Exploring the Impact of a Frictionless Pulley on Acceleration

In summary, the frictionless pulley in this setup has rotational inertia and requires torque to accelerate. The net force is equal to the acceleration multiplied by the mass of the two blocks and the effective mass of the pulley (I/r^2). This equation can be derived by applying Newton's 2nd law to each mass and the pulley. Torque is a measure of how much a force causes an object to rotate, and it "uses up" force in a similar way to pushing a mass. The rotational inertia of the pulley can be calculated using I = MR^2 / 2, but the effective mass is not equal to M = 2 * I / R^2. By deriving the equation, it is
  • #1
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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  • #2
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.
 
  • #3
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?
 
  • #4
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.)
 
  • #5
Alright, thanks for the help. I think I understand torque and rotation a little better now.
 

1. How does a frictionless pulley affect the acceleration of a system?

A frictionless pulley reduces the overall friction within a system, allowing for a more efficient transfer of energy. This results in a higher acceleration of the system as a whole.

2. Does the mass of the pulley affect the acceleration of the system?

No, in a frictionless pulley system, the mass of the pulley does not affect the acceleration of the system. This is because the pulley does not contribute to the overall mass of the system and only serves as a mechanism for redirecting the force.

3. How does the angle of the rope on the pulley affect acceleration?

The angle of the rope on the pulley does not directly affect the acceleration of the system. However, a more acute angle can result in a larger tension force on the rope, which can impact the acceleration of the system.

4. Is the acceleration of a system with a frictionless pulley constant?

The acceleration of a system with a frictionless pulley may not always be constant. This depends on the forces acting on the system, such as gravity and tension, which can vary throughout the motion.

5. How can we experimentally determine the impact of a frictionless pulley on acceleration?

To determine the impact of a frictionless pulley on acceleration, an experiment can be set up using different masses and angles on the pulley and measuring the acceleration of the system. The data can then be analyzed to observe any patterns or relationships between the variables.

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