IP A wheel on a game show is given an initial angular speed of $1\mathrm{.}02$ rad$/$srad$/$s $.$ It comes to rest after rotating through $0\mathrm{.}75$ of a turn.

If the mass of the wheel is doubled and its radius is halved, will the angle through which it rotates before coming to rest increase, decrease, or stay the same?$($Assume that the average torque exerted on the wheel is unchanged.$)$