Rotational Kinematic 3
Rotational analog of v² = v₀² + 2a(x - x₀). Time-independent rotational kinematic equation.
Variables
Derivation
Eliminate t from rotational kinematic equations 1 and 2.
Your notes
Check value
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- ω₀ = 5 rad/s (Initial angular velocity)
- α = 4 rad/s² (Angular acceleration)
- θ = 3 rad (Final angle)
- θ₀ = 2 rad (Initial angle)
Result: ω = 5.7445626 rad/s
Other mechanics formulas with the same quantities
- Angular Acceleration (Rotational Motion) shares Angular acceleration
- Newton's Second Law (Rotation) (Rotational Motion) shares Angular acceleration
Where this formula is listed
- Mechanics formulas, under Rotational Motion, alongside Angular Velocity, Linear-Angular Velocity Relation, Centripetal Acceleration, Centripetal Force and Torque.
- In the mechanics list it comes after Rotational Kinematic 2 and before Moment of Inertia (Disk/Cylinder).
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Rotational Kinematic 3 formula?
Rotational Kinematic 3 is written ω² = ω₀² + 2α(θ − θ₀). Rotational analog of v² = v₀² + 2a(x - x₀). Time-independent rotational kinematic equation. It belongs to Mechanics, under Rotational Motion.
What are the units in ω² = ω₀² + 2α(θ − θ₀)?
In SI units, ω is final angular velocity, measured in rad/s; ω₀ is initial angular velocity, measured in rad/s; α is angular acceleration, measured in rad/s²; θ is final angle, measured in rad; θ₀ is initial angle, measured in rad.
How is the Rotational Kinematic 3 formula derived?
Eliminate t from rotational kinematic equations 1 and 2. The result is ω² = ω₀² + 2α(θ − θ₀).