(Solved): Consider the conical pivot bearing below. Calculate external torque magnitude, \( T \), required fo ...

Consider the conical pivot bearing below. Calculate external torque magnitude, \( T \), required for the pivot bearing to rotate at the constant angular speed shown. For the conical pivot bearing of problem 3, say that the external torque of magnitude \( T \) is suddenly taken away. How long will take for the bearing to slow down from \( 4200 \mathrm{rpm} \) to \( 2100 \mathrm{rpm} \). Note: Conservation of angular momentum for the pivot bearing says that the sum of torque magnitudes acting on the pivot is \[ \left(\sum T\right)_{\text {pivot }}=-m_{\text {pivot }} I_{\text {pivot }} \frac{d \omega}{d t} \] where \( I_{\text {pivot }}=3 r_{o}^{2} / 10 \). The mass of the pivot can be taken as \( m_{\text {pivot }}=1 \) slug and \( r_{o} \) is the radius of the base of the cone, which from the sketch of problem 3 is \( 0.1 \) in.