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Femme_physics
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So, we learned that the units of Moment of Inertia are mm^4. My question is how do they use moment of inertia in static calculation (where we use Newtons), if Moment of Inertia is in mm^4?
1) Double checking my notes the units for the result of Moment of Inertia are [mm^4]. Perhaps it's because we're working in 2D, or haven't started calculus yet?maimonides said:Please doblecheck your notes or your textbook.
The unit of moment of inertia is mass times length squared, in SI kgm^2.
In statics you often use a related quantity called radius of gyration.
If you really need to use mm^4: You know how to convert mm to m, square mm to sqare m, cubic mm to cubic m, don´t you?.
If you're given the moment of inertia in mm^4, you need to know the thickness and density of the circular disc, so you can figure out the moment of inertia in units of M*L^2Femme_physics said:Let's say I applied on a circular object a 50 Newton force at an ideal location to cause rotation (i.e. away from the COM). I need to relate that 50 Newton force to cubic m [or let's say to mm^4], yes?
To convert mm^4 to other units of Moment of Inertia, you can use the following conversion factors:
1 mm^4 = 1.0 x 10^-12 m^4
1 mm^4 = 1.0 x 10^-6 cm^4
1 mm^4 = 1.0 x 10^-8 in^4
1 mm^4 = 1.0 x 10^-10 ft^4
Simply multiply the value of mm^4 by the corresponding conversion factor to get the equivalent value in the desired unit.
To calculate Moment of Inertia using mm^4 units, you need to know the mass of the object, the distance of each mass element from the axis of rotation, and the square of that distance. The formula for calculating Moment of Inertia is I = ∑mr^2, where m is the mass and r is the distance from the axis of rotation. Simply plug in the values and units (mm^4) and then perform the necessary operations to get the final value.
Yes, mm^4 units can be used for all types of objects as long as the dimensions of the object are in millimeters. However, if the dimensions are in other units, you will need to convert them to mm before using mm^4 units for Moment of Inertia calculations.
No, Moment of Inertia can be measured in various units such as m^4, cm^4, in^4, ft^4, etc. The choice of units depends on the dimensions of the object being measured. In some cases, it may be more convenient to use other units, but the calculations are essentially the same.
Using mm^4 units does not affect the accuracy of Moment of Inertia calculations as long as the dimensions of the object are measured consistently in millimeters. The conversion to other units does not change the actual value of Moment of Inertia, it only changes the numerical value due to the different magnitudes of the units.