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Buzzdiamond1
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What is the correct formula for a double cone, is it 3/10 mr^2, or 3/5 mr^2..?
Welcome to the PF.Buzzdiamond1 said:What is the correct formula for a double cone, is it 3/10 mr^2, or 3/5 mr^2..?
I understand what you are asking, but I'm trying to get you to help us help you to figure it out. The answer should be available via a Google search, and you offer two possible expressions which means you probably have done those searches. If you could post links to the two different results, we can probably help you to pick the right one.Buzzdiamond1 said:Thanks for chiming in Berkeman, much appreciated. I'm not exactly sure what you're asking me, but my question is, what the correct formula for a double cone, is it: I = 3/10 x m x rr or I = 3/5 x m x rr..?
So you are talking about a double cone (e.g. a pair of ice cream cones tip to tip) rotating around the central axis of symmetry.Buzzdiamond1 said:Hello everyone, I'm still trying to get a concrete answer to this puzzle. Is the MOI of a double cone 3/10 MR^2 or 3/5 MR^2..?
Why would I agree to that? Per unit mass, the moments of inertia are 0.3 for the cone and 0.4 for the sphere.Buzzdiamond1 said:Wouldn't you agree that a spinning top is harder to move than a spinning sphere..?
That's if you believe the numbers we've been presented with. I'm contesting those numbers, with my arguments to back it up, along with a physics study report that was performed a while back in my post above dated Nov. 29th. Isn't it common sense knowledge that if you spin a marble and spin a top next to each other, if you blow at them, the marble will be blown off the table and the top will still be standing relatively close to the same position..? Or, if you blow the marble towards the top, upon impact, the marble will go flying, not the other way around..? Again, I don't believe the 3/10 MR^2 formula is correct, hence this discussion.jbriggs444 said:Why would I agree to that? Per unit mass, the moments of inertia are 0.3 for the cone and 0.4 for the sphere.
The cones I'm referring to are joined base to base, with the axis of rotation spinning like a top.Nugatory said:There's a bit of talking past one another going on here, because the answer is different for different axes of rotation. Just to be sure that we're talking about the same problem.
Are the cones joined tip to tip or base to base? Is the axis of rotation a line that passes through both tips and the center of both bases, or is it perpendicular to that line? That's two questions with two answers for a total of four possibilities, and only two of the four have the same answer.
The experiments you point to do not test moment of inertia.Buzzdiamond1 said:That's if you believe the numbers we've been presented with. I'm contesting those numbers, with my arguments to back it up, along with a physics study report that was performed a while back in my post above dated Nov. 29th. Isn't it common sense knowledge that if you spin a marble and spin a top next to each other, if you blow at them, the marble will be blown off the table and the top will still be standing relatively close to the same position..? Or, if you blow the marble towards the top, upon impact, the marble will go flying, not the other way around..? Again, I don't believe the 3/10 MR^2 formula is correct, hence this discussion.
That's not a test of the moment of inertia, it's a test of the surface area, surface velocity, and drag coefficient of the solid (with some more complicated second-order effects thrown in).Buzzdiamond1 said:if you spin a marble and spin a top next to each other, if you blow at them, the marble will be blown off the table and the top will still be standing relatively close to the same position..? Or, if you blow the marble towards the top, upon impact, the marble will go flying, not the other way around..? Again, I don't believe the 3/10 MR^2 formula is correct, hence this discussion.
It is possible, and a good way to check that possibility would be for you to evaluate the integral (as @berkeman suggested in post #4 above) and if you don't come up with the currently accepted results post your work. Either you've found a mistake that has gone undetected for more than three centuries or you've made a mistake yourself - and with the calculation posted people will be able to figure out which it is.Is it not possible for a mistake..?
Buzzdiamond1 said:Is it not possible for a mistake..? Are you suggesting that nothing can change, the Earth is still flat or Einstein wasn't wrong on occasion..? Clearly, these forums do suggest Einsteins formulas are being put to the test and I'm quite sure, he has been wrong at least once in his life, correct..?
So one last chance -- post your work on the integrals showing the error, or this thread will be closed. We don't let newbie posters come here and show no work and waste the valuable time of our helpers. Please do this...Nugatory said:It is possible, and a good way to check that possibility would be for you to evaluate the integral (as @berkeman suggested in post #4 above) and if you don't come up with the currently accepted results post your work. Either you've found a mistake that has gone undetected for more than three centuries or you've made a mistake yourself - and with the calculation posted people will be able to figure out which it is.
If the M is the mass of the single cone, that result would be correct. If the M is the mass of the double cone then it is wrong.Buzzdiamond1 said:double cone is 3/5 MR^2, outlined here
Wrong. That's why I specified a plane of symmetry for the reflection. It's not a rotation. It's a reflection with respect to a particular plane.Buzzdiamond1 said:I appreciate your response, but I will respectfully have to disagree. Reason being, it's not like we're taking a cylinder and taking another cylinder, flipping it around 180* on top of it, as all you'd get is a longer cylinder. When you take a single cone, then flip around another cone 180* so the two bases connect, you get a totally different shape, which now would have different properties, similar to taking two rods and forming a cross. Now you would have two different MOI's, one for a rod and one for a cross, correct..?
Can you recite the definition of moment of inertia for us? This blather leads one to suppose otherwise.Another thing is, if you stacked a second cone on top of the first cone, with the base sitting on the point, I'm assuming based on the responses the MOI formula won't change, because all you're doing is changing the mass, am I following the logic correctly..? Now I could believe that, but when 2 cones are stacked this way, it won't spin for very long without toppling over. On the other hand, when you invert one of the cones, stacking both bases together, you get a totally different spin time, spinning much longer, correct..? Therefore, this would lead one to believe the MOI would also be different, unless I'm missing something..?
If you change the torque (e.g. by having it spin on its flat base instead of its pointed tip),you change the time taken to spin down without necessarily changing the moment of inertia. So you cannot measure moment of inertia by looking at how long a top takes to spin down without also considering how much torque is applied.Buzzdiamond1 said:Yes, it's a quantity expressing a body's tendency to resist angular acceleration.
My understanding of this is basically, when an object is spinning, how much force would it take to move it from a standing position and/or in a change of direction. Am I way off base here with my thinking..?
If you want to calculate a moment of inertia, you should, as has already been suggested, calculate a moment of inertia. The way to do that is to learn calculus, not to watch videos about inclined planes.Buzzdiamond1 said:I'm trying to calculate the MOI of a double diamond, base to base and/or verify the physics study that was already done. I've watched some videos on MOI but it seems like a higher MOI is similar to high RG and low RG, based on how fast objects roll.
Valid reference, please.Buzzdiamond1 said:It's already done for me in Dr. Joseph Howard's report
Yes. The moment of inertia tells you how the spinning speed (think revolutions per minute) of an object changes when you apply a torque to it (try to spin it faster or slower, or rotate it). It has very little to do with moving an object from a standing position or changing its direction if it's already moving.Buzzdiamond1 said:My understanding of this is basically, when an object is spinning, how much force would it take to move it from a standing position and/or in a change of direction. Am I way off base here with my thinking..?
Dr. Joseph Howard is a physics professor at Salisbury University, why would there be any doubt to the validity of his work, which was done as a class project..? All you're saying is no, it's wrong, without providing any of your work on this subject to substantiate YOUR claim. Seems a bit hypocritical to me..?jbriggs444 said:Valid reference, please.
Ahh, you seem to believe that the Bowling pin web page mentioned earlier is valid and that the formula on page 3 is validly obtained. However, as I had pointed out in #22, that result would be valid only if M is taken as the mass of a half-cone.
Nugatory said:Yes. The moment of inertia tells you how the spinning speed (think revolutions per minute) of an object changes when you apply a torque to it (try to spin it faster or slower, or rotate it). It has very little to do with moving an object from a standing position or changing its direction if it's already moving.
The formula for calculating the moment of inertia of a double cone is I = (3/10)mr^2, where m is the mass of the cone and r is the radius of the base.
The moment of inertia of a double cone is greater than that of a single cone because it has two axes of rotation, whereas a single cone only has one.
No, the moment of inertia of a double cone cannot be negative. It is always a positive value because it represents the resistance of an object to changes in its rotational motion.
The moment of inertia of a double cone is affected by the mass and radius of the cone, as well as the distribution of the mass around the axes of rotation.
The moment of inertia of a double cone is used in engineering and physics to analyze the rotational motion of objects, such as gyroscopes and flywheels. It is also used in designing structures and machines to ensure stability and balance.