving with a constant velocity (zero acceleration). The First Law of Motion states that an object remains at rest or moves with a constant velocity unless acted upon by an external force.

Let’s assume the following:
– \(F\) = Net external force acting on the particle (resultant force)
– \(m\) = Mass of the particle
– \(a\) = Acceleration of the particle

According to Newton’s Second Law of Motion, we have: \[ F = m \cdot a \] Now, for the First Law of Motion, we want to consider the case when the particle is at rest or moving with a constant velocity. This means the acceleration (\(a\)) is zero. In other words, the net external force acting on the particle is also zero. \[ a = 0 \quad \Rightarrow \quad F = m \cdot 0 \quad \Rightarrow \quad F = 0 \] This implies that if the net external force acting on the particle is zero (\(F = 0\)), the acceleration of the particle (\(a\)) is also zero. Therefore, the particle will either be at rest or move with a constant velocity.

Hence, we have derived the First Law of Motion (Law of Inertia) from Newton’s Second Law of Motion, which states that an object remains at rest or moves with a constant velocity unless acted upon by an external force.

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