System of Particles and Rotational Motion NEET Notes | Definitions, Formulas, Applications

System of Particles and Rotational Motion NEET Notes

System of Particles and Rotational Motion is an important chapter in NEET Physics that deals with the motion of rigid bodies, rotational dynamics, and moment of inertia. Understanding rotational motion is crucial for solving numerical problems related to mechanics.

Importance of System of Particles and Rotational Motion in NEET

• Forms the basis of Rigid Body Dynamics.
• Frequently asked questions on torque, angular momentum, and rolling motion.
• Essential for solving rotational kinematics and moment of inertia problems.
• Helps in understanding the motion of planets, satellites, and mechanical systems.

Understanding System of Particles and Rotational Motion

1. Centre of Mass (COM)

The Centre of Mass (COM) of a system is the point where the entire mass of the system is considered to be concentrated.

Formula for Centre of Mass:

X_com = (m₁x₁ + m₂x₂ + ... + m_nx_n) / (m₁ + m₂ + ... + m_n)

Similarly, Y_com and Z_com can be calculated in 2D and 3D cases.

2. Torque

Torque is the rotational equivalent of force and measures the ability of a force to cause rotation.

Formula: Torque (τ) = r × F = rF sinθ

Where:

• r: Distance from axis of rotation
• F: Applied force
• θ: Angle between force and lever arm

3. Angular Momentum

Angular momentum (L) is the rotational equivalent of linear momentum.

Formula: L = r × p = Iω

Where:

• r: Radius vector
• p: Linear momentum
• I: Moment of inertia
• ω: Angular velocity

4. Moment of Inertia (I)

Moment of inertia (I) measures the rotational inertia of a body.

Formula: I = Σ m_ir_i²

Common moments of inertia:

• Ring about its central axis: I = MR²
• Solid sphere about its diameter: I = (2/5)MR²
• Rod about its center: I = (1/12)ML²

5. Rotational Kinetic Energy

Rotational kinetic energy is the energy due to rotational motion.

Formula: KE = (1/2) Iω²

6. Rolling Motion

Rolling motion is a combination of translation and rotation.

Formula for Rolling Motion:

v = rω

Where:

• v: Linear velocity
• r: Radius of rolling object
• ω: Angular velocity

Key Formulas for System of Particles and Rotational Motion (NEET)

• Centre of Mass: X_com = Σ m_ix_i / Σ m_i
• Torque: τ = r × F = rF sinθ
• Angular Momentum: L = Iω
• Moment of Inertia: I = Σ m_ir_i²
• Rotational Kinetic Energy: KE = (1/2) Iω²
• Rolling Motion: v = rω

Why Study System of Particles and Rotational Motion for NEET?

• Essential for understanding rotational dynamics.
• Frequently asked in NEET Physics numerical problems.
• Helps in solving rigid body motion and moment of inertia questions.
• Useful for advanced physics and engineering applications.

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