You measured the torque caused by the gyroscope's weight by lifting up the end of the gyroscope (at 7.5 inches). If you measured at a different distance, say you attached the spring scale at 5 inches from the pivot point, would the spring scale read a different value? Would the torque be a different value? Does this explain why you do not need to measure the spring scale at the center of mass location, where the moment of gravitational force is located? (provide an argument as well as your measurement report.)

i) No, the spring scale does not read a different value

ii) The torque will read a different value, it will reduce

iii) The spring scale does not need to be measured at the center of mass location.

Explanation:

The torque caused by the gyroscope can be given by the relation,

r × f

The torque measured by the gyroscope varies directly with the distance, r.

A decrease in the distance r will also cause a decrease in the value of the torque measured. When the distance, r is reduced from 7.5 inches to 5 inches, the torque caused by the gyroscope's weight also reduces.

The weight of the gyroscope remains constant despite the reduction in the distance because the weight  of the gyroscope is not a function of the distance from the gyroscope. Therefore, the spring scale will not read a different value.

Yes, the spring scale does not need to be measured from the center of mass location because the weight does not depend on the location of measurement. The reading of the sprig scale remains constant.