The discussion focuses on the concept of the radian as a unit of measurement in angular motion, emphasizing its dimensionless nature. Participants clarify that while radians appear in formulas such as angular frequency (ω = √(k/m)), they are fundamentally ratios of lengths and thus dimensionless. The conversation highlights the importance of distinguishing between radians and degrees, noting that radians can be omitted in calculations without loss of meaning, unlike degrees. The confusion surrounding the radian's role in angular velocity and other dimensionless units is also addressed, particularly in relation to practical examples like rotational motion.
PREREQUISITESPhysics educators, students learning about angular motion, and professionals in engineering fields who require a clear understanding of angular measurements and their applications.
You can omit specifying radians, but you can not omit specifying degrees.stefano77 said:unit of measurement '' rad '' appears and disappears as in calculating angular frequency as square root of k/m in spring-mass model.how can l explain to students?not as a dogma? you can say unit of measuremnt is the inverse of second, but what about the final formula of rad/ s ? rad appears in final result as a ghost
Confusingly the dimensionless something affects what unit is used for something/second: Hertz vs. Becquerel.Mister T said:A disc of circumference 2.0 m spins at a rate of 3.0 rotations per second.
I never thought about it before, but perhaps that confusion is another layer that conflates the confusion over the use of the radian.A.T. said:Confusingly the dimensionless something affects what unit is used for something/second: Hertz vs. Becquerel.