How Do You Calculate the Mass of a Rotating Square Plate?

[SteveS]

Homework Statement

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.

Homework Equations

t = lα

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

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.

 

[SteamKing]

Looks good!

 

[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.

 

[SteveS]

Yeah, that's 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"

 

[haruspex]

Yeah, that's 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"

Yes, could be intended as iota.

 

[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

 

[haruspex]

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

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.

 

[chemtal]

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.

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

 

[haruspex]

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

Yes.