# Regarding moments of inertia

1. Apr 11, 2015

### SteveS

1. The problem statement, all variables and given/known data
1. A square plate has a side length of 1.2 m. An applied torque of 300 N · m gives the plate an angular acceleration of 4.8 rad/s2 about an axis through the centre of the plate. Determine the plate’s mass.

2. Relevant equations

t = lα

l = 1/12M(l^2 + w^2)

3. The attempt at a solution

I substituted the second equation into the first and rearranged to isolate mass getting

M = t / (1/12 * (1.2^2 + 1.2^20) * (4.8 rad / s^2)) = 260.42 kg, or 2.6x10^2 kg

I'm just wondering if I've done this question correctly.

2. Apr 11, 2015

### SteamKing

Staff Emeritus
Looks good!

3. Apr 11, 2015

### haruspex

One query... you seem to have used a lower case "el" (lower case L) for both a length and the moment of inertia. It would be more usual to use an uppercase "eye" (I) for the latter.

4. Apr 11, 2015

### SteveS

Yeah, thats something i've picked up from my textbook. I know its supposed to be an "eye" but i've been in the habit of using a symbol that looks like an I but with a rounded tail on the bottom.. maybe this character, ι, not sure why my text uses that at times. Thanks for pointing it out, mentally I think "eye"

5. Apr 11, 2015

### haruspex

Yes, could be intended as iota.

6. Apr 25, 2017

### chemtal

when substituting into I = 1/12M(L^2 + w^2), i understand that L= 1.2m but how did u come to the conclusion that w is also 1.2 m. I understand that if this were a square but its a plate

7. Apr 25, 2017

### haruspex

It states "square plate".
The one thing that is not entirely clear is the orientation of the axis. It just says it is through the centre, but in principle that could be in any direction.

8. Apr 25, 2017

### chemtal

so it is safe to assume that the length and width are both 1.2?

9. Apr 25, 2017

Yes.