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Rotational inertia measures how much an object resists changing rotation. In linear motion, according to Newton's Second Law, we use mass to gauge an object's resistance to change but in rotational motion, rotational inertia serves the same purpose. Rotational inertia is a scalar, not a vector and is dependent upon the radius of rotation according to the formula rotational inertia = mass x radius^2.
Rotational inertia, rotational inertia is the measure of an object's resistance to change in its rotation. Okay you've all experienced this or maybe you have, if you've ever played baseball and you've gotten the bat and let's say the only bat they have is this big heavy bat and the big guy in the team can pick that up and he can really swing that. He can really get that to accelerate, you're a little guy and you're having a hard time getting this big heavy bat to accelerate you just don't have the ability to apply that same force. Right, well you can apply that same force and you can do that by chocking up on the bat. So instead of grabbing it down here you're going to grab it up here. And what you're doing is you're decreasing the radius of that rotation and that's going to make it easier to get that bat up to speed and to get a good hit and get on base okay. So the formula that we're going to use for rotational inertia is i that's the symbol rotational inertia equals the mass times the radius squared.
Okay so again the longer that radius the more rotational inertia okay and the units we're going to use is kilograms times meter squared. So let's look at some problems you'd be asked to solve using rotational inertia okay. The first problem over here, what's the rotational inertia of a 3 kilogram ball revolving around a pole 4 meters away? So thhe radius is 4 meters, the mass of the ball is 3 kilograms and they're asking you for the rotational inertia. So this is pretty straight forward if you can just remember this formula okay. So rotational inertia is the mass times the radius squared and let's go ahead and plug those numbers in I have 3 kilograms times the radius squared is 4 meters squared okay. So 4 meters squared is 16 meters squared times 3 kilograms so my rotational inertia here is going to be 16 times 3 which is 48 kilograms times meters squared okay so there's my answer for that first one.
Lots of times they won't ask you just for the rotational inertia they'll maybe give you the rotational inertia and they'll give you one of these two values and they'll ask you to solve for that. Okay, well that's no problem we can just put in the values that we have and solve in a similar way. So let's look at another example over here, how far from the axis so I want to know what the radius is. Is a 4 kilogram ball with a rotational inertia of 64 kilograms times meters square, okay so let's put the same formula in i equals mr squared but this time they're giving us the rotational inertia, they're giving us the mass and we have to solve for r. Okay, so let's put those values in we've got 64 equals again I don't know what r is but I do know what my mass is. My mass is 4 kilograms okay. So again if I want to simplify this equation I'm going to divide by 4 kilograms and divide this by 4 kilograms and I'm going to get reducing that r squared is going to equal 64 divided by 4 is 16 and my kilograms cancel and I get meters squared okay.
Well 16 meters squared is equal to what meters so my r for this if I simplify that r equals 4 meters. So in this case r is 4 meters okay. So this is how could solve 2 different types of problems involving rotational inertia.