$^1H$ nuclear magnetic resonance (NMR) relaxations have been investigated in ammonium sulfate $((NH_4)_2SO_4)$ power at temperatures ranging form 102 K to 440 K. There is a bottleneck in the spin-lattice relaxation between the nuclear spin system and the hindered rotation of ammonium ions, which is certified by measuring the relaxation according to the initial condition of the spin system. For temperatures below 318 K the $^1H$ spin-lattice relaxations have double-exponential behaviors with the exponent, n, having a value 2>n>1 initially and n=l after a long time. Above 318 K not only is the relaxation exponential initially with exponent n=1, but it is a single-exponential over the entire time, resulting in one $T_1$ value. The two types of $NH_4^+$ ions have different activation energies for hindered rotation, $E_a^1=0.27{pm}0.02eV$ and $E_a^11=0.12{pm}0.0eV$, in the ferroelectric phase.