Dimensional Analysis: Torque, Moment of Inertia & Angular Acceleration

[Mikealvarado100]

Hi
The relation between torque, moment of inertia and angular acceleration is:
T=Ia
Have a look to it's units:
(N.m)=(kg.m^2).(Rad/s^2) >>>> N=kg.m.Rad/s^2
Please explain the equation Dimensionally. How (kg.m.Rad/s^2) is equal to N?
Thanks.

 

[Svein]

Please explain the equation Dimensionally. How (kg.m.Rad/s^2) is equal to N?

Starting with F = m⋅a, the dimensions give N = kg⋅m/s². Insert this in your equation and remember that "Rad" is dimensionless (arc length/radius gives m/m).