[hamdani yusuf (OP)]

Option 3: Change the unit of a rotational radius to meters per radian, while keeping the unit of a geometric radius in meters. A radius is geometric if it can still have a defined value while the object is stationary. Rotational radius is only defined when there's a rotation.
Pros:
- Solve the problem from option 0.
- Solve the problem from option 1.
Cons:
- Something needs to be done.
- Currently existing textbooks need to be revised.
- Requires more characters because the unit of rotational angle can not be omitted.
- People need to unlearn the old standard and relearn the new standard, which can be hard for some of them.

*All options except option 0 share these cons.

[paul cotter]

The "problem" only exists in your confusion.

[alancalverd]

So, there are cases where the unit of a radius is more appropriate to be expressed in meters per radian,

Isn't that the track length on a great circle? Excellent for long range fuel planning, but buggerall use for tightening a bolt without stripping the thread,

[hamdani yusuf (OP)]

The "problem" only exists in your confusion.

You can avoid confusion by being unaware of the problem. But then you won't be able to solve it, nor stopping anyone else to find it.

https://pubs.aip.org/aapt/pte/article-abstract/31/2/84/270995/The-radian-That-troublesome-unit

Unfortunately, the rest of the article is behind a paywall, with Pay-Per-View Access $40.00

[hamdani yusuf (OP)]

So, there are cases where the unit of a radius is more appropriate to be expressed in meters per radian,

Isn't that the track length on a great circle? Excellent for long range fuel planning, but buggerall use for tightening a bolt without stripping the thread,

When there is no rotation, there is zero rotation angle, zero rotational arc length, and undefined rotational radius.

[alancalverd]

So when I hang a weight on the end of a 1 m bar that doesn't move,

(a) it doesn't exert any torque on the bolt?   or

(b) the length of the bar is undefined?

[hamdani yusuf (OP)]

So when I hang a weight on the end of a 1 m bar that doesn't move,

(a) it doesn't exert any torque on the bolt?   or

(b) the length of the bar is undefined?

If the bolt doesn't change in any way, it doesn't produce torque. But it isn't likely the case, since no bolt is perfectly rigid. Nor is the thread that prevent it from turning.

When it doesn't rotate, the radius of rotation is undefined. You just assume that the length of the bar will be equal to radius of rotation, which is not necessarily true.

[alancalverd]

I really wonder about the competence of the AAPT Committee to teach teachers. The radian is a unit of angle. What more needs to be said? Why is it "troublesome" when a degree isn't?

[alancalverd]

When it doesn't rotate, the radius of rotation is undefined. You just assume that the length of the bar will be equal to radius of rotation, which is not necessarily true.

You are adding to your own confusion by introducing rotation. The brake pads on your car must exert a torque to stop the car from rolling down a hill. The radius from the pad to the hub is obvious, the tangential force is calculable, the rotation is (or should be ) zero.

[hamdani yusuf (OP)]

The "problem" only exists in your confusion.

You can avoid confusion by being unaware of the problem. But then you won't be able to solve it, nor stopping anyone else to find it.

https://pubs.aip.org/aapt/pte/article-abstract/31/2/84/270995/The-radian-That-troublesome-unit

Unfortunately, the rest of the article is behind a paywall, with Pay-Per-View Access $40.00

I understand that this is not an easy problem. Otherwise it would have been solved already a long time ago.
Furthermore, its subtlety has prevented many people from realizing about its existence in the first place, let alone trying to solve it.

[alancalverd]

Please explain how your redefinition of torque helps you analyse the parking brake in reply #488. It's very important, because we don't like vehicles  to roll away when parked on a hill. So we need to calculate the brake pad force required to prevent the wheels turning, assuming a coefficient of friction of, say, 0.8 between the pad and the disc.
 

[hamdani yusuf (OP)]

Please explain how your redefinition of torque helps you analyse the parking brake in reply #488. It's very important, because we don't like vehicles  to roll away when parked on a hill. So we need to calculate the brake pad force required to prevent the wheels turning, assuming a coefficient of friction of, say, 0.8 between the pad and the disc.
 

I didn't redefine torque. You did.

1
: a force that produces or tends to produce rotation or torsion
an automobile engine delivers torque to the drive shaft
also : a measure of the effectiveness of such a force that consists of the product of the force and the perpendicular distance from the line of action of the force to the axis of rotation
2
: a turning or twisting force

It seems like the problem comes from our failure to distinguish between geometric radius and rotational radius.

[hamdani yusuf (OP)]

When it doesn't rotate, the radius of rotation is undefined. You just assume that the length of the bar will be equal to radius of rotation, which is not necessarily true.

You are adding to your own confusion by introducing rotation. The brake pads on your car must exert a torque to stop the car from rolling down a hill. The radius from the pad to the hub is obvious, the tangential force is calculable, the rotation is (or should be ) zero.

When the wheel is decelerating, you must exert torque, from formula torque equals rotational inertia times angular acceleration. When angular acceleration is zero, the torque is zero.

[hamdani yusuf (OP)]

Since you seem to already forget about my examples, here I remind you.

Here's another thought experiment. This picture shows a table with rounded feet on a smooth floor. Its weight is distributed evenly between its leg on the left and right sides. The floor exerts normal force equal and opposite to the total weight, thus the table is stationary.


A force is applied to the top right corner of the table, directed 45 degree to the up left direction. The table is only accelerated horizontally, but isn't accelerated vertically. It doesn't rotate, hence the net torque is zero.


Just like before, a force is applied to the top right corner of the table, directed 45 degree to the up left direction. But a wedge is placed to the left side of the left leg. The left leg of the table is raised while the right leg is not. Thus it is rotated clockwise.


Just like before, a force is applied to the top right corner of the table, directed 45 degree to the up left direction. But a wedge is placed to the left side of the right leg. The right leg of the table is raised while the left leg is not. Thus it is rotated counter-clockwise.


I show this to emphasize that the same active force to the same object can produce different torque which lead to different rotation of the object.

How do you define radius of rotation in each case?

[alancalverd]

When angular acceleration is zero, the torque is zero.

So why doesn't the car roll down the hill when you apply the parking brake?

[paul cotter]

Confusion, ad infinitum!

[alancalverd]

How do you define radius of rotation in each case?

I suggest you first remind yourself of the resolution of vectors. Then revise moments and levers. This is all very elementary statics, the kind of stuff you did in primary school.

[hamdani yusuf (OP)]

When angular acceleration is zero, the torque is zero.

So why doesn't the car roll down the hill when you apply the parking brake?

Because the torque is zero, thus angular acceleration is zero.
So why does the car roll down the hill when you don't apply the parking brake?

[hamdani yusuf (OP)]

How do you define radius of rotation in each case?

I suggest you first remind yourself of the resolution of vectors. Then revise moments and levers. This is all very elementary statics, the kind of stuff you did in primary school.

Would it be too complicated to write in a few sentences?

[hamdani yusuf (OP)]

I really wonder about the competence of the AAPT Committee to teach teachers. The radian is a unit of angle. What more needs to be said? Why is it "troublesome" when a degree isn't?

Instead of judging someone else's competence, it would be better to point out their mistakes, and tell what should be done to correct them.

You can't simply omit the unit degree in an angle. While omitting the unit radian is a norm.