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Physics/gravity and rotation around a tipped axis

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QUESTION: Hello.  My brother and I are doing a science fair project in which we are trying to measure the effects of different amounts of gravity on plant growth, and we have a question that has to do with physics. We are hoping to put plants in containers and then rotate the containers around their axes.  So, for example, if we spin the plant around a vertical axis (our control), there will be the usual amount of gravity (we're spinning it slowly enough to neglect centripetal force), but if we tip the container 90 degrees and spin it around a horizontal axis, the net effect of gravity 'felt' by the plant will be zero (it will cancel out). Our question is, how do we figure out what fraction of the usual gravity a plant is feeling if we tip it at some other angle and spin it around an axis at that angle? Will it 'feel' half of the usual gravity when it is at 45 degrees or at some other angle?  We think this might have something to do with trig and with vectors, but we don't know exactly how to calculate things.  Thank you so much for your time!

ANSWER: This is interesting, I did this experiment in 6th grade and won the Pittsburgh regional science fair (6th grade division) when I grew plants at approximately 9*g.  The plants at high gravity grew faster than the identical and non-rotating control wheel, presumably due to the acceleration of chemical processes.  The fact that this has been done should not stop you, the results weren't exactly published in Science magazine.  

The question is, why would you not just spin it around a vertical axis fast enough to ignore gravity, instead of ignoring centripetal force?  I mean...isn't the point to find the effect of the centripetal acceleration?  You can use the very simple formulae (my mother helped me with this, back in the day) that a=v^2/r, where a is the acceleration, v is the velocity, and r is the radius.  The acceleration is towards the center.  You seem to be talking about accelerating the plants with variable "gravity" if you're spinning them in a vertical plane. To get constant acceleration, you need a horizontal plane.  You can figure out the angle that you should have to accelerate them towards the bottom of the growing device (I recommend a test tube, with seeds on the outside and a wet paper towel rolled up and stuffed in the middle) to give them pure acceleration towards the top of the tube based on trig, yes, where the angle to the vertical (theta) is given by tan(theta)=a/g, where a is given by the formula above and g is the acceleration of gravity (9.8 m/s^2).

Good luck, get back to me if you need further advice.

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This is known as geotropism, by the way.  Other tropisms are phototropism (plants grow towards the light) and even magnetotropism.  As far as I know, electrotropism (plants grown under voltage, and therefore an electric field, very easy to test) has never been tested.

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QUESTION: Hello,
Thank you so much for your detailed answer!!  This is so nice of you to take the time to help us!  

That's funny that you did a similar project when you were around our age.

The difference between your project and ours that I think we didn't explain well enough is that we're trying to see what happens to a plant when it is grown under a gravitational force that is LESS THAN g. That could tell us some things about how plants might grow in space or on mars (at least in terms of the amount of gravity).

The way we have things set up, our plants rotate very slowly (2 rpm) so centripetal force is not significant.  When the seeds spin around a horizontal axis, the seeds spend as much time "upside down" as "right side up.”  In other words, they spend as much time tipped one way as exactly the opposite, so the net effect of gravity is zero.

We still aren't sure what fraction of g the plants might experience if the seeds are rotated around an axis that is at a particular angle. We’re not looking for an equation that involves the velocity, because we’re ignoring centripetal forces.  Instead, we’re looking for an equation that would take into account the fact some of the effects of gravity will get cancelled out because the plants are spinning slowly and are therefore in different orientations towards the earth.  We know that there is full gravity when the axis is vertical and no net gravity when the axis is horizontal, we just don’t know how to calculate how much gravity is cancelled out when it is spinning on an axis that is tilted at any other specific angle.

Thank you again for your time!  This is so amazing to get this help!

Answer
You can't grow something under less than g on Earth.  If you rotate it slowly enough that centripetal force is not a factor, then you still have gravitation to orient the plant and cause chemical reaction.  The tumbling, is well studied in cloning plants, which is quite common with orchid growers.  The process is called mericloning.  Interestingly, this is something I did as a kid with my parents, who had an extensive orchid greenhouse which we built.  We seem to have a large number of weird coincidences here.  I'm not sure of the origin of the name.  However, gravitation is still present.  This has now passed from a physics problem into pure biology, since you don't really need any equation for slow rotation.  Gravity is always there and always points downward.  If you need a direction, then you need a simple trig function like the sine or cosine of the angle with respect to the vertical (or horizontal, just switch them).  But gravity is never fully "canceled out" in this process.  It's there, just changing direction as you rotate.  That has very little to do with physics, and everything to do with the biology of cell differentiation.

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Dr. Stephen O. Nelson

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I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.

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I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

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Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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