This is an introduction to moment of inertia, a fundamental physical quantity. Moment of ineffi
ciency (MOI) can be used determine the amount of rotation that a body undergoes when it’s moving through space and time. Inertia is quantified by dividing MOI into two quantities: mass times velocity squared divided by distance traveled
Moments of inertia are the resistance to rotation. The moments of inertia of this object about the axes indicated is 1/2.
As seen in the illustration, two identical uniform solid spheres are joined by a solid uniform thin rod. The rod is located on a line that connects the two spheres’ centers of mass. Axes A, B, C, and D are in the plane of the page (which also includes the centers of mass of the spheres and the rod), but axes E and F (shown by black dots) are perpendicular to the plane. (See Figure 1).
Rank this object’s moments of inertia about the axis specified. Sort the list from biggest to smallest. Overlap objects to rate them as comparable.
ABC
ABC
Answer
Rank this object’s moments of inertia about the axis specified. Sort the list from biggest to smallest. Overlap objects to rate them as comparable.
Moments of inertia are affected by mass and perpendicular distance from the axis of rotation. It may be stated mathematically as
I=Δmr2 The distance of the center of mass of the items in question to the axis of rotation affects the moment of inertia, hence in this situation
Because the spinning body’s center of mass is furthest from these two axes of rotation, axes C and F would have the greatest moments of inertia. C and F, on the other hand, would
have identical moments of inertia because their centers of mass are equal distances from their respective axes of rotation.
B is the next biggest since it is the closest distance from the center of mass.
A and E would be the next in line because, although being directly between the two spinning masses, they still create a moment of inertia equal to (y/2)2.
Finally, since the perpendicular distance from the axis of rotation never exceeds the radius of one of the balls, D has the lowest moment of inertia. So, from top to lowest,
lowest: (C and F), (B), (A and E), and (D).
The “which of the following are units for expressing rotational velocity, commonly denoted by ω?” is a question that would require you to rank the moments of inertia of this object about the axes indicated.
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