NEET Physics: Waves – NCERT Masterclass & 100 MCQ Quiz

SYSTEMS OF PARTICLES & ROTATIONAL MOTION

Complete NCERT Study Notes & 5-Part Mega Quiz for NEET

1. Centre of Mass (COM)

The centre of mass of a system of particles is that single point where the entire mass of the system is supposed to be concentrated. For a system of '$n$' particles, the position vector of the centre of mass is given by:

$$\vec{R}_{cm} = \frac{\sum m_i \vec{r}_i}{M}$$

Motion of COM: The centre of mass of a system moves as if the entire mass of the system is concentrated at this point and all the external forces are applied directly to it. Internal forces cannot change the trajectory of the centre of mass.

2. Cross Product and Angular Variables

Unlike translational motion, rotational kinematics involves angles. The linear velocity $\vec{v}$ of a particle in a rotating body is related to its angular velocity $\vec{\omega}$ by the vector cross product:

$$\vec{v} = \vec{\omega} \times \vec{r}$$

Right-Hand Rule: The direction of angular velocity $\vec{\omega}$ and angular acceleration $\vec{\alpha}$ is always along the axis of rotation, determined by the right-hand grip rule.

3. Torque and Angular Momentum

Torque ($\vec{\tau}$): The turning effect of a force. It is the cross product of the position vector and the force vector: $\vec{\tau} = \vec{r} \times \vec{F}$.

Angular Momentum ($\vec{L}$): The rotational equivalent of linear momentum: $\vec{L} = \vec{r} \times \vec{p}$.

Conservation of Angular Momentum: If the net external torque on a system is zero, its total angular momentum remains strictly conserved ($\vec{L} = \text{constant}$).

4. Moment of Inertia & Equilibrium

Moment of Inertia ($I$): The rotational analog of mass. It represents the inertia of a body against rotational motion. $I = \sum m_i r_i^2$. It depends on the mass, its distribution, and the axis of rotation.

• Theorem of Parallel Axes: $I = I_{cm} + Md^2$
• Theorem of Perpendicular Axes (for planar bodies): $I_z = I_x + I_y$

Equilibrium: A rigid body is in complete mechanical equilibrium if both the net external force is zero ($\sum \vec{F} = 0$) and the net external torque is zero ($\sum \vec{\tau} = 0$).

5. Rotational Dynamics and Rolling Motion

Newton's Second Law for Rotation: $\tau = I \alpha$.

Pure Rolling: Rolling without slipping occurs when the velocity of the point of contact with the ground is zero. In this case, $v_{cm} = \omega R$. The total kinetic energy of a rolling body is the sum of its translational and rotational kinetic energies:

$$K_{total} = \frac{1}{2} M v_{cm}^2 + \frac{1}{2} I \omega^2$$

← Back to NEET Resource Hub

🚀 NEET ROTATIONAL MOTION MEGA QUIZ (100 MCQ)

Solve the 5 parts below to master Centre of Mass, Torque, and Rolling Dynamics.

← Back to NEET Resource Hub