What is angular acceleration?

Angular Acceleration

Angular acceleration is the rate of change of angular velocity. It is a vector quantity that describes how quickly an object's rotational speed and/or direction is changing.

• Definition: Angular acceleration ($\alpha$) is defined as the change in angular velocity ($\omega$) divided by the change in time ($t$). Mathematically, it is expressed as:

  $\alpha = \frac{\Delta \omega}{\Delta t}$

• Units: The standard SI unit for angular acceleration is radians per second squared (rad/s²).

• Relationship to Torque: Angular acceleration is directly proportional to torque ($τ$) and inversely proportional to the moment of inertia ($I$) of the object. This relationship is described by the rotational analog of Newton's second law:

  $τ = I \alpha$

• Constant Angular Acceleration: When the angular acceleration is constant, analogous equations to linear kinematics can be used:

  • $\omega_f = \omega_i + \alpha t$
  • $\theta = \omega_i t + \frac{1}{2} \alpha t^2$
  • $\omega_f^2 = \omega_i^2 + 2 \alpha \theta$ Where $\omega_f$ is final angular velocity, $\omega_i$ is initial angular velocity, $\theta$ is angular displacement, and $t$ is time.

• Direction: The direction of the angular acceleration vector is along the axis of rotation. It follows the right-hand rule: if the angular velocity is increasing, the angular acceleration is in the same direction as the angular velocity; if the angular velocity is decreasing, the angular acceleration is in the opposite direction.