How Does a Frictionless Pulley Influence Acceleration in Connected Masses?

Click For Summary

Discussion Overview

The discussion revolves around the influence of a frictionless pulley on the acceleration of two connected masses. Participants explore the role of the pulley’s rotational inertia and its effect on the net force and acceleration in the system, addressing both theoretical and conceptual aspects of the problem.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question how a frictionless pulley can affect acceleration, given its rotational inertia and radius.
  • There is a proposal that the net force can be expressed as Acceleration * (Mass of two blocks + I/r^2), with some understanding of the mass components but uncertainty about the I/r^2 term.
  • One participant suggests that the I/r^2 term can be thought of as the effective mass of the pulley, but acknowledges that this equation is a shortcut and recommends deriving a version using Newton's 2nd law.
  • Participants discuss the nature of torque, with one asserting that torque does not "use up" force in the same way that pushing a mass does, while another counters that it does consume force in a similar manner.
  • There is a discussion about the rotational inertia of the pulley, with one participant stating the formula I = MR^2 / 2 and questioning if the mass could be expressed as M = 2 * I / R^2, which is challenged by another participant who suggests deriving the equation instead.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of torque and the role of the pulley’s rotational inertia. There is no consensus on the correct approach to deriving the equations related to the system.

Contextual Notes

Participants highlight the need for careful derivation of equations and the implications of treating the pulley as a uniform disk, indicating potential limitations in assumptions made during the discussion.

123yt
Messages
30
Reaction score
0
Pretend there are two accelerating masses connected to a massless string with a frictionless pulley between them. How can the frictionless pulley (Rotational inertia and radius given) affect acceleration in any sort of way?

Also, why is the net force equal to Acceleration * (Mass of two blocks + I/r^2)? I understand the part with the two blocks, but not with the I/r^2.
 
Physics news on Phys.org
123yt said:
Pretend there are two accelerating masses connected to a massless string with a frictionless pulley between them. How can the frictionless pulley (Rotational inertia and radius given) affect acceleration in any sort of way?
The pulley has rotational inertia and thus requires a torque to accelerate it.
Also, why is the net force equal to Acceleration * (Mass of two blocks + I/r^2)? I understand the part with the two blocks, but not with the I/r^2.
You can think of I/r^2 as the effective mass of the pulley. But that equation is a bit of a short cut. Rather than use it directly, derive your own version by applying Newton's 2nd law to each mass and the pulley itself.
 
Doc Al said:
The pulley has rotational inertia and thus requires a torque to accelerate it.

But torque is just a measure of how much a force causes an object to rotate. It doesn't "use up" any force to rotate it, right?

You can think of I/r^2 as the effective mass of the pulley. But that equation is a bit of a short cut. Rather than use it directly, derive your own version by applying Newton's 2nd law to each mass and the pulley itself.

The rotational inertia of the pulley is I = MR^2 / 2, so shouldn't the mass be M = 2 * I / R^2?
 
123yt said:
But torque is just a measure of how much a force causes an object to rotate. It doesn't "use up" any force to rotate it, right?
It "uses up" force in a manner similar to how pushing a mass "uses up" force.
The rotational inertia of the pulley is I = MR^2 / 2, so shouldn't the mass be M = 2 * I / R^2?
No. If you derive the equation, you'll see where that I/R^2 term comes from. (No reason to treat the pulley as a uniform disk.)
 
Alright, thanks for the help. I think I understand torque and rotation a little better now.
 

Similar threads

  • · Replies 16 ·
Replies
16
Views
3K
Replies
12
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
1
Views
1K
Replies
1
Views
1K
  • · Replies 17 ·
Replies
17
Views
5K
  • · Replies 8 ·
Replies
8
Views
7K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 21 ·
Replies
21
Views
5K
Replies
15
Views
2K