Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_44

6/44 A vibration test is run to check the design adequacy of bearings $A$ and $B$. The unbalanced rotor and attached shaft have a combined mass of $2.8\text{ kg}$. To locate the mass center, a torque of $0.660\text{ N}\cdot\text{m}$ is applied to the shaft to hold it in equilibrium in a position rotated $90^\circ$ from that shown. A constant torque $M = 1.5\text{ N}\cdot\text{m}$ is then applied to the shaft, which reaches a speed of $1200\text{ rev/min}$ in $18$ revolutions starting from rest. (During each revolution the angular acceleration varies, but its average value is the same as for constant acceleration.) Determine (a) the radius of gyration $k$ of the rotor and shaft about the rotation axis, (b) the force $F$ which each bearing exerts on the shaft immediately after $M$ is applied, and (c) the force $R$ exerted by each bearing when the speed of $1200\text{ rev/min}$ is reached and $M$ is removed. Neglect any frictional resistance and the bearing forces due to static equilibrium. For parts (b) and (c), take the rotor to be in the position shown.