Torque, force and rotational acceleration

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Discussion Overview

The discussion revolves around the relationship between torque, force, and rotational acceleration when a mass is moved along a massless ruler or stick. Participants explore how the distance of the mass from the pivot point affects the force required to maintain stability, considering both static and dynamic scenarios.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that if a mass (m) is moved from a distance d to 2d from the hand, the force required to keep it stable should be twice the original force, based on the constant gravitational force (mg) and the torque equation.
  • Another participant argues that the force would need to be quadrupled due to the increase in rotational inertia, which is proportional to the square of the distance (m(2d)^2).
  • A later reply introduces the idea that there are two different situations—static and dynamic—which may lead to different answers regarding the force required.
  • One participant seeks clarification on the distinction between static and dynamic scenarios, asserting that the stick remains stable throughout.

Areas of Agreement / Disagreement

Participants express differing views on whether the force required is doubled or quadrupled when the mass is moved. The discussion remains unresolved, with multiple competing perspectives on the relationship between torque, force, and rotational inertia.

Contextual Notes

There are unresolved assumptions regarding the definitions of static and dynamic situations, as well as the implications of rotational inertia on the required force. The discussion does not reach a consensus on these points.

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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