Moment of inertia particle problem

[ehabmozart]

Homework Statement

Four particles with masses 2 kg (top left corner), 3 kg (bottom left corner), 4 kg (bottom right corner), and 5 kg (top right corner) are connected by rigid rods of negligible mass. The origin is centered on the center of the rectangle of sides 0.8 length and 0.6 breadth. If the system rotates in the XY plane about the z axis with angular speed of w=5 rad.sec. What is the rotational kinetic energy.

Homework Equations

I=mr^2 and KE rot = .5 Iω^2

The Attempt at a Solution

I can use the formulas but the main problem for me is to determine the axis of rotation. Why did it mention both XY plane and Z axis. Which one exactly is the axis of rotation. Moreover, if it is the Z axis, how can we get R? Thanks to whoever contributes.

 

[gneill]

Reread the problem statement. It tells you that the system (masses) lie in the xy plane, that it rotates around the z-axis, and where the origin is located.

 

[ehabmozart]

where is the word LIE?

 

[gneill]

where is the word LIE?

If the system rotates in the xy plane, then by direct inference it lies in the xy plane.

 

[ehabmozart]

I want to have a better view. How will it rotate... If it rotates out of the page, then we have to draw a diagonal or vertical or horizontal line??

 

[gneill]

The masses form a rectangle in the xy plane. The z axis passes through the center of the rectangle. The rectangle rotates around the z-axis.

 

[ehabmozart]

So how would you approach the question if it says that it rotates clockwise or anticlockwise??

 

[gneill]

So how would you approach the question if it says that it rotates clockwise or anticlockwise??

Does the problem state what direction it rotates? Does it matter? Does rotational kinetic energy depend upon the direction of rotation?

 

[ehabmozart]

No, i mean is this a similar statement to say that it rotates clockwise for example??

 

[gneill]

No, i mean is this a similar statement to say that it rotates clockwise for example??

Sorry, I don't know exactly what you're asking. All I can tell from the question statement as presented is that the system is rotating, as a whole, in the xy-plane and that the center of rotation is at the center of the rectangle. Whether that rotation is clockwise or counterclockwise is not given, nor does it matter for determining the rotational KE.