![]() You can find tables of the moments of inertia for common objects in lots of references, such as Hyperphysics and Wikipedia. So, what's this "moment of inertia" thing, I? Well, it depends on the mass of the object and also the distribution of that mass relative to the axis of rotation. We can write this in terms of force and distance and the "moment of inertia" I, which is the analogue of mass for a rotating system: Where τ is the torque exerted, Δ t is the time the torque is applied, and L is the symbol for angular momentum, for some obscure reason. This is determined from the Angular Momentum Principle which relates torque to change in angular momentum: The relevant quantity for our purposes is the change in the angular speed of the door (ω, the rate at which it's rotating) for a given applied force. Then again, a round door probably has more surface area than a rectangular door of the same height, meaning it contains more material, and would thus be harder to move. It also gives you a longer lever arm- halfway across a round door is farther from the hinge than halfway across a narrower rectangular door. (Image from this collection of PR stills) A round door is, after all, exactly as wide as it is tall, which makes for dramatic framing of arriving dwarves: Well, Kate raised an interesting point: it might actually be the case that the knob-in-the-center for a round door is less dumb than for an ordinary rectangular door. So, having established that putting the knob in the middle is kind of dumb from a physics perspective, how can we wring some more physics out of this. I use this in class as an example of how physics turns up in unexpected places in the design of everyday objects. If you guess wrong, you end up trying to open the door by pushing on the near edge, and end up looking like an idiot as you walk smack into the glass. Which is one reason why doorknobs are usually located on the opposite side of the dor from the hinges, and also why it's really annoying when office buildings have those glass doors where you can't easily tell the location of the hinge as you approach. To most effectively open a door, then, you want to push on it as far away from the hinges as you can manage. For making something rotate, what matters is not just the force, but the torque you exert, which is the product of the force you exert and the distance from the rotation axis to the point where you exert that force. Why does this matter at all? Well, because when you push open a door, what you're really doing is trying to make a solid object rotate about an axis defined by the hinges. My comment to Kate when she mentioned this was "See, that's why we had a Revolution- to get out from under people dumb enough to do that." ![]() ![]() BoneJ gave results of 19200.48 kg m^2 for I_.3 kgm^2 around I_3.Number Ten Downing St. My paper calculations are using the formula for a hollow rectangular section listed here ( ). Unfortunately I have not been successful at the conversion after many attempts. I used BoneJ to calculate the moments around the axes and was hoping to use the calibration factor of 1.8 g/cm^3 and work backwards to convert the results to paper calculations of a rectangle with the same dimensions. I made a calibration image consisting of a white rectangle of dimension 300 x 100 on a black background, with a line width of 1 pixel. The units of these parameters are given in kg*m^2, but I would like to convert them to mm^4. I am most interested in the second moment of area values around the longest and shortest principal axes (I_1, I_3). I have used the moment of inertia function in BoneJ to calculates the second moments of area for a set of thresholded cortical bone slices. ![]()
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