The spin and charge of quarks, including the up quark, are fundamental properties that are determined through experimental observations and theoretical models in particle physics.
Spin is an intrinsic property of elementary particles, such as quarks, and it is related to their angular momentum. Quarks are fermions, which means they have half-integer spin. The up quark, along with the other quarks, is assigned a spin of 1/2 based on experimental measurements and theoretical consistency within the framework of the Standard Model.
Charge, on the other hand, is a property related to the electromagnetic interaction. In the case of quarks, their charge is quantized in units of the elementary charge, denoted as e. The up quark is assigned a charge of +2/3e, which is positive and two-thirds the magnitude of the elementary charge. The down quark, by contrast, has a charge of -1/3e.
These assignments of spin and charge for quarks are consistent with the observed properties of quarks and the behavior of the strong and electromagnetic interactions in particle physics experiments. However, it's worth noting that these properties are not derived from first principles but are determined through experimental measurements and theoretical considerations. Our current understanding of quark properties is based on the framework of the Standard Model, and any new experimental observations or theoretical advancements could potentially lead to modifications or refinements in our understanding of these fundamental properties.