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
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.
 

Thread '1:1 versus 2:1 Mechanical Advantage debate'

The rope is tied into the person (the load of 200 pounds) and the rope goes up from the person to a fixed pulley and back down to his hands. He hauls the rope to suspend himself in the air. What is the mechanical advantage of the system? The person will indeed only have to lift half of his body weight (roughly 100 pounds) because he now lessened the load by that same amount. This APPEARS to be a 2:1 because he can hold himself with half the force, but my question is: is that mechanical...
View full post »

Thread 'average velocity as a weighted mean'

Hello everyone, Consider the problem in which a car is told to travel at 30 km/h for L kilometers and then at 60 km/h for another L kilometers. Next, you are asked to determine the average speed. My question is: although we know that the average speed in this case is the harmonic mean of the two speeds, is it also possible to state that the average speed over this 2L-kilometer stretch can be obtained as a weighted average of the two speeds? Best regards, DaTario
View full post »

Thread 'Newton's first law?'

Some physics textbook writer told me that Newton's first law applies only on bodies that feel no interactions at all. He said that if a body is on rest or moves in constant velocity, there is no external force acting on it. But I have heard another form of the law that says the net force acting on a body must be zero. This means there is interactions involved after all. So which one is correct?
View full post »

Similar threads

1 pulley with mass, 1 mass on the cord, 1 external force, no gravity
Replies
16
Views
3K
Angular Acceleration: Understanding the Relationship Between Connected Pulleys
Replies
12
Views
2K
Torque to rotate pulley with equal mass on each side.
Replies
3
Views
2K
Does the Relation ##T_2 = T_1 e^{\mu \theta}## Hold for an Accelerating Capstan?
Replies
1
Views
1K
Distance Traveled by an object on a pulley
Replies
17
Views
5K
Will a Massless Pulley with Friction Rotate with Unequal Masses on Either Side?
Replies
1
Views
1K
Angular acceleration of a massless pulley
Replies
8
Views
7K
Why does adding more pulleys increase the force on a block?
Replies
21
Views
4K
Analyzing acceleration of block on a ramp connected to a pulley
Replies
15
Views
1K
Pulleys with Strings Having Mass
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top