Plasma confinement with a transport barrier such as an H mode or an internal transport barrier mode is examined under the constraint due to the conservation of total angular momentum. The results are tested against actual experimental data and the general characteristics of plasma confinement with a transport barrier are well understood in terms of this constraint. This implies that the confinement of tokamak plasmas can be determined by the decay rate of the total angular momentum. It also suggests that the confinement with a transport barrier is good, since electrostatic fluctuations cannot affect this constraint, but that electromagnetic fluctuations such as ELMs can cause the confinement to deteriorate.