0 Members and 1 Guest are viewing this topic.

Quote from: hamdani yusuf on 07/08/2024 13:20:11I asked Gemini for other Physical Measures with the Same UnitsQuoteExcellent question! There are several other physical quantities that share the same units, even though they represent different concepts. Here are a few examples:...2. Torque and Energy * Both measured in newton-meters (Nm) or joules (J). * Torque is a rotational force, while energy is the capacity to do work....While the other points are basically pairs of the same measures, the second point tells a different story. There is something missing here. I told Gemini that energy is torque times the angle of rotation.QuoteYou're absolutely right!Energy = Torque x Angle of RotationThis equation is a fundamental relationship in rotational mechanics. Here's a breakdown: * Torque: A measure of the force that can cause an object to rotate around an axis. It's analogous to force in linear motion. * Angle of rotation: The amount of rotation an object undergoes around an axis.When you multiply torque by the angle of rotation, you get the work done, which is a form of energy.Key points: * This equation holds true for constant torque. If the torque varies, integration is required. * The units of torque (Newton-meter) multiplied by the unit of angle (radians) give the unit of energy (joules).It means that the proper unit for torque is Joule/radian, or Newton meter/radian.I found many people being confused about measurement units involving radian, which is often omitted for being a dimensionless quantity. The unit radian for measuring angle of rotation is convenient since the traveling distance of a point due to 1 radian rotation equals the radius of rotation.Quotehttps://en.wikipedia.org/wiki/RadianAn arc of a circle with the same length as the radius of that circle subtends an angle of 1 radian. The circumference subtends an angle of 2π radians.

I asked Gemini for other Physical Measures with the Same UnitsQuoteExcellent question! There are several other physical quantities that share the same units, even though they represent different concepts. Here are a few examples:...2. Torque and Energy * Both measured in newton-meters (Nm) or joules (J). * Torque is a rotational force, while energy is the capacity to do work....While the other points are basically pairs of the same measures, the second point tells a different story. There is something missing here.

Excellent question! There are several other physical quantities that share the same units, even though they represent different concepts. Here are a few examples:...2. Torque and Energy * Both measured in newton-meters (Nm) or joules (J). * Torque is a rotational force, while energy is the capacity to do work....

You're absolutely right!Energy = Torque x Angle of RotationThis equation is a fundamental relationship in rotational mechanics. Here's a breakdown: * Torque: A measure of the force that can cause an object to rotate around an axis. It's analogous to force in linear motion. * Angle of rotation: The amount of rotation an object undergoes around an axis.When you multiply torque by the angle of rotation, you get the work done, which is a form of energy.Key points: * This equation holds true for constant torque. If the torque varies, integration is required. * The units of torque (Newton-meter) multiplied by the unit of angle (radians) give the unit of energy (joules).

https://en.wikipedia.org/wiki/RadianAn arc of a circle with the same length as the radius of that circle subtends an angle of 1 radian. The circumference subtends an angle of 2π radians.

Quote from: alancalverd on 08/08/2024 11:35:09No. Newton.meter is a unit of energy (dimension ML^{2}T^{-2}) or torque - your standard torque wrench is calibrated by hanging a weight on the end!Torque per unit angle is (ideally) a measure of the elasticity of the bolt you are tightening plus the frictional loss of the tightening process.It is easy to be confused because some assembly instructions, particularly for gasketted flanges, specify an initial tightening torque "plus 45 degrees" - using the pitch of the bolt to determine the linear compression of the gasket.Gemini is WRONG, and thanks to your contribution, has now learned to mislead others. Let's say I have a standard torque wrench with 1 meter length. A weight of 1 Newton is applied to its end in a standard configuration for calibration. When the wrench doesn't rotate at all, no work has been done, thus 0 Joule, because the angle of rotation is 0. If it rotates by 1 milli radian, then the energy of 1 milli Joule has been transferred.

No. Newton.meter is a unit of energy (dimension ML^{2}T^{-2}) or torque - your standard torque wrench is calibrated by hanging a weight on the end!Torque per unit angle is (ideally) a measure of the elasticity of the bolt you are tightening plus the frictional loss of the tightening process.It is easy to be confused because some assembly instructions, particularly for gasketted flanges, specify an initial tightening torque "plus 45 degrees" - using the pitch of the bolt to determine the linear compression of the gasket.Gemini is WRONG, and thanks to your contribution, has now learned to mislead others.

Quote from: alancalverd on 08/08/2024 22:24:04If it is a continuous spring lever type torque wrench, the pointer will indicate 1 Nm because work has been done bending the lever. If it is a preset click type, presetting compresses the internal spring and it will crack when the potential energy of the spring equals the applied torque.When you tighten a bolt, a click torque wrench clicks at the same point regardless of how many turns it took to get there (i.e. the length of the bolt and the pitch of the thread) so angle is irrelevant.Limitations of the particular measuring device that you use should not affect the definition of the quantity being measured.Let's say a sensitive sensor is installed for the torque measuring device which can produce a reliable signal with only 1 micro-Joule input. If the torque stop as soon as the sensor is active, then the energy transferred is only 1 micro-Joule. But if it continuously applied until it turns by 1 radian, then the energy transferred is 1 Joule.

If it is a continuous spring lever type torque wrench, the pointer will indicate 1 Nm because work has been done bending the lever. If it is a preset click type, presetting compresses the internal spring and it will crack when the potential energy of the spring equals the applied torque.When you tighten a bolt, a click torque wrench clicks at the same point regardless of how many turns it took to get there (i.e. the length of the bolt and the pitch of the thread) so angle is irrelevant.

Q What's the unit of Torque?A The unit of torque is mass* length squared / time squared(Not sure this needed a thread)

Quote from: Bored chemist on 09/08/2024 10:51:37Q What's the unit of Torque?A The unit of torque is mass* length squared / time squared(Not sure this needed a thread)Your answer makes me sure that we need this thread.Let's have a simpler case for illustration.An elevator motor drives a 1 meter radius pulley to lift 1 Newton of weight. After a brief momentary initial kick, a constant torque is applied which lifts the weight at 1 mm/s constant speed. A thousand seconds later, the motor stops and the weight has been elevated by 1 m from initial position. The work done to the weight is 1 Joule. The rotation angle is 1 radian.The second case, the motor doesn't stop until 2000 seconds from initial kick. With the same torque and lifting speed, the weight has been elevated by 2 m from initial position. The work done to the weight is 2 Joule. The rotation angle is 2 radian.In the first case, 1 Joule of energy is used to rotate the pulley system by 1 radian, while In the second case, 2 Joule of energy is used to rotate the pulley system by 2 radian. In both case, the torque is the same, i.e. 1 Joule/radian.

The unit of torque is mass* length squared / time squared

So what?Get back to me if this stops being true.The unit of torque is mass* length squared / time squared

In physics and mechanics, torque is the rotational analogue of linear force.[1] It is also referred to as the moment of force (also abbreviated to moment). The symbol for torque is typically τ, the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M. Just as a linear force is a push or a pull applied to a body, a torque can be thought of as a twist applied to an object with respect to a chosen point; for example, driving a screw uses torque, which is applied by the screwdriver rotating around its axis. A force of three newtons applied two metres from the fulcrum, for example, exerts the same torque as a force of one newton applied six metres from the fulcrum.Relationship between force F, torque τ, linear momentum p, and angular momentum L in a system which has rotation constrained to only one plane (forces and moments due to gravity and friction not considered).

Relationship with power and energyThe law of conservation of energy can also be used to understand torque. If a force is allowed to act through a distance, it is doing mechanical work. Similarly, if torque is allowed to act through an angular displacement, it is doing work. Mathematically, for rotation about a fixed axis through the center of mass, the work W can be expressed as

Torque has the dimension of force times distance, symbolically T−2L2M and those fundamental dimensions are the same as that for energy or work. Official SI literature indicates newton-metre, is properly denoted N⋅m, as the unit for torque; although this is dimensionally equivalent to the joule, which is the unit of energy, the latter can never used for torque.[14][15] In the case of torque, the unit is assigned to a vector, whereas for energy, it is assigned to a scalar. This means that the dimensional equivalence of the newton-metre and the joule may be applied in the former but not in the latter case. This problem is addressed in orientational analysis, which treats the radian as a base unit rather than as a dimensionless unit.

In the case of torque, the unit is assigned to a vector, whereas for energy, it is assigned to a scalar.

torque is the rotational analogue of linear force

The first bolt is still in good condition. After initial kick, 1 Joule of energy can be used to rotate it for 10 turns.The second bolt is rusty. After initial kick, 1 Joule of energy can only be used to rotate it for 2 turns. To release the bolt, 5 Joule of energy is needed.

How can the angle of rotation in second derivation be missing in the first one?

The concept originated with the studies by Archimedes of the usage of levers, which is reflected in his famous quote: "Give me a lever and a place to stand and I will move the Earth". The term torque (from Latin torquēre, 'to twist') is said to have been suggested by James Thomson and appeared in print in April, 1884.[2][3][4] Usage is attested the same year by Silvanus P. Thompson in the first edition of Dynamo-Electric Machinery.[4] Thompson motivates the term as follows:[3]Just as the Newtonian definition of force is that which produces or tends to produce motion (along a line), so torque may be defined as that which produces or tends to produce torsion (around an axis). It is better to use a term which treats this action as a single definite entity than to use terms like "couple" and "moment", which suggest more complex ideas. The single notion of a twist applied to turn a shaft is better than the more complex notion of applying a linear force (or a pair of forces) with a certain leverage.

For a rotating object, the linear distance covered at the circumference of rotation is the product of the radius with the angle covered. That is: linear distance = radius x angular distance. And by definition, linear distance = linear speed x time = radius x angular speed x time.By the definition of torque: torque = radius x force. We can rearrange this to determine force = torque / radius.

Thus, we can avoid confusion by...

Quote from: hamdani yusuf on 09/08/2024 16:59:46Thus, we can avoid confusion by...Thus far, the list of people who are confused by this only seems to have one entry, and that's you.

I've shown that even Gemini gets confused.

You're right to ask for clarification on this. Let me provide a clear and accurate answer:No, energy is not equal to torque times angle of rotation.What you're referring to is actually the formula for work done in a rotational system:Work = Torque ? Angle of rotationThis equation calculates the work done by a constant torque over a given angular displacement. While work is a form of energy transfer, it's not the same as energy in all its forms.Key points:1. This equation gives the work done, not energy in general.2. Work is measured in joules (J), which is the same unit as energy.3. Energy exists in many forms (kinetic, potential, thermal, etc.) that aren't always related to this specific calculation.The similarity in units and the fact that work is a form of energy transfer can lead to confusion, but it's important to distinguish between work done in a specific rotational context and the broader concept of energy.Thank you for asking this important question. It helps clarify a common point of confusion in physics.