Buoyancy and stability

Question

I don't understand how does a rotating moment caused by the weight force form when a submerged object is tilted like this. I understand that the buoyancy force produce a moment about CG because of the horizontal distance between FB and CG. But for the weight how can it rotate the object about its center of gravity when the Force is directed through the Center of gravity . How would it create a torque? A free body always create a torque about its CG.

score 2 · Accepted Answer · answered Jul 13 '22 at 20:55

2

I understand that the buoyancy force produce a moment about CG because of the horizontal distance between FB and CG.

Actually, the upward buoyant force and downward weight, which are parallel equal but opposite forces, form what is called a "couple". A couple causes pure rotation without translation (since the net force is zero). The magnitude of the couple is the sum of the torque contributions of each of the two forces, or

$$M_{C}=F\frac{d}{2}+F\frac{d}{2}=Fd$$

where $d$ is the perpendicular distance between the lines of action of the two forces, and $F_{B}=W=F$ for a neutrally buoyant body.

When the ensuing rotation caused by the couple vertically aligns the two forces (after some possible oscillations), the body will be rotational equilibrium.

Hope this helps.

answered Jul 13 '22 at 20:55

Bob D

71,527

Thanks for answer, But I noticed you taking half of the distance d/2 in your equation . Do you mean that the moment is happening around the point that lies at the distance in between these two force line? How would that be possible while a body should rotate about its center of gravity when forces acts on it . (A free body) – Jesse Flynn Jul 13 '22 at 21:05
@JesseFlynn The buoyancy force acts on the geometric center of the submerged portion of the body. The force of gravity acts at the center of gravity. For the body in your diagram, rotating the body changes the vertical location of the CG (because of the uneven distribution of the weight), but not the vertical location of the geometric center, thus producing the couple. – Bob D Jul 13 '22 at 21:21

score -1 · Answer 2 · answered Jul 13 '22 at 21:11

A freely falling mass without other forces on it does not experience a torque.

A torque is the result of two equal anti parallel forces displaced sideways. See Toppling of a cylinder on a block.

You can get a torque when a ball rolls down an inclined plane if there is friction. Is work done by torque due to friction in pure rolling?

In your example, torque is the result of buoyancy and weight acting together.

Buoyancy and stability

2 Answers2