rotational motion

Rotational Motion

Occurs when an object spins around an axis.

Angular Displacement

The angle through which an object has rotated about a fixed axis.

Angular Velocity

The rate of change of angular displacement, measured in radians per second.

Angular Acceleration

The rate of change of angular velocity, represented in radians per second squared.

Torque (τ)

The rotational equivalent of force, calculated as τ = r × F, where r is the distance from the pivot to the force application point.

Moment of Inertia (I)

The rotational analog of mass, measuring resistance to rotation based on mass distribution around the axis.

Conservation of Angular Momentum

In the absence of external torque, the total angular momentum of a system remains constant.

Angular Momentum (L)

Expressed as L = I × ω, where I is moment of inertia and ω is angular velocity.

Equation for Angular Displacement

θ = θ0 + (1/2)(ω0 + ω)t for constant angular acceleration.

Equation for Angular Velocity

ω = ω0 + αt for calculating final angular velocity.

Equation for Angular Acceleration

ω^2 = ω0^2 + 2αθ relating angular acceleration and displacement.

Applications of Rotational Motion

Relevant in fields like engineering, astrophysics, and practical scenarios such as wheels and gears.