- #1

dara bayat

- 8

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I have a question regarding radians and the unit of rotational energy (which has been probably asked several times elsewhere but is still confusing for me :-) ).

As I understand radian (rad) is a UNIT that is dimensionless (thus cannot be omitted), correct ?

Now if I want to look at the unit of Energy I think it goes as follows :

Er = T*theta -->

*unit=N.m.rad*Er : rotational energy

T : torque

theta : angle

but also

Er = 1/2*I*w² --> unit=kg.m².rad².s⁻²=

*N.m.rad²*I : moment of inertia

w : angular velocity

however since w=sqrt(k/I) , k is the torsion spring constant :

Er = 1/2*k*theta² = 1/2*I*w²*theta² (I saw this formula in a textbook) --> unit=

*N.m.rad⁴*I also read in other posts that the unit of rotational energy is sometimes

*N.m/rad*which one is correct ? Am I making a mistake ?

can I just omit radians and say that rotational energy is N.m? if yes, why ? If no, why ? :-)

is this really confusing ? Or have I not understood something ?

Thanks in advance for your help

Dara