Kinetomagnetism refers to magnetization, or more generally to pseudovector responses with the same symmetry as magnetization, induced by the linear momentum k or by external stimuli that transform in the same way as k. It provides a symmetry-based origin for both longitudinal and transverse nonlinear responses of either even or odd order. The necessary and sufficient symmetry condition for kinetomagnetism is the breaking of parity-time symmetry (PT), which likewise permits spin splitting in electronic band structures. Consequently, all altermagnets, characterized by spin-split electronic bands with full spin compensation, can exhibit kinetomagnetism. Here we examine the connection between kinetomagnetism and altermagnetism within the generalized SAM classification framework. We show that S- and M-type altermagnets can host even-order kinetomagnetism, whereas A-type altermagnets can host odd-order kinetomagnetism. This kinetomagnetic perspective provides a unified framework for understanding altermagnets and related phenomena, including higher-order nonlinear Hall effects, piezomagnetism, and spin-splitting torques, while allowing their nonrelativistic spin-splitting contributions to be predicted from spin symmetries.