Rotational Dynamic 

In mechanics, we usually deal with linear motion first — objects moving in a straight line. But many bodies in the real world rotate: wheels, fans, planets, atoms… that’s where rotational dynamics comes in. 

Key idea 

Rotational motion is very similar to linear motion — the concepts correspond like this:

• Linear Motion (Translational)

• Rotational Motion

• Force (F)

• Torque (τ)

• Mass (m)

• Moment of Inertia (I)

• Linear Acceleration (a)

• Angular Acceleration (α)

• Momentum (p = mv)

• Angular Momentum (L = Iω)

• Kinetic Energy (½mv²)

• Rotational K.E. (½Iω²)

So you can think of rotational dynamics as the “spinning version” of Newton’s laws. 

 Rigid Body Dynamics

A rigid body is one in which the distance between any two particles remains constant.

Motion can be:

Pure translation: All particles have same velocity.

Pure rotation: All particles rotate about an axis.

General motion: Combination of translation + rotation.

Angular Variables 

Moment of Inertia 

Parallel Axis Theorem 

The moment of inertia of a body about an arbitrary axis is equal to the sum of its moment of inertia about a parallel axis passing through its center of mass and the product of its mass and the square of the distance between the two axes. 

Perpendicular Axis Theorem 

For any planar rigid body, the moment of inertia about an axis perpendicular to the plane of the body is equal to the sum of the moments of inertia about two perpendicular axes in the plane of the body that intersects the first axis.