PhysRefPhysics reference
Mechanics
Mechanics

Rotational Kinematic 2

θ=θ0+ω0t+12αt2\theta = \theta_0 + \omega_0 t + \frac{1}{2}\alpha t^2

Rotational analog of x = x₀ + v₀t + ½at². Relates angular position to time.

Variables

θ
Final angle
Angular position at time t
rad
θ₀
Initial angle
Angular position at t=0
rad
ω₀
Initial angular velocity
Angular velocity at t=0
rad/s
α
Angular acceleration
Constant angular acceleration
rad/s²
t
Time
Elapsed time
s

Derivation

Integrate ω = ω₀ + αt: θ = ∫ω dt = ω₀t + ½αt² + θ₀.

Your notes

0/5000

Common questions

What is the Rotational Kinematic 2 formula?

Rotational Kinematic 2 is written θ= θ₀ + ω₀ t + 1/2αt². 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 + ω₀ t + 1/2αt²?

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 + ω₀ t + 1/2αt².