# Moment of Inertia vs. Inertia Constant

1. Jun 17, 2014

### hansherman

The following equations are found in the following reference (Page 119):

By definition, the inertia constant for a synchronous machine is defined as

$$H = (1/2 J \omega_0^2) / S$$

where

$$a) H= \text{constant of inertia } (s)$$
$$b) S = \text{rated power of synchronous machine } (MW)$$
$$c) \omega_0 = \text{nominal angular frequency } (rad/s)$$
$$d) J = \text{moment of inertia for rotor } (kg m^2)$$

I.e.

$$J = 2HS/\omega_0^2$$

can be used to find the moment of inertia. Based on the units of a), b) and c) the unit of J is

$$s MW/(rad^2/s^2)$$

However, i cannot see that this is the same as kg/m^2, as the result is supposed to yield from d). Can anyone help me?

2. Jun 17, 2014

### D H

Staff Emeritus
Hint #1: Radians are unit less, so you can drop that term.
Hint #2: The watt (and hence megawatts) is a derived unit. What are its primitive units?

3. Jun 17, 2014

### dauto

Hint #3: Instead of using MW (megawatts) you should just use W (watts). M is just a numerical factor of 1000000 and therefore is unitless. The Watt is the standard unit of power for the metric system.

4. Jun 17, 2014

### nasu

There is no reference to this on page 119.

However, the quantity defined in your post have units of seconds (energy/power).
The confusion may be due to the fact that (at least) two different quantities may be called the same name: "inertia constant".

See for example here:

You are talking here about the second quantity, the H defined on page 540 of that book and not the first one (I*ω) which is also called inertia constant, on the same page.

5. Jun 18, 2014

### hansherman

I do not understand why Radians are unit less. Can anyone explain this? Thanks for the answers.

6. Jun 18, 2014

### TheAustrian

Because you divide [Length] by [Length]

θ = s /r

s is arc length (of a circle)