I could use help in finding angular acceleration ω of a pivoting mechanical assembly that oscillates ~41 degrees in total or 20.5 degrees +/- about is centre axis where the pivoting action is controlled by a crankshaft / connecting rod assembly of 5 mm crank radius and 17 mm connecting rod length. The crankshaft rotates at 6000 rpm. The radius of the pivoting assembly to the small end of the connecting rod is 14.3 mm.
The JM value of the pivoting assembly is 0.022 kgm^2. The aim is to find the maximum torque in Nm imposed on the pivoting assembly. The formula for torque in an accelerating rotating body is JM * ω^2 in Nm which is the answer sought.
The linear acceleration in m/s^2 of the small end of the connecting rod is higher at TDC than at BDC. We are looking for the maximum value that occurs at TDC.
At TDC the acceleration is r * ω^2 * (1+ lbd) = 0.005 * (6000*pi/30)^2 * (1+lbd) = 0.005 * 628.3^2 *1.295 /.937 (correction factor) = 2,730 m/s^2. How is that now converted to ω^2 of the pivoting assembly to find the maximum torque of the pivoting assembly in Nm? The difference in radius is 14.3 mm to 5 mm.
Thanks.