The math of a 'moment of inertia' in application

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SUMMARY

The discussion focuses on calculating the moment of inertia (MOI) for an object mounted in bearings with a filament and weight system. The user, John, has determined the torque to be 12.2 in.lbf and angular acceleration to be 3.84 rad/sec². The confusion arises from the differing definitions of moment of inertia in lb.in² and in.lb.sec², specifically how torque divided by angular acceleration translates to MOI. Key insights include the distinction between pound-force and pound-mass in the context of MOI calculations.

PREREQUISITES
  • Understanding of basic physics concepts such as torque and angular acceleration.
  • Familiarity with units of measurement, specifically pound-force and pound-mass.
  • Knowledge of moment of inertia and its significance in rotational dynamics.
  • Ability to perform unit conversions and dimensional analysis.
NEXT STEPS
  • Study the relationship between torque and angular acceleration in rotational motion.
  • Learn about the different units of moment of inertia and their applications in physics.
  • Explore the concept of dimensional analysis to clarify unit conversions.
  • Investigate practical applications of moment of inertia in engineering and mechanics.
USEFUL FOR

Physics students, mechanical engineers, and anyone involved in rotational dynamics or engineering mechanics will benefit from this discussion.

JohnG
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I am trying to detemine the moment of interia of an object, not too accurately.

I have the object mounted in bearings, and on the shaft of the object I have a ring (radius of 2.5in) which I have a filament wrapped around which drops to a weight of 5lbs (mass of .1554 slug). I can release the weight and time the travel over a known distance (approx 24in in 5sec, an acceleration 'a' of 9.6in/sec^2). Angular acceration is 'a'/'r' or 3.84rad/sec^2. I have determined the tension in the filament to be 4.88lbf by F=ma, m=.1554slug * (subtracting 'a'(conv. to ft/sec^2) from g(ft/sec^2)). The torque would then be 4.88lbf * 2.5in or 12.2in.lbf.

My problem has come down to the math. I have seen moment of inertia defined in both lb.in^2 and in.lb.sec^2. I cannot seem to figure out how torque (in.lbf) / angular acceleration (rad/sec^2) can be conveyed to MOI of either version, the units don't seem to cancel out right.

Any input would be greatly appreciated, until then I will have fun putting a sharp stick in my eye.

John
 
Last edited:
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Moment of inertia has units [M]*[L]2 (mass times length squared)
When you see inch*pound*second^2, the "pound" is pound-force.
When you see pound*inch^2. the "pound" is pound-mass.
Also note that radians are unitless dimensions.
I hope that helps.
 

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