Q:  If the Sun were to shrink to the size
    of a neutron star, about 10 km in radius,
    how fast would it rotate?

        current period of Sun  =       30 days (roughly)
        current radius of Sun  =  696,000 km
        new radius of Sun      =       10 km
     

        Using conservation of angular momentum,
        we see

                                                               2
                                                ( size after  )
         period afterwards  =  period before  * ( ----------- )
                                                ( size before )


                                                              2
                                                (   10 km    )
                            =  (30 days)      * ( ---------- )
                                                ( 696,000 km )


                            =  (30 days)      *  2.1 x 10^(-10)

                            =  6.2 x 10^(-9) days

                            =  0.000 54  seconds