A person is sitting on a stool which can rotate about own axis as shown in figure that is initially not rotating and is holding a spinning wheel. The moment of inertia of the person and stool about vertical axis passing through the centre of stool $I_{sp}$. The moment of inertia of the wheel about an axis, perpendicular to the plane of the wheel, passing through the centre of mass of the wheel, is $I_{\omega }=\left(\frac{1}{4}\right)I_{sp}$. The mass of wheel is $m_{\omega }$ . Suppose that the person holds the wheel as shown in the sketch such that the distance of an axis passing through the centre of mass of wheel to the axis of rotation of stool is d and $m_{\omega }{d}^2=\frac{1}{3}{I}_{\omega }$. Suppose that wheel is spinning initially at angular velocity ${\omega }_s$. The person then turns the spinning wheel upside down without changing the magnitude with respect to him. You may ignore any frictional torque in the bearing of the stool. Then the correct statement(s) among the following