A uniform wheel with radius R is rolling without sliding on an incline with angle 0....

 

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A uniform wheel with radius R is rolling without sliding on an incline with angle 0. The figure shows the free-body diagram of the wheel. A string, which is wound around the wheel, maintains a constant tension, T. At the contact point with the incline, C, the static friction F, as well as the normal force n acts. The moment of inertia of the wheel for the axis passing through its center is Icm = mR²/5. Let a denote the angular acceleration of the wheel as a result of these forces. The equation of motion (namely the net = Ia equation) can be written in infinitely many different ways depending on where you choose the origin. Two most common choices are the contact point C and the center point of the wheel O. Below, you are going to write the equation of motion for these two choices. (You don't need to solve the problem). Coding note: F, must be coded as F_s (with an underline), 8 and a are coded as theta and alpha resp.. Your equations must contain only m. g, R, T. n, F.0 and a as variables. T (a) Write the equation of motion (Thet = Ix) for the case origin is at O. Equation: (b) Write the equation of motion (Tnet = Iα) for the case origin is at C. Equation: F, mg (X AT A uniform wheel with radius R is rolling without sliding on an incline with angle 0. The figure shows the free-body diagram of the wheel. A string, which is wound around the wheel, maintains a constant tension, T. At the contact point with the incline, C, the static friction F, as well as the normal force n acts. The moment of inertia of the wheel for the axis passing through its center is Icm = mR²/5. Let a denote the angular acceleration of the wheel as a result of these forces. The equation of motion (namely the net = Ia equation) can be written in infinitely many different ways depending on where you choose the origin. Two most common choices are the contact point C and the center point of the wheel O. Below, you are going to write the equation of motion for these two choices. (You don't need to solve the problem). Coding note: F, must be coded as F_s (with an underline), 8 and a are coded as theta and alpha resp.. Your equations must contain only m. g, R, T. n, F.0 and a as variables. T (a) Write the equation of motion (Thet = Ix) for the case origin is at O. Equation: (b) Write the equation of motion (Tnet = Iα) for the case origin is at C. Equation: F, mg (X AT

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