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Angular Velocity by Initial and Final Values

The angular velocity of a rotating body is defined as the rate of change of angular displacement.

The average of the final and initial angular velocity is the angular displacement divided by the time required for that displacement.

Formula

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

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

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Angular Velocity by Initial and Final Values"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject["Angular Velocity by Initial and Final Values"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Angular Velocity by Initial and Final Values"], {QuantityVariable[ \!\(\*SubscriptBox[\("\[Theta]"\), \("f"\)]\),"Angle"] -> Quantity[2, "Radians"], QuantityVariable[ \!\(\*SubscriptBox[\("\[Omega]"\), \("i"\)]\),"AngularVelocity"] -> Quantity[1, ("Radians")/("Seconds")]}]
Out[3]=

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