Proving units for angular acceleration

[Jack999]

So the equation for angular acceleration on the AP physics sheet reads α = ΣT / I. I am required to prove that the units on each side are the same however I can't figure out how to get the rad/s^2 unit for angular acceleration into the same form as the right side which is N*m/ kgm^2

Any help would be appreciated.

 

[fresh_42]

So the equation for angular acceleration on the AP physics sheet reads α = ΣT / I. I am required to prove that the units on each side are the same however I can't figure out how to get the rad/s^2 unit for angular acceleration into the same form as the right side which is N*m/ kgm^2

Any help would be appreciated.

What is one Newton?

 

[Jack999]

Its 1 kgm/s^2 right? I don't understand how you get radians out of kgm^2/s^2 / kgm^2 which simplifies to kgm^2 / kgm^2s^2

 

[fresh_42]

It simplifies further as you can cancel there. Radians isn't a unit. It's a dimensionless number.

 

[Jack999]

so you are saying 1/s^2 is the same as rad/s^2 in terms of units?

 

[fresh_42]

so you are saying 1/s^2 is the same as rad/s^2 in terms of units?

Yes. Alternatively you would have to keep track on the angular part on both sides of the equation. You must not take it into account on the LHS and disrespect it on the RHS. What are your variables $\Sigma, T , I\,$? Where's the angular hidden in it?

 

[haruspex]

I am required to prove that the units on each side are the same

That may be what was asked of you, but it is not what they mean. What you can do is show the dimensions are the same. Units don't come into it until you plug in numbers.
E.g. F=ma is dimensionally consistent. If the mass is 1kg and the acceleration is 1m/s² then I can write the force in Newtons:
1N=(1kg)(1m/s²).
But I also could write the force in dynes:
10⁵ dynes =(1kg)(1m/s²).