Equations of Rotational Motion Video Lessons

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Problem: An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle θ in the time t, through what angle did it rotate in the time t/2? Express your answer in terms of θ.

FREE Expert Solution

This problem involves rotational kinematics.

We'll represent the two parts using known variables and kinematic equations. We'll then use one equation to substitute into the other equation and solve for the target. 

Rotational kinematic equations:

ωf=ω0 + αtθ=12(ω0+ωf)tθ=ω0t +12αt2ωf2=ω02+2αθ

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Problem Details

An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle θ in the time t, through what angle did it rotate in the time t/2? Express your answer in terms of θ.

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