How Does a Frictionless Pulley Influence Acceleration in Connected Masses?

AI Thread Summary
The discussion centers on how a frictionless pulley affects the acceleration of two connected masses. The presence of rotational inertia in the pulley requires torque for acceleration, which is factored into the net force equation as I/r^2, representing the effective mass of the pulley. Participants clarify that torque does not consume force but rather influences the system's dynamics similarly to how mass does. The rotational inertia formula, I = MR^2 / 2, is referenced, but participants emphasize deriving the equations rather than relying on shortcuts. Overall, the conversation enhances understanding of the relationship between torque, rotational inertia, and acceleration in connected mass systems.
123yt
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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.
 
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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.
 

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