Find Centre of Mass: Angle AC & Horizontal- 9.46°

• Kajan thana
In summary, the lamina is able to freely rotate around a horizontal axis passing through point A, and is in equilibrium. The problem asks to find the angle between AC and the horizontal, with a given solution of 9.46 degrees. The solution may seem incorrect at first, but upon further examination, it is correct as it takes into account the rotation of the lamina so that the center of mass is below the pivot.
Kajan thana

Homework Statement

The lamina is free to rotate about a fixed smooth horizontal axis, perpendicular to the plane of the lamina, passing through the point A. and hangs in equilibrium.
Find the angle between AC and the horizontal.

I have attached a the solution to the question, it seems like there is no line to the question and theta there are showing in the working out.

Homework Equations

I think the answer is 9.46 degree as tanφ= 1/6

The Attempt at a Solution

.[/B]
I have attached screenshot to this thread. Is the solution wrong or have I been thinking in a wrong way? What are looking at that theta shown in the screenshot?

Attachments

• Screen Shot 2017-01-29 at 22.21.04.png
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Kajan thana said:
have I been thinking in a wrong way

More like thinking upside down . If you were holding the lamina in the position shown what would happen when you let go of it ?

lamina will turn so the centre of mass is below the pivot.

That's it .

Kajan thana
Nidum said:
That's it .
yes but my question why have they goy theata there when they ask for the theta between the horizontal and AC

Last edited:
Nidum said:
That's it .
i thought about it. It makes sense what they have done.

1. What is the purpose of finding the centre of mass using Angle AC and Horizontal- 9.46°?

The centre of mass is the point at which the entire mass of a body can be considered to be concentrated for the purpose of calculations. In this case, using Angle AC and Horizontal- 9.46° allows for a more accurate determination of the centre of mass for objects with irregular shapes or distributions of mass.

2. How is Angle AC related to finding the centre of mass?

Angle AC is the angle formed by the horizontal line and the line connecting the point of rotation to the centre of mass. This angle is necessary for calculating the horizontal component of the centre of mass, which is used in determining the final position of the centre of mass.

3. Can the centre of mass be located outside of the object?

Yes, the centre of mass can be located outside of the object. This can occur if the object has an irregular shape or if the mass is unevenly distributed within the object.

4. How is the horizontal component of the centre of mass calculated?

The horizontal component of the centre of mass is calculated using the formula: x = (m1x1 + m2x2 + ...) / (m1 + m2 + ...), where m is the mass and x is the horizontal distance from the point of rotation. This formula takes into account the distribution of mass within the object to determine the final position of the centre of mass.

5. What is the importance of finding the centre of mass in scientific experiments?

Finding the centre of mass is important in scientific experiments because it allows for accurate predictions of the motion and stability of objects. It is also crucial in engineering and design, as it helps in determining the most efficient and effective placement of mass in structures and machines.

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