Torque, force and rotational acceleration

AI Thread Summary
When moving a mass from distance d to 2d on a massless ruler, the force required to maintain stability depends on the rotational inertia. The initial confusion arises from the relationship between torque and distance, where torque is calculated as the product of distance and force. While the force due to gravity remains constant, the rotational inertia increases with the square of the distance, leading to a requirement for quadrupling the force to maintain stability. The discussion highlights the distinction between static and dynamic scenarios, suggesting different calculations may apply based on the system's state. Understanding these principles clarifies the mechanics involved in maintaining equilibrium with changing distances.
The_Journey
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This isn't a homework question.

I'm really confused at this, say you're holding a massless ruler / stick and there is a mass (m) on it at a distance d from your hand. If you move the mass to 2d from your hand, would you have to apply twice the force as before, or quadruple to keep it stable?

I know torque = r cross F. F is constant (mg), so the force you would have to apply should be twice if you move it to 2d. But my teacher said it is quadruple because the rotational inertia of the stick would be m(2d)^2 which is 4 times the rotational inertia as before.

Can anybody explain to me if the force would have to be twice or 4 times as before?

Again NOT a homework problem, I just thought of this.

Some equations and math would be nice too.
 
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Nvm I'll just put this in the homework section.
 
NVM...you have two different situations, one static, one dynamic, hence two different answers...if you know the formula for rotational inertia you can work out that result using
v = wr
 
Naty1 said:
NVM...you have two different situations, one static, one dynamic, hence two different answers...if you know the formula for rotational inertia you can work out that result using
v = wr

Can you explain what you mean by static and dynamic? The stick is always stable.
 

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