A uniform rod with a mass of 0.50 kg and a length of 1 m has a moment of inertia of 0.10 kg-m ^2 about an axis perpendicular to it. Determine the distance from this axis to the middle point of the rod.

Step-by-step solution

The moment of inertia of a uniform rod about an axis passing through its center of mass and perpendicular to its length is given by: I_ cm = mL^2 12 Substituting the given values m = 0.50 kg and L = 1 m : I_ cm = 0.50 (1)^2 12 = 1 24 kg-m ^2 According to the parallel axis theorem, the moment of inertia I about any parallel axis is: I = I_ cm + md^2 where d is the distance from the axis to the center of mass (middle point) of the rod. Given I = 0.10 kg-m ^2 , substituting the values gives: 0.10 = 1 24 + 0.50 d^2 1 1