Torque, force and rotational acceleration

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SUMMARY

The discussion centers on the relationship between torque, force, and rotational acceleration when a mass is moved along a ruler. When a mass (m) is positioned at a distance (d) from a pivot and then moved to 2d, the required force to maintain stability is quadrupled due to the increased rotational inertia, which is calculated as m(2d)^2. This conclusion is based on the understanding that torque is defined as the cross product of the radius and force (τ = r × F), and the rotational inertia plays a critical role in determining the force needed in dynamic scenarios. The distinction between static and dynamic situations is also highlighted, indicating that different calculations apply based on the system's state.

PREREQUISITES
  • Understanding of torque and its formula (τ = r × F)
  • Knowledge of rotational inertia and its calculation (I = m * r^2)
  • Familiarity with static versus dynamic systems in physics
  • Basic grasp of linear and angular motion equations (v = ωr)
NEXT STEPS
  • Study the principles of rotational dynamics and how they differ from linear dynamics
  • Learn about the applications of torque in real-world scenarios, such as in machinery
  • Explore the concept of angular momentum and its conservation
  • Investigate the effects of varying mass distribution on rotational inertia
USEFUL FOR

Physics students, educators, and anyone interested in understanding the mechanics of rotational motion and the implications of torque in practical applications.

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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