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11.10 Dynamic balance of a rotating shaft/wheel (rigid body with simple angular velocity). Consider an unsymmetric rigid body B supported by two ideal (frictionless) bearings so B spins with a simple angular velocity a, b, in a Newtonian reference frame N, where b, is fixed in both B and N. parallel to the bearings axes, and di- rected vertically upward (opposite gravity). Point B, of B is at the midpoint between the bearings (along B's axis of rotation in N). • Draw a unit vector b, fixed in B and perpendicular to b such that Bem's position from B, is rem bx + som b • Draw body B's free-body diagram (FBD). Ensure your FBD shows force/torque measures at each bearing. Note: Assume the two bearings are ideal/frictionless, i.e., the b, measure of the moment on B from each bearing is 0. The set of all forces on B from the two bearings can be replaced by the set's resultant force F = F, b, + F, b, + F, b, applied at B, and a torque on B of T = T, b, + T, by +T, b Determine F. Fy, F.. Tr, Ty, and , in terms of symbols in the following table... Result: Type Description Symbol 9 Constant F, Constant F₂ m F₁ T₂ Earth's local gravitational acceleration Mass of B b, and b, measures of B.'s position from B B's moments of inertia and products of inertia about B, for b, b,. b, Tem Fem 1x lyy la xy? Constant Constant Constant b, measure of B's angular velocity in N Variable Note: This problem relates to dynamic tire balancing, for smooth rides and low wheel bearing stress/fatigue. T, I ولد OH B # =