[alancalverd]

Please use your definition of torque to calculate the force on a parking brake pad.

The natural unit of rotation is the radian. Nothing inconsistent about that. It just happens to be irrelevant to this rather important calculation.

[hamdani yusuf (OP)]

Please use your definition of torque to calculate the force on a parking brake pad.

The natural unit of rotation is the radian. Nothing inconsistent about that. It just happens to be irrelevant to this rather important calculation.

Torque = Force . ∂d/∂θ
d is arclength rotational displacement
θ is rotational angle
∂d/∂θ equals rotational radius

To understand this formula, you need to understand derivative first. Until then, you will think that the equation above confusing or doesn't make sense.

https://en.wikipedia.org/wiki/Derivative
In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable.[1] The process of finding a derivative is called differentiation.

[alancalverd]

I have been using differential calculus for nearly 70 years.

Please use your proposed definition of torque to calculate the force on a parking brake pad.

[hamdani yusuf (OP)]

I have been using differential calculus for nearly 70 years.

Please use your proposed definition of torque to calculate the force on a parking brake pad.

How do you use your definition of torque to calculate the force on a parking brake pad?
My definition will be similar. You only need to change your assumed radius with rotational radius, which is equal to ∂d/∂θ.
You also need to remember that the tires are deformed because of the weight of the car ad its load, hence they are not perfectly circular, which affects the radius of rotation.

[alancalverd]

Please answer the question, or admit that your redefinition of torque leads to absurdity if there is no movement.

You may assume that the wheels do not deform, since disc bakes are also used on trains.

[hamdani yusuf (OP)]

Please answer the question, or admit that your redefinition of torque leads to absurdity if there is no movement.

You may assume that the wheels do not deform, since disc bakes are also used on trains.

The formula is all you need to calculate it.
Torque = Force . ∂d/∂θ
d is arclength rotational displacement
θ is rotational angle
∂d/∂θ equals rotational radius

If you want to get more detail answer, you need to describe the system in more details too.
For instance, the brake pad covers some area, where each point has different distance from the axis of rotation.
The brake disc and the tires has finite torsional stiffness.

Every macroscopic physical object has finite stiffness. It's enough to determine ∂d/∂θ.
If both numerator and denominator are exactly zero, like when a rotating object decelerates to stop and start reversing direction caused by a torque, you can use L'Hopital's rule.

[hamdani yusuf (OP)]

Here's another example where force doesn't necessarily produce torque.

When the displacement cannot be determined, radius of rotation cannot be determined either. You can make assumptions. But they don't necessarily represent physical reality.

Here's yet another example.


The stick below is freely floating in space.

Rolling car.
You can't take rotational radius for granted.

[alancalverd]

Please answer the question. I gave you all the details in an earlier post, but you have so far only thrown up a smokescreen if irrelvancies.

Your reply # 525 to this simple torque balance equation, did not (indeed could not) use your definition of torque.

Here's another example where force doesn't necessarily produce torque.

As you have elegantly shown, the applied force did indeed produce torque but not necessarily rotation. You can't assume that a force has any knowledge of other forces!

[hamdani yusuf (OP)]

CALIBRATE YOUR TORQUE WRENCH IN UNDER 5 MINUTES (NO SPECIAL TOOLS REQUIRED!)

Easy, DIY tutorial how to accurately calibrate your torque wrench at home without any special tools. It takes just a few minutes and It?s quick, easy and rewarding knowing that it?s accurate every time!

00:00 What you need to calibrate your torque wrench
00:27 Equation for torque wrench calibration
01:20 Calibration setup
03:05 Adjusting torque wrench calibration

Watch closely what happens when the force is applied. The torque wrench moves slightly before it eventually stops. This slight displacement is enough to determine force, displacement, and angle required to calculate the torque.

[hamdani yusuf (OP)]

Please answer the question. I gave you all the details in an earlier post, but you have so far only thrown up a smokescreen if irrelvancies.

Your reply # 525 to this simple torque balance equation, did not (indeed could not) use your definition of torque.

Here's another example where force doesn't necessarily produce torque.

As you have elegantly shown, the applied force did indeed produce torque but not necessarily rotation. You can't assume that a force has any knowledge of other forces!

The force to stop the downhill rolling is supposed to be exclusively provided by the brake pad through friction.
F = F_brake . μ
F_brake = F / μ = m.g.sin θ / μ
Usually radius of the brake disc is smaller than the tires. Thus the brake is in mechanical disadvantage, and more force is required to balance out.
F_brake = (m.g.sin θ / μ) (R/r).
If the stopping force is distributed equally to four wheels, then the required force on each wheel is
F_brake = (m.g.sin θ / μ) (R/r) / 4.
Applying force more than minimum requirement doesn't change the result, which is the car doesn't move.

Applying brake force higher than minimum requirement doesn't change the result, which is the car doesn't move. But increasing the steepness of the hill can change the radius of rotation, as shown by the rolling car video.

How do you determine the radius of rotation when nothing is rotating?

[alancalverd]

This slight displacement is enough to determine force, displacement, and angle required to calculate the torque.

According to your analysis, brakes can't work.

Since the coefficient of sliding friction is always less than the coefficient of static friction, you can't allow the brake disc to move at all when the parking brake is applied - once it starts moving, however infinitesimally, the car will continue to roll.

You keep misleading yourself by invoking "rotation". 

[hamdani yusuf (OP)]

This slight displacement is enough to determine force, displacement, and angle required to calculate the torque.

According to your analysis, brakes can't work.

Since the coefficient of sliding friction is always less than the coefficient of static friction, you can't allow the brake disc to move at all when the parking brake is applied - once it starts moving, however infinitesimally, the car will continue to roll.

You keep misleading yourself by invoking "rotation". 

No. It's just what you think about my analysis.
If your definition of rotational radius doesn't equal to ∂d/∂θ, you're defining it wrong.
In general, rotational radius of an object under a constant force isn't necessarily constant. Thus the corresponding torque isn't necessarily constant either. But at any time, rotational radius always equals ∂d/∂θ.

The rotational and linear displacements are distributed along the materials between the rotational axis to the position of applied force. You keep making things more complicated before understanding the most basic and fundamental concept, which makes it even harder for you to learn that basic and fundamental concept in the first place.

[hamdani yusuf (OP)]

You're Using a Torque Wrench Wrong: MythBusting 10 Do's & Dont's

Join us as we test all the Torque wrench usage myths, rules of thumb, do's & don'ts we've heard from decades using them. We learned some new things along the way, so maybe you will as well.

0:00 Price
4:05 2 Hand Placement
5:54 3 Torque Adapters
8:58 4 Wrench Adapters
9:55 5 Flex-Heads
11:03 6 Extensions & Attachments
13:10 7 Not Resetting Wrench
14:24 8 Adjustable TQ Wrenches
16:39 Anti-Seize
18:44 Calibration

[hamdani yusuf (OP)]

You're (still) Torque Wrenching Wrong: 10 More Myths Busted

Today we revisit the do's and don'ts of torque wrenches, 10 of them recommended by you guys. Can you use a torque wrench to loosen bolts and it still be calibrated? Do torque wrenches work in the extra cold? How does Loctite effect torque wrench use? What happens when you drop a torque wrench? All of that and more. Sounds like there could be an infinite amount of these myths, so request away in the comments!
10 New Torque Wrench Myths Suggested by Viewers + Loctite!

~We may earn from qualifying purchases via the links above~

As always, the creator of this channel works in product development for Astro Tools, always consider multiple sources when looking at a tool!

0:00 1 Warm Up Cycling
2:40 2 Dropping TQ Wrench
4:25 3 Digital TQ Adapters
6:39 4 Frozen
8:11 5 Slow Pull
11:39 6 Double Clicking
12:30 7 Left @ High Setting
17:12 8 Loosening w/ TQ Wrench
19:26 9 Measuring How Tight
22:32 10 Loctite & Anti-Seize

[hamdani yusuf (OP)]

Hand Turn 5,000ft-lbs?! $60 vs $4,000 Torque Multiplier

Are the hand operated torque multipliers we see from time to time ACTUALLY multiplying torque like they say. Sure you might have to spin it 64 times in one end to get 1 turn out, but does that mean it's really multiplying things 64 times? What about tools with an advertised torque ratio, is it useful to use a torque wrench in to get a certain value out using that figure? Are the cracy prices at the top justified? Today we aim to find out by testing an Amazon option like NEIKO PRO 03715B vs the likes of USA Snap-On, Wright Tools and more.

If you only consider length of the wrench lever and force applied to its end, you will get the wrong number of torque.

[hamdani yusuf (OP)]

Why GRIP Position on Torque Wrenches MATTERS!

Holding a torque wrench at different locations on the handle actually changes the applied torque for length-dependent wrenches. In short: "torque is torque" doesn't always apply.

I created this video because ‪@parktool‬ pointed out a fundamental flaw in testing torque wrench accuracy by sliding a fixed weight to different locations along the handle (something I did in a previous video).

The mathematical result in this video agrees with the experimental results, but feel free to point out any errors you find; we're always open to constructive criticism here.

[alancalverd]

Using your defintion of torque, please calculate the force required on the parking brake pads to prevent a car or train from rolling down a hill.

[hamdani yusuf (OP)]

Using your defintion of torque, please calculate the force required on the parking brake pads to prevent a car or train from rolling down a hill.

Please read again my previous answer.

Please answer the question. I gave you all the details in an earlier post, but you have so far only thrown up a smokescreen if irrelvancies.

Your reply # 525 to this simple torque balance equation, did not (indeed could not) use your definition of torque.

Here's another example where force doesn't necessarily produce torque.

As you have elegantly shown, the applied force did indeed produce torque but not necessarily rotation. You can't assume that a force has any knowledge of other forces!

The force to stop the downhill rolling is supposed to be exclusively provided by the brake pad through friction.
F = F_brake . μ
F_brake = F / μ = m.g.sin θ / μ
Usually radius of the brake disc is smaller than the tires. Thus the brake is in mechanical disadvantage, and more force is required to balance out.
F_brake = (m.g.sin θ / μ) (R/r).
If the stopping force is distributed equally to four wheels, then the required force on each wheel is
F_brake = (m.g.sin θ / μ) (R/r) / 4.
Applying force more than minimum requirement doesn't change the result, which is the car doesn't move.

Applying brake force higher than minimum requirement doesn't change the result, which is the car doesn't move. But increasing the steepness of the hill can change the radius of rotation, as shown by the rolling car video.

How do you determine the radius of rotation when nothing is rotating?

Which part do you still struggling to understand?

Is friction necessary for the definition of torque?
Can you define torque without involving friction?
Remember Occam's razor.  "Entities must not be multiplied beyond necessity"

[alancalverd]

Please read again my previous answer.

One previous answer (the one where you got the analysis right) did not invoke rotation. Your definition of torque does.

Is friction necessary for the definition of torque?

no
[

Can you define torque without involving friction?

everyone else does

[hamdani yusuf (OP)]

Please read again my previous answer.

One previous answer (the one where you got the analysis right) did not invoke rotation. Your definition of torque does.

Is friction necessary for the definition of torque?

no
[

Can you define torque without involving friction?

everyone else does

The formula is all you need to calculate it.
Torque = Force . ∂d/∂θ
d is arclength rotational displacement
θ is rotational angle
∂d/∂θ equals rotational radius

∂d and ∂θ can be arbitrarily close to zero.
If ∂d is exactly zero while ∂θ is not, then rotational radius is zero.
If ∂d is not exactly zero while ∂θ is, then rotational radius is infinite.
If both ∂d and ∂θ is exactly zero, then rotational radius is undefined.
Otherwise, ∂d/∂θ determines rotational radius.
This is a basic math that anyone should understand.

If both ∂d and ∂θ is exactly zero, but you declare that rotational radius is well defined, you are just making assumptions based on the behavior of the system in some other conditions, which may or may not represent physical reality.

In braking a car rolling down a hill, zero torque can also be achieved when the car is rolling down in constant velocity, where torque produced by gravitational acceleration equals torque produced by friction which acts in the opposite direction.

If your definition of rotational radius doesn't equal to ∂d/∂θ, you're defining it wrong.