A solid sphere of radius $20$ cm and mass $0\mathrm{.}7$ kg is fixed to a horizontal axle of length $0\mathrm{.}5$m$,$ diameter $1$cm and mass $0\mathrm{.}25$kg$.$ The axle is mounted in two frictionless bearings. The rotor $($consisting of the axle and the ball$)$ is initially at rest, but it is marked on one side, so we can track its rotation. bearings At time t$0=0$ a torque of $0\mathrm{.}4$Nm is applied to the axle, for $10$ s$.$ Find the angle of the rotor as a function of time for $06$t $620$ s$,$ if $($t$0)=0$ rad