Paul Quincey makes a compelling argument for recognizing angle as a base quantity with the radian as the base unit. Solid angle is then a derived quantity with the steradian a derived unit equal to one square radian. The author demonstrates how the familiar equations of the SI appear to result from ‘setting the radian equal to one’—the so-called radian convention. He claims, but without any physical foundation (other than by analogy with translational motion), that, for rotation, the ‘improved’ units for torque, angular momentum and moment of inertia must be J/rad, J/(rad/s) and J/(rad/s)2, respectively, and that the conventional units (N m, kg m2 s–1 and kg m2) result from application of the radian convention to these quantities. However, based on sound physical principles, I demonstrate here that the radian convention is simply a (confusing) change of notation, applicable (only) to angle and its time derivatives. It does not apply to torque, angular momentum or moment of inertia. Analogies can be helpful in identifying relationships between quantities, but they do not dictate the physics. The appropriate units for torque, angular momentum and moment of inertia are, respectively, the well-established angle-independent units: newton metre, kilogram metre-squared per second and kilogram metre-squared.

Paul Quincey makes a compelling argument for recognizing angle as a base quantity with the radian as the base unit. Solid angle is then a derived quantity with the steradian a derived unit equal to one square radian. The author demonstrates how the familiar equations of the SI appear to result from ‘setting the radian equal to one’—the so-called radian convention. He claims, but without any physical foundation (other than by analogy with translational motion), that, for rotation, the ‘improved’ units for torque, angular momentum and moment of inertia must be J/rad, J/(rad/s) and J/(rad/s)2, respectively, and that the conventional units (N m, kg m2 s–1 and kg m2) result from application of the radian convention to these quantities. However, based on sound physical principles, I demonstrate here that the radian convention is simply a (confusing) change of notation, applicable (only) to angle and its time derivatives. It does not apply to torque, angular momentum or moment of inertia. Analogies can be helpful in identifying relationships between quantities, but they do not dictate the physics. The appropriate units for torque, angular momentum and moment of inertia are, respectively, the well-established angle-independent units: newton metre, kilogram metre-squared per second and kilogram metre-squared.