Why Force Due to Friction Not in Equation of Motion?

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The force due to friction (ft) is not included in the equation of motion for a cylinder rolling without slipping because it does not perform work on the cylinder's translational motion. Instead, friction facilitates the rolling motion by providing the necessary torque. The equation of motion remains valid as it accounts for the net forces acting on the cylinder. The absence of ft in the equation does not invalidate the motion analysis, as it is implicitly considered in the rolling condition. Understanding the role of friction in rolling dynamics is crucial for accurate motion equations.
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Why is ft (the force due to the friction between the cylinder and the ramp) not included in the equation of motion?
 
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eurekameh said:
Why is ft (the force due to the friction between the cylinder and the ramp) not included in the equation of motion?
Because the cylinder "rolls without slipping".
 
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For this situation, is my Fx equation of motion not true then?
 

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