Angular Acceleration

4.1.4 Angular Acceleration

23. Definition of Angular Acceleration

Angular acceleration is the rate of change of angular velocity.

α = Δω / Δt

Its SI unit is:

rad s⁻²

24. Average Angular Acceleration

α_avg = ω_f − ω_it

Here:

• ω_i is initial angular velocity.
• ω_f is final angular velocity.

25. Instantaneous Angular Acceleration

α = lim (Δt → 0) (Δω / Δt)

Using calculus notation:

α = dω / dt

26. Sign of Angular Acceleration

Angular acceleration is positive when angular velocity increases in the selected positive rotational direction.

When an object slows down:

• Angular velocity and angular acceleration act in opposite directions.
• Their signs are opposite.

Negative angular acceleration does not always mean decreasing speed. The directions of ω and α must be compared.

27. Equations of Rotational Motion

For constant angular acceleration:

First Equation

ω_f = ω_i + αt

Second Equation

Δθ = ω_i t + ½ α t²

Third Equation

ω_f² = ω_i² + 2α Δθ

Average-Angular-Velocity Relation

Δθ = (ω_i + ω_f2) t

28. Linear and Rotational Equations Comparison

Linear and Rotational Equations Comparison