Which one of the following statements concerning the moment...

Which one of the following statements concerning the moment of inertia $I$ is false? $\bigcirc$ I depends on the location of the rotation axis relative to the particles that make up the object. $\bigcirc$ I depends on the angular acceleration of the object as it rotates. $\bigcirc$ Of the particles that make up an object, the particle with the smallest mass may contribute the greatest amount to $I$. $\bigcirc$ I depends on the orientation of the rotation axis relative to the particles that make up the object. $\bigcirc$ I may be expressed in units of $kg \cdot m^2$.

Transcript

00:01 Here we have the question about moment of inertia in which we have five options and we have to choose out of these options which one is false.

00:07 So let's check them one by one.

00:09 Now before checking this, we know that the moment of inertia i equals sigma of m i r i squared.

00:19 So i will use this concept to check these options.

00:23 So it says of the particle that make of the object the particle with the smallest mass may contribute the greatest amount to the moment of inertia.

00:31 So it seems to be the correct statement because we know that i equals sigma mi r i squared.

00:38 So the i doesn't depend upon mass only.

00:41 It depends upon r also.

00:44 So if if my r i will be more, so the r i squared will be more, i will be more, this is the correct statement.

01:03 Now let's check the next option.

01:05 So it says about the si.

01:06 Unit of i now we know that i equals sigma m i r i squared so unit of i will be of m i i squared that is kg multiplied by the s i unit of r that a distance is meter and it is squared so it will be kg meter square it is also a correct option now let's check the next option it says i depends upon the angular acceleration of the object it rotated.

01:44 So we have the dependence of i on mass and distance only.

01:50 So we can say that i depends upon mass and distance only, distance from the axis.

02:04 And it doesn't depend upon the angular acceleration...

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