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Frigus
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Earlier I read that as distance from centre of axis of rod increases it's inertia increases but why does torque increases isn't it like that if inertia increases for same force the less force should be produced?
Hemant said:Earlier I read that as distance from centre of axis of rod increases it's inertia increases but why does torque increases isn't it like that if inertia increases for same force the less force should be produced?
I want to say for same force why does more rotational effect producePeroK said:Force is not produced; force is applied.
Can you describe more clearly the scenarion you have in mind?
Are you familiar with mechanical advantage and as it applies to levers?Hemant said:I want to say for same force why does more rotational effect produce
Yes sirruss_watters said:Are you familiar with mechanical advantage and as it applies to levers?
That's torque!Hemant said:Yes sir
Hemant said:I want to say for same force why does more rotational effect produce
You can show it without the concepts of torque or work:Hemant said:I want to say for same force why does more rotational effect produce
Hemant said:why does torque increases isn't it like that if inertia increases for same force the less force should be produced?
The MA of that particular capstan is zero because there is no load. No rope is attached. The tourists are busy doing nothing but turning the dead weight.sophiecentaur said:The MA of that Capstan in the above picture will be hopelessly worse than the VR might suggest.
sophiecentaur said:'They' didn't invent torque before there was a need to. No one said "I know, let's take Force times Perpendicular Distance and call it Torque"
What was found was that long levers need less force when applied against short levers. (Obvs, of course) An empirical rule was postulated and then confirmed by countless measurements and observations. The principle of Moments was born. Torque was the word which described the effect of levers.
I don't think there can be any actual proof of this - any attempt would involving just re-stating an idea and then re-stating it in a different way - proving nothing. It's just like Momentum (another quantity that we have found to be always conserved (when you get rid of all the practicalities of an experiment)
In the case of many so-called Machines, the geometry of the thing gives a theoretical 'Velocity Ratio' and that's often confused (even PF is incredibly sloppy about this) with 'Mechanical Advantage', which is the measured ratio of load one effort. It always falls short of VR because of Inefficiency. People ignore the dead weight of lever arms, friction and the weight of pulley blocks. The MA of that Capstan in the above picture will be hopelessly worse than the VR might suggest.
Their eyes would certainly be bulging a bit more if a chain and anchor were attached. (They are working with an MA of 0!)jbriggs444 said:The MA of that particular capstan is zero because there is no load. No rope is attached. The tourists are busy doing nothing but turning the dead weight.
Instead of asking why we multiply, let us examine a simpler question: Does multiplication work?Hemant said:when we say something is directly proportional to something then why do we multiply the to directly proportional terms for example if I say x directly proportional to y and I also say that x is also directly proportional to z then while writing the whole why do we say that the x is directly proportional to y z
Sir but i want to know why we multiply these terms not added nor subtracting why we multiply these without any reason.jbriggs444 said:Instead of asking why we multiply, let us examine a simpler question: Does multiplication work?
Take, for instance, the formula for gravitational force:$$F=G\frac{m_1 m_2}{r^2}$$
Is that formula for F directly proportional to ##m_1##?
Is that formula for F directly proportional to ##m_2##?
Is that formula for F inversely proportional to ##r^2##?
If so then what is the problem? The formula works, so use it.
But there is a reason. It's defined that way. And the reason it's defined that way is because it's useful. When something is in rotational equilibrium (that is, it's not rotating or it's rotating at a steady speed) it's always found that the net torque is zero. If you calculate torque as force times lever arm you find that the net torque is zero. If you define torque some other way then you may find that the net torque is not zero, and so torque is not useful for determining rotational equilibrium.Hemant said:Sir but i want to know why we multiply these terms not added nor subtracting why we multiply these without any reason.
Mister T said:But there is a reason. It's defined that way. And the reason it's defined that way is because it's useful. When something is in rotational equilibrium (that is, it's not rotating or it's rotating at a steady speed) it's always found that the net torque is zero. If you calculate torque as force times lever arm you find that the net torque is zero. If you define torque some other way then you may find that the net torque is not zero, and so torque is not useful for determining rotational equilibrium.
This is the way it goes in science and technology. People invent quantities and if those quantities are useful then others use them and they make their way into the textbooks and students are asked to learn them. Quantities that are not useful get discarded and do not appear in textbooks.
The axioms and terms of arithmetic are well established. I am not totally clear about your notation here but I think your final statement could be wrong or incomplete. Simple proportionality is between two variables. If z is constant then it is a constant of proportionality and there is still a 'straight line graph' for x against y. If that is not made clear and (say) z is a function of x, the proportionality no longer holds.Hemant said:when we say something is directly proportional to something then why do we multiply the to directly proportional terms for example if I say x directly proportional to y and I also say that x is also directly proportional to z then while writing the whole why do we say that the x is directly proportional to y z
Yep. That's very often the way 'laws' of nature are found to apply. Everything has to be verified by measurement in the end after intelligent guesses about the probable maths involved. This is one of the problems that people have with String Theory; we just don't have the necessary equipment to test them so String Theory should perhaps be called String Hypothesis or String Conjecture.Hemant said:So sir it is like that scientists done hit and trial and make formulas by guessing And try to do application of it and if they get successful then we use that equation.
Very often, yes.Hemant said:So sir it is like that scientists done hit and trial and make formulas by guessing And try to do application of it and if they get successful then we use that equation.
"Yo, ho, ho, me hearties! And a big, big welcome to this nautical version of the dude ranch! Heave away with a will, now, me lubbers, if you don't want to feel the end o' this cat o' nine tails!"jbriggs444 said:The MA of that particular capstan is zero because there is no load. No rope is attached. The tourists are busy doing nothing but turning the dead weight.
Answer my questions and I will answer yours.Hemant said:Sir but i want to know why we multiply these terms not added nor subtracting why we multiply these without any reason.
Suppose you spent $2 for coffee every day for 30 days. How much money did you spend on coffee in total? Is it 2*30=$60 or 2+30=$32? What is the reason?Hemant said:Sir but i want to know why we multiply these terms not added nor subtracting why we multiply these without any reason.
Thanks sir I understood it.PeroK said:One way to understand this is through energy. Imagine a uniform rod of length ##2L## fixed at the centre:
1) Apply a force ##F## at the end of the rod through one revolution.
2) Apply a force ##F## a distance ##L/2## from the centre through one revolution.
Then, look at the work done by the force in each case:
1) ##W_1 = Fd_1 = F(2\pi L) = 2\pi FL##
2) ##W_2 = Fd_2 = F(2 \pi L/2) = \pi FL##
The work done by the force in the first case is twice that done by the force in the second case. The rod, therefore, has more rotational kinetic energy (RKE) in the first case.
We can then use the energy equation to find the equation for angular acceleration and angular momentum. I can leave that as an exercise for you.
Torque is defined as the measure of the force that can cause an object to rotate around an axis. As we increase the distance from the centre axis, the perpendicular distance between the force and the axis also increases. This results in a larger moment arm, which increases the torque.
The distance from the centre axis directly affects the torque. The farther away the force is from the axis, the larger the moment arm and the greater the torque.
Yes, there is a limit to how much torque can increase as we increase the distance from the centre axis. This limit is determined by the amount of force applied and the distance from the axis. Once the force is too far from the axis, the moment arm becomes too large and the object may become unstable or even break.
The shape of an object can affect torque as we increase the distance from the centre axis. Objects with a larger surface area or longer shape will have a larger moment arm and therefore a greater torque at a given distance from the axis.
Yes, torque can be increased without changing the distance from the centre axis. This can be achieved by increasing the magnitude of the force applied, as torque is directly proportional to force. Alternatively, the angle at which the force is applied can also affect torque, as a force applied at a greater angle will have a larger moment arm and therefore a greater torque.