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Mechanics
Mechanics

Rotational Kinematic 3

ω2=ω02+2α(θ−θ0)\omega^2 = \omega_0^2 + 2\alpha(\theta - \theta_0)

Rotational analog of v² = v₀² + 2a(x - x₀). Time-independent rotational kinematic equation.

Variables

ω
Final angular velocity
Angular velocity at angle θ
rad/s
ω₀
Initial angular velocity
Angular velocity at angle θ₀
rad/s
α
Angular acceleration
Constant angular acceleration
rad/s²
θ
Final angle
Final angular position
rad
θ₀
Initial angle
Initial angular position
rad

Derivation

Eliminate t from rotational kinematic equations 1 and 2.

Your notes

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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).