Kinematics Formulas

The Kinematic Equations apply to one-dimmensional motion with costant acceleration from point 1, situated d1 from a point of reference to point 2, situated d2 from the same point of reference. v1 is the velocity at point 1 and v2 is the velocity at point 2.

v2 = v1 + a·t

d2 = d1 + (v1 + v2)·t/2

d2 = d1 + v1·t + a·t2/2

d2 = d1 + v2·t - a·t2/2

v22 = v12 + 2a(d2 - d1)

 

Average velocity: vav = Δd/Δt

Average acceleration: aav = Δv/Δt

 

Rotational kinematics equations with constant angular acceleration:

ω2 = ω1 + α·t

Φ2 = Φ1 + (ω1 + ω2)·t/2

Φ2 = Φ1 + ω1·t + α·t2/2

Φ2 = Φ1 + ω2·t - α·t2/2

ω22 = ω12 + 2α(Φ2 - Φ1)

 

Average angular velocity: ωav = Δθ/Δt

Average angular acceleration: αav = Δω/Δt

Frequency: f = ω/2π

Period: T = 2π/ω

 

Relations between angular and linear variables:

l = Φ·r

v = ω·r

a = α·r

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