Meriam, Kraige & Bolton — Introduction to Three-Dimensional Dynamics of Rigid Bodies: Problem 7_124

7/123 The uniform circular disk of 4-in. radius and small thickness weighs 8 lb and is spinning about its \(y'\)-axis at the rate \(N = 300\) rev/min with its plane of rotation tilted at a constant angle \(\beta = 20^\circ\) from the vertical \(x\)-\(z\) plane. Simultaneously, the assembly rotates about the fixed \(z\)-axis at the rate \(p = 60\) rev/min. Calculate the angular momentum \(\mathbf{H}_O\) of the disk alone about the origin \(O\) of the \(x\)-\(y\)-\(z\) coordinates. Also calculate the kinetic energy \(T\) of the disk. 7/124 Rework Prob. 7/123 if \(\beta\), instead of being constant at \(20^\circ\), is increasing at the steady rate of 120 rev/min. Find the angular momentum \(\mathbf{H}_O\) of the disk for the instant when \(\beta = 20^\circ\). Also compute the kinetic energy \(T\) of the disk. Is \(T\) dependent on \(\beta\)?