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Angular Acceleration
Angular acceleration is the rate of change of angular velocity. For constant α, rotational kinematics equations mirror linear ones.
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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
αavg = ωf − ωit
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
ωf = ωi + αt
Second Equation
Δθ = ωi t + ½ α t²
Third Equation
ωf² = ωi² + 2α Δθ
Average-Angular-Velocity Relation
Δθ = (ωi + ωf2) t
28. Linear and Rotational Equations Comparison
Linear and Rotational Equations Comparison
| Linear motion | Rotational motion |
|---|---|
| vf = vi + at | ωf = ωi + αt |
| s = vi t + ½ a t² | Δθ = ωi t + ½ α t² |
| vf² = vi² + 2as | ωf² = ωi² + 2α Δθ |
| s = (vi + vf2) t | Δθ = (ωi + ωf2) t |
Exam Focus
Exam Focus
Important points
- α = Δω / Δt
- ω = ω₀ + αt
- θ = ω₀t + ½αt²
- ω² = ω₀² + 2αθ
Important formulas
- α = Δω / Δt
- ω = ω₀ + αt
- θ = ω₀t + ½αt²
- ω² = ω₀² + 2αθ
Common Mistakes
Common Mistakes
- Mistake
Using degrees directly in s = rθ.
- Mistake
Confusing angular position with angular displacement.
- Mistake
Writing angular velocity in m s⁻¹.
- Mistake
Assuming different points have different angular velocities on a rigid body.
- Mistake
Forgetting that tangential speed depends on radius.
- Mistake
Directing angular velocity tangent to the circle.
- Mistake
Mixing centripetal acceleration with tangential acceleration.
- Mistake
Forgetting the negative sign during angular deceleration.
- Mistake
Confusing rad s⁻¹ with rpm.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
α = Δω / Δt
ω = ω₀ + αt
θ = ω₀t + ½αt²
ω² = ω₀² + 2αθ
Angular acceleration is the rate of change of angular velocity. For constant α, rotational kinematics equations mirror linear ones.
α = Δω / Δt
- Definition
- Angular acceleration is the rate of change of angular velocity. For constant α, rotational kinematics equations mirror linear ones.
- Formula
- α = Δω / Δt
- Critical warning
- Using degrees directly in s = rθ.
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