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I'm studying pendulums, and the units have me a bit confused.

In a pendulum, Iw^2=mgL.

Putting together the units of the left side of the equation, we get gm^2 (rads^-1)^2=g(m^2)(s^-2)(rad^2).

But the units of the right side of the equation equal g(m^2)(s^-2)

Where does the unit radian fit in? How do I deal with the unit radian when dealing with measures of linear speed?

Qmechanic
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newtophysics
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  • Possible duplicates: https://physics.stackexchange.com/q/351543/2451 and links therein. – Qmechanic May 05 '20 at 12:13
  • The radian unit should not be written. It is just a name for a unit-less measure. For example, radians-per-seconds should be written $\mathrm{[s^{-1}]}$. The radian unit is defined as how many radius-lengths along the periphery an angle corresponds to. It is periphery-length-per-radius, meaning metres-per-metres, and therefore unit-less. – Steeven May 05 '20 at 12:19

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