Rotational Kinematic 2
Rotational analog of x = x₀ + v₀t + ½at². Relates angular position to time.
Variables
Derivation
Integrate ω = ω₀ + αt: θ = ∫ω dt = ω₀t + ½αt² + θ₀.
Your notes
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- θ₀ = 2 rad (Initial angle)
- ω₀ = 3 rad/s (Initial angular velocity)
- α = 4 rad/s² (Angular acceleration)
- t = 5 s (Time)
Result: θ = 67 rad
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 1 and before Rotational Kinematic 3.
- 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 2 formula?
Rotational Kinematic 2 is written θ = θ₀ + ω₀t + (1/2)αt². Rotational analog of x = x₀ + v₀t + ½at². Relates angular position to time. It belongs to Mechanics, under Rotational Motion.
What are the units in θ = θ₀ + ω₀t + (1/2)αt²?
In SI units, θ is final angle, measured in rad; θ₀ is initial angle, measured in rad; ω₀ is initial angular velocity, measured in rad/s; α is angular acceleration, measured in rad/s²; t is time, measured in s.
How is the Rotational Kinematic 2 formula derived?
Integrate ω = ω₀ + αt: θ = ∫ω dt = ω₀t + ½αt² + θ₀. The result is θ = θ₀ + ω₀t + (1/2)αt².