Dynamics of Rigid Bodies Formula for NEET

Dynamics of Rigid Bodies Formula : Dynamics of rigid bodies refers to the branch of classical mechanics that deals with the motion of objects that maintain a constant shape and size under the influence of external forces. In other words, it involves the study of how rigid bodies move and respond to forces and torques (rotational forces) applied to them.

Dynamics of Rigid Bodies formula for NEET

Translational Motion - Translational motion refers to the movement of an object in which every point of the object moves along parallel paths. In translational motion, the entire object moves from one place to another without changing its orientation.

Rotational Motion - Rotational motion, is the movement of an object in a circular path around a fixed point or axis. In rotational motion, the object spins or rotates about a central point. Each point of the object moves in a circular path, and the object changes orientation.

Moment of Inertia Definition

Basic Formula Moment of Inertia

I=mr ²

Moment of Inertia for Different Objects

• $m$ represents mass,
• $r$ is the perpendicular distance from the axis of rotation to the mass element,
• $L$ is the length of the rod,
• $a$ and $b$ are the sides of the rectangular plate,
• $R$ is the radius of the cylinder or sphere,
• R ₁ ​ and R _{2 ​} are the inner and outer radius of the hollow cylinder or disk,
• I ₁ ​ and I ₂ ​ are the individual moments of inertia for composite objects.

Radius of Gyration

• $I$ is the moment of inertia of the object,
• $m$ is the mass of the object, and
• $k$ is the radius of gyration.

Relation Between Torque and Moment of Inertia

τ=Iα

Angular Momentum Definition

Formula for Angular Momentum

$L=I\omega$

• $L$ is the angular momentum,
• $I$ is the moment of inertia of the object, and
• $\omega$ is the angular velocity of the object.

Relation Between Angular Momentum and Torque

τ=dt/dL ​

• τ is the torque applied to the object,
• L is the angular momentum of the object,
• dt/dL represents the time rate of change of angular momentum.