Rotational Dynamics - Lecture 01

Fundamental vocabulary and concepts from the first lecture on Rotational Dynamics, covering circular motion types, accelerations, angular kinematics, and characteristics of motion.

Circular Motion

The motion of a particle along the circumference of a circle.

Uniform Circular Motion (UCM)

A type of circular motion where the speed of the particle remains constant at any instant.

Non-uniform Circular Motion (Non-UCM)

A type of circular motion where the speed of the particle is variable at any instant.

Centripetal Acceleration ($a_c$)

Also called radial acceleration ($a_r$), it is always directed towards the centre; circular motion is not possible without it.

Tangential Acceleration ($a_t$)

The component of acceleration that increases or reduces tangential velocity; it occurs only in Non-uniform Circular Motion (Non-UCM).

Radial Acceleration Formula

The relationship expressed as $a_c = a_r = \frac{v^2}{R} = R \times \text{ω}^2 = v \times \text{ω}$.

Angular Displacement ($θ$)

The angular analog of linear displacement ($s$), measured in units of $rad$, related by the formula $s = R \times θ$.

Angular Velocity ($ω$)

The angular analog of linear velocity ($v$), measured in units of $rad\,s^{-1}$, related by the formula $v = R \times ω$.

Angular Acceleration ($α$)

The angular analog of linear acceleration ($a$), measured in units of $rad\,s^{-2}$, related by the formula $a = R \times α$.

Centre of Mass (COM)

A point inside or outside the body where the whole mass of the body is assumed to be concentrated.

Accelerated Motion

A characteristic of circular motion where acceleration exists because the direction of velocity changes at every instant.

Periodic Motion

A characteristic of circular motion where the particle repeats its path along the same trajectory over time.

Kinematical Equations (Angular)

Equations used for constant angular acceleration: 1) $ω_f = ω_i + α \times t$, 2) $θ = ω_i \times t + \frac{1}{2} \times α \times t^2$, 3) $ω_f^2 = ω_i^2 + 2 \times α \times θ$.