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Equation of Circular Motion under Constant Acceleration

The equation of circular motion describes an object moving under constant angular acceleration in a circular as a function of time.

The final position for ciruclar motion equals the intial angle plus the initial angular velocity times the time plus half the angular acceleration times the time squared.

Formula

QuantityVariable[Subscript["θ", "f"], "Angle"] == (QuantityVariable["t", "Time"]^2*QuantityVariable["α", "AngularAcceleration"])/2 + QuantityVariable[Subscript["θ", "i"], "Angle"] + QuantityVariable["t", "Time"]*QuantityVariable[Subscript["ω", "i"], "AngularVelocity"]

symbol description physical quantity
θf final angle "Angle"
t time "Time"
α angular acceleration "AngularAcceleration"
θi initial angle "Angle"
ωi initial angular velocity "AngularVelocity"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Equation of Circular Motion under Constant \ Acceleration"]
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Get the formula:

In[2]:=
FormulaData[ ResourceObject[ "Equation of Circular Motion under Constant Acceleration"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Equation of Circular Motion under Constant Acceleration"], \ {QuantityVariable[ \!\(\*SubscriptBox[\("\[Theta]"\), \("i"\)]\),"Angle"] -> Quantity[0, "Radians"], QuantityVariable["\[Alpha]","AngularAcceleration"] -> Quantity[1, ("Radians")/("Seconds")^2], QuantityVariable["t","Time"] -> Quantity[1, "Seconds"]}]
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