When the 40-lb wheel shown is attached to a balancing machine and made to spin at a rate of 750 rpm, it is found that the forces exerted by the wheel on the machine are equivalent to a force-couple system consisting of a force F = (36.2 lb)j applied at C and a couple Mc = (10.85 lb ??? ft)k, where the unit vectors form a triad which rotates with the wheel.

(a) Determine the distance from the axis of rotation to the mass center of the wheel and the products of inertia Ixy and Ixz.

(b) If only two corrective weights are to be used to balance the wheel statically and dynamically, what should these weights be and at which of the points A, B, D, or E should they be placed?

a O