[alancalverd]

When nothing is rotating, the term "radius of rotation" is meaningless. Which is why we don't use it in the definition of torque.

"A force applied perpendicularly to a lever multiplied by its distance from the lever's fulcrum (the length of the lever arm) is its torque. Therefore, torque is defined as the product of the magnitude of the perpendicular component of the force and the distance of the line of action of a force from the point around which it is being determined."

No movement is expressed or implied.

[hamdani yusuf (OP)]

When nothing is rotating, the term "radius of rotation" is meaningless. Which is why we don't use it in the definition of torque.

"A force applied perpendicularly to a lever multiplied by its distance from the lever's fulcrum (the length of the lever arm) is its torque. Therefore, torque is defined as the product of the magnitude of the perpendicular component of the force and the distance of the line of action of a force from the point around which it is being determined."

No movement is expressed or implied.

You are defining torque of a lever, which is an extremely narrow application. The most general definition must be based on something that's fundamentally conserved, like angular momentum. Torque on an object is defined as the rate of change of its angular momentum. Similarly, force on an object is defined as the rate of change of its momentum.

The general definition can be used even when the radius of rotation is not constant, like a spinning ice skater. Or when the force is not concentrated on a single point, like a blower or a pump.

[hamdani yusuf (OP)]

It means you've never been assigned with tasks that required consistency in units of rotational quantities.

On the contrary, I have used torsion balances and suspensions of various kinds, used torque wrenches to assemble clocks and trucks, measured stall torque of electric and pneumatic motors, been involved with dynamic balancing of cricket bats, wheels and propellors, applied in-flight countertorques to the various gyroscopic, vortex, thrust and differential drag torques associated with powered aircraft and gliders, and repaired and used the brakes on all sorts of road vehicles and aircraft.

At no time has it been appropriate to describe torque as anything but force x distance. A thorough understanding of torque is essential when taking off in a tail-heavy aircraft, recovering from a spin, or teaching the principles of attitude, turn, magnetic compass, direction indicator and tachometer instruments, d'Arsonval meters, piano tuners, or magnetic resonance imaging. So far, neither I nor any of my students, pianos or patients have suffered from the correct definition of torque.

You don't seem to be aware of the inconsistency in current standard units of rotational quantities, as shown clearly in this table.


Compare them with the new proposed standard units, which are consistent with the relating equations.


It implies that your jobs don't require consistency in the units of rotational quantities.

[alancalverd]

Torque on an object is defined as the rate of change of its angular momentum.

So no force is required on the brake pads to prevent the car from rolling down the hill. Fascinating.

The general definition can be used even when the radius of rotation is not constant, like a spinning ice skater.

There is no torque involved here. Conservation of angular momentum is absolute.

You don't seem to be aware of the inconsistency in current standard units of rotational quantities, as shown clearly in this table.

If there were any inconsistencies, my life would be littered with bent or lost aeroplanes, cars that roll down hills when the parking brake is applied, and MRI machines that don't perform predictably. Much time would have been wasted balancing wheels and propellers, and every bolt I ever tightened would have broken because however much force I applied to the spanner, the torque would have decayed to zero when it stopped turning. 
 

[alancalverd]

Incidentally the quantity with SI units Nm/rad is known as the "torsional stiffness" of an object. It is the key characteristic of spiral springs, torsional suspensions, taut-band meters, and suchlike.

[paul cotter]

Very good, Alan, that argument in your last two posts represents an unambiguous and accurate response. Hopefully this will end this excessively long thread.

[hamdani yusuf (OP)]

Torque on an object is defined as the rate of change of its angular momentum.

So no force is required on the brake pads to prevent the car from rolling down the hill. Fascinating.

The general definition can be used even when the radius of rotation is not constant, like a spinning ice skater.

There is no torque involved here. Conservation of angular momentum is absolute.

You don't seem to be aware of the inconsistency in current standard units of rotational quantities, as shown clearly in this table.

If there were any inconsistencies, my life would be littered with bent or lost aeroplanes, cars that roll down hills when the parking brake is applied, and MRI machines that don't perform predictably. Much time would have been wasted balancing wheels and propellers, and every bolt I ever tightened would have broken because however much force I applied to the spanner, the torque would have decayed to zero when it stopped turning. 
 

Force is required to make the car roll down the hill. No force, no acceleration. No torque, no change in angular momentum.

The angular momentum of spinning ice skater is reduced by friction from the ice and the air, which means they produce torque.

The inconsistencies can be ignored in case of the conversion factor is numerically 1, which makes you get the same number, although the explicit unit is inconsistent. In your case, you can ignore the unit inconsistencies. In other cases where the conversion factor is not 1, you will get incorrect numbers.

[hamdani yusuf (OP)]

Incidentally the quantity with SI units Nm/rad is known as the "torsional stiffness" of an object. It is the key characteristic of spiral springs, torsional suspensions, taut-band meters, and suchlike.

In the new proposed units, it would be Nm/rad^2.

[alancalverd]

Force is required to make the car roll down the hill. No force, no acceleration.

On my planet, and AFAIK throughout the universe, that force is supplied by gravity.

The angular momentum of spinning ice skater is reduced by friction from the ice and the air, which means they produce torque.

In real life, yes, but  not in physics! Ice, or roller skates, simply helps you approach the ideal.

[alancalverd]

Incidentally the quantity with SI units Nm/rad is known as the "torsional stiffness" of an object. It is the key characteristic of spiral springs, torsional suspensions, taut-band meters, and suchlike.

In the new proposed units, it would be Nm/rad^2.

Which would obviously be nonsense. The torsional equivalent of Hooke's Law makes force linearly proportional to deflection. 

[paul cotter]

Where does the Nm/rad squared come from? Previously you have stated that your conception of torque would be Nm/rad, which Alan has pointed out is the expression for torsional stiffness.

[hamdani yusuf (OP)]

Force is required to make the car roll down the hill. No force, no acceleration.

On my planet, and AFAIK throughout the universe, that force is supplied by gravity.

The angular momentum of spinning ice skater is reduced by friction from the ice and the air, which means they produce torque.

In real life, yes, but  not in physics! Ice, or roller skates, simply helps you approach the ideal.

If there's no change in angular momentum, then the net torque on the system is zero. If the momentum is also constant, then the net force on the system is also zero.
If your physics doesn't represent real life, then it's inaccurate.

[paul cotter]

.

In the new proposed units, it would be Nm/rad^2.
Again, where does this expression come from?

[hamdani yusuf (OP)]

Incidentally the quantity with SI units Nm/rad is known as the "torsional stiffness" of an object. It is the key characteristic of spiral springs, torsional suspensions, taut-band meters, and suchlike.

In the new proposed units, it would be Nm/rad^2.

Which would obviously be nonsense. The torsional equivalent of Hooke's Law makes force linearly proportional to deflection. 

What's obvious to you may not be obvious to someone else. What you think is obviously true might be considered obviously false by someone else. What's important is the justification for your conviction. In these cases at least one of you must have a false assumption.

[hamdani yusuf (OP)]

Where does the Nm/rad squared come from? Previously you have stated that your conception of torque would be Nm/rad, which Alan has pointed out is the expression for torsional stiffness.

In linear motion, Stiffness is the extent to which an object resists deformation in response to an applied force.
https://en.m.wikipedia.org/wiki/Stiffness
For rotational stiffness, the linear deformation must be replaced by rotational deformation, while linear force must be replaced by torque.
In my proposed standard units, torque is measured in Nm/rad, while rotational deformation is in radian. Following the equation, torque divided by rotational deformation is rotational stiffness, which is in Nm/rad^2

[hamdani yusuf (OP)]

It means you've never been assigned with tasks that required consistency in units of rotational quantities.

On the contrary, I have used torsion balances and suspensions of various kinds, used torque wrenches to assemble clocks and trucks, measured stall torque of electric and pneumatic motors, been involved with dynamic balancing of cricket bats, wheels and propellors, applied in-flight countertorques to the various gyroscopic, vortex, thrust and differential drag torques associated with powered aircraft and gliders, and repaired and used the brakes on all sorts of road vehicles and aircraft.

At no time has it been appropriate to describe torque as anything but force x distance. A thorough understanding of torque is essential when taking off in a tail-heavy aircraft, recovering from a spin, or teaching the principles of attitude, turn, magnetic compass, direction indicator and tachometer instruments, d'Arsonval meters, piano tuners, or magnetic resonance imaging. So far, neither I nor any of my students, pianos or patients have suffered from the correct definition of torque.

You don't seem to be aware of the inconsistency in current standard units of rotational quantities, as shown clearly in this table.


Compare them with the new proposed standard units, which are consistent with the relating equations.


It implies that your jobs don't require consistency in the units of rotational quantities.

It seems like many people are struggling to understand the implications brought by the tables above. So I should elaborate a bit further. Let's analyze them row by row.

The first row shows standard unit for rotational angle, which is currently set in radian. But the equation relating rotational angle with work and torque suggests that it has no unit, which creates inconsistency.

In the second row, standard unit for rotational velocity is currently set in radian per second. But the equation relating rotational velocity with angular momentum and rotational inertia suggests that its unit is second^(-1), or Hertz. This also creates inconsistency.

In the third row, standard unit for rotational acceleration is currently set in radian per second squared. But the equation relating rotational acceleration with torque and rotational inertia suggests that its unit is second^(-2), or Hertz squared. This also creates inconsistency.

[hamdani yusuf (OP)]

The fourth row shows standard unit for rotational inertia, which is currently set in kg.meter^2. But the equation related to torque and angular acceleration suggests that its unit is kg.meter^2/rad, which creates inconsistency.
You can continue for the next rows in the first table, where every row contains inconsistency.

In the second table, standard units for radius of rotation is set to meter per radian. Applying the equations, every row produce consistent results.

[paul cotter]

Nm/rad squared for torsional stiffness is totally inconsistent with the known laws of mechanics. You are just digging yourself into an ever deeper hole.

[hamdani yusuf (OP)]

The fifth row shows standard unit for angular momentum, which is currently set in kg.meter^2/sec. But the equation related to angular velocity and rotational inertia suggests that its unit is kg.meter^2 rad/ sec , which creates inconsistency.

In the second table, standard units for angular momentum is set to kg meter^2/(rad sec), which is consistent with the result from equation.

[hamdani yusuf (OP)]

Nm/rad squared for torsional stiffness is totally inconsistent with the known laws of mechanics. You are just digging yourself into an ever deeper hole.

Which laws?