Useless mind ramblings

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broli

Useless mind ramblings « on: 2025-03-06, 12:02:35 »

Group: Moderator
Sr. Member

Posts: 335

What was the saying again about trying the same thing but expecting different results?

Well here is the latest brain pasta. You guys still remember friction right? How about belt friction. A good explanation on this can be found here:

https://www.youtube.com/watch?v=a0SiiNPnrm8
https://www.youtube.com/watch?v=a0SiiNPnrm8
https://www.youtube.com/watch?v=SLQdp1V0c9k

Essentially most of these calculations tell you the tensions required as to avoid slippage. But what happens exactly when the belt or rope starts to slip?

Take this setup for example. A rigid disc that has a peg sticking out on one side with a rope looped around it:

If the forces are unbalanced the rope starts to slip which will make it slide over the peg. This slippage produces a torque due to the tangential slipping force between the rope and the surface of the peg.

But that means it would now induce a torque on the entire setup. That can't be right. How can a linear force acting on the center of mass of the setup induce a constant torque? And if it's a constant torque wouldn't the whole setup keep accelerating indefinitely as long as there is a constant force or rather power being applied to sustain the friction in the rotating frame perhaps by a tiny little motor inside the rotating frame?

Or replacing ropes with magnets as shown in a previous thread:

Straight lines making loops sure keep that brain pasta busy.

F6FLT

Re: Useless mind ramblings « Reply #1 on: 2025-03-06, 17:40:36 »

Group: Experimentalist
Hero Member

Posts: 2148

Quote from: broli on 2025-03-06, 12:02:35

...
But that means it would now induce a torque on the entire setup. That can't be right. How can a linear force acting on the center of mass of the setup induce a constant torque?
...

Your intuition is wrong. The force acts on the tangential point where the rope separates to go upwards and the other end downwards. The force is Fu upwards and Fd downwards. The difference multiplied by the peg radius gives us the torque relative to the center of the peg.

The resultant of the friction forces, as they are equally distributed around the peg, is necessarily zero if we rotate through 360°. This leaves only Fu-Fd to take into account at the tangential point. If Fu=Fd, there is no torque.

---------------------------

"Open your mind, but not like a trash bin"

broli	Re: Useless mind ramblings « Reply #2 on: 2025-03-06, 21:30:54 »
Group: Moderator Sr. Member Posts: 335	Quote from: F6FLT on 2025-03-06, 17:40:36 If Fu=Fd, there is no torque. Correct. The point is that a constant power, so (Fu-Fd)*v supplied by a power source INSIDE the system (ex. a motor) provides a constant torque that rotates the entire otherwise 'closed' system. This overall torque is decoupled from the inside source that is providing said constant power. So the overall rotational speed is only limited by its structural limits. Or an alternate way to look at it is to use water where you push the water around using 2 (to keep things balanced) pumps at the central location. These pumps can be assumed to be very close to the center as to provide negligible overall torque on the system. However as the water goes around the tube it applies friction tangential to the walls inducing a constant torque on the entire setup. Because the behavior of water and friction do not change due to the overall rotation the whole assembly will thus keep accelerating to infinity and beyond.

F6FLT	Re: Useless mind ramblings « Reply #3 on: 2025-03-10, 19:53:22 »
Group: Experimentalist Hero Member Posts: 2148	Intuition still wrong. There's no reason for the whole thing to rotate. The torque you see on the large disk is real. But it's the system's reaction to the motor torque. The assembly would turn if the motor stator wasn't attached to the assembly. But it is, otherwise it wouldn't be able to apply its torque, so the torque it produces compensates for the inverse torque of your system. Action/reaction. --------------------------- "Open your mind, but not like a trash bin"

broli	Re: Useless mind ramblings « Reply #4 on: 2025-03-18, 10:37:48 »
Group: Moderator Sr. Member Posts: 335	Quote from: F6FLT on 2025-03-10, 19:53:22 Intuition still wrong. There's no reason for the whole thing to rotate. The torque you see on the large disk is real. But it's the system's reaction to the motor torque. The assembly would turn if the motor stator wasn't attached to the assembly. But it is, otherwise it wouldn't be able to apply its torque, so the torque it produces compensates for the inverse torque of your system. Action/reaction. It's power that is of interest, not torque. The torque caused by the motor can be made arbitrary small, until its axle radius is 0, if you will. Which you can also see by the previous diagrams. The motor can even be mounted just above the center point in a side ways matter using a bevel gear to eliminate any torque caused by the motor/housing. This idea is not new, here is a similar setup: https://www.youtube.com/watch?v=dG8YOp_njFs However notice how in that scenario there is no interaction with the 'assembly' the wheel is acting like a fly wheel and thus only relies on inertial forces. This means that the whole assembly only accelerates if the fly wheel is accelerating. However when 'friction' is introduced on the rotating mass it starts to interact with the, seemingly static, assembly by transferring power from the motor to the assembly. It's a tangency problem.

F6FLT	Re: Useless mind ramblings « Reply #5 on: 2025-03-18, 14:17:20 »
Group: Experimentalist Hero Member Posts: 2148	Quote from: broli on 2025-03-18, 10:37:48 It's power that is of interest, not torque. ... P = T.w where T is torque and w is rotational speed. Power and torque are completely related. What's more, it's the power that's of no interest, since it's linked to time. You can generate 1 MW by discharging a simple capacitor. So what? Power says absolutely nothing about energy. Quote ... However notice how in that scenario there is no interaction with the 'assembly' the wheel is acting like a fly wheel... Wasn't it you who mentioned “friction”? There's friction in what's driven by the motor, and that's why the larger disc turns. As the motor is attached to the assembly, there is therefore an interaction between the two. Either you don't understand the device you described, or you're telling me about another one, and it keeps changing... --------------------------- "Open your mind, but not like a trash bin"

broli	Re: Useless mind ramblings « Reply #6 on: 2025-03-19, 11:29:33 »
Group: Moderator Sr. Member Posts: 335	Quote from: F6FLT on 2025-03-18, 14:17:20 P = T.w where T is torque and w is rotational speed. Power and torque are completely related. What's more, it's the power that's of no interest, since it's linked to time. You can generate 1 MW by discharging a simple capacitor. So what? Power says absolutely nothing about energy. Wasn't it you who mentioned “friction”? There's friction in what's driven by the motor, and that's why the larger disc turns. As the motor is attached to the assembly, there is therefore an interaction between the two. Either you don't understand the device you described, or you're telling me about another one, and it keeps changing... I know torque and power are related. I was trying to say that the 'motor' in this case is providing constant power in the form of P = F*v in the form of two force vectors that are essentially co-linear pointing in opposite directions. The motor axle, aka radius, is therefore infinitesimal small hence rotational speed and the effect of the torque of the motor has no meaning in the whole picture. These forces act exactly on the center of the assembly. Imagine a person sitting in a fixed chair at exactly the center of the assembly and pushing the off center wheel with his feet. His reaction force acts exactly on the center of the assembly but due to the tangent nature the off center wheel rotates and provides friction which reacts with the whole assembly making it turn. Thus a purely linear force is converted into a circular force aka torque. Mirror this and you have the above setup.