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jjellybean320
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i need to find the moment of inertia for a cardboard boomerang. what equation could i use?
gneill said:Moment of inertia about what axis? Have you considered an experimental approach? You might find its center of gravity by suspending it from two separate points and see where the vertical plumb lines intersect. You could suspend it from a point as a physical pendulum and time its period,...
jjellybean320 said:can you explain how to find moment of inertia from knowing the center of gravity? I know how to find center of gravity but i don't know how that relates to finding a numerical value for the moment of inertia.
and can you explain how i can get a value of moment of inertia through knowing the period?
thanks
gneill said:
jjellybean320 said:do i hang the boomerang at its center with the 3 blades spanning outward?
also do you know of a mathematical way i could use to check my moment of inertia value?
ideasrule said:Note that if you use the pendulum approach, air resistance will be a big issue for a cardboard boomerang, so you might not get accurate results.
jjellybean320 said:if the moment of inertia = m r^2
could i just find the moment of inertia of each of the 3 blades separately and then multiplying by 3?
so for example if each blade weighed 2 grams and was 15 cm long (i'm rotating around the end of the blade) then the moment of innertia would be (15^2)*2
would that work if i wanted simply an approximate value?
gneill said:Can you provide an image of the boomerang you have in mind so that we might be better able to advise on methodology? Approximate physical dimensions would also be a help.
jjellybean320 said:each blade is approximately 5 inches by 1.25 inches. and it is made from a christmas card.
jjellybean320 said:http://www.livephysics.com/tables-of-physical-data/mechanical/moment-of-inertia.html
the rectangular plate equation on that page is
(1/12)*Mass*(a^2+b^2)
where a and b are the length and width
but this equation is if the axis is through the center.
if the axis is at one end like my boomerang, would i just substitute (1/12) with (1/3)?
gneill said:No. Look up the Parallel Axis Theorem as I suggested. You need to be precise about where the center of rotation is with respect to the center of the plate -- in your case it won't be precisely at the end of the plate, but a bit in from the end. Measure and be sure.
jjellybean320 said:the center of rotation is about 1 cm from the center of the plate. i looked at the wikipedia page for the parallel axis theorem and it was really confusing. I've only taken ap calculus ab.
The moment of inertia for an irregularly shaped object can be determined by breaking down the object into smaller, simpler shapes with known moments of inertia. Then, using the parallel axis theorem, the moments of inertia for each individual shape can be added together to find the total moment of inertia for the irregularly shaped object.
No, there is no single formula that can be used for all types of shapes. The moment of inertia is dependent on the shape and distribution of mass of an object. Different formulas and methods must be used for different types of shapes.
The distribution of mass directly affects the moment of inertia. A larger concentration of mass farther away from the axis of rotation will result in a larger moment of inertia, while a smaller concentration of mass closer to the axis of rotation will result in a smaller moment of inertia.
Yes, the moment of inertia of an object can change if there is a change in the distribution of mass or the axis of rotation. For example, if an object is rotated to a different axis, its moment of inertia will also change.
The moment of inertia is an important concept in physics and engineering, and is used in various real-world applications. For instance, it is used to calculate the stability and rotation of objects, such as in the design of bridges or skyscrapers. It is also used in the analysis of rotational motion, such as in the design of vehicles and machines.