Question

What is maximum and minimum amount of volume a thing with 10kg mass can consist

Answer 1

Answer:

University Physics Volume 1

10 Fixed-Axis Rotation

10.5 Calculating Moments of Inertia

LEARNING OBJECTIVES

By the end of this section, you will be able to:

Calculate the moment of inertia for uniformly shaped, rigid bodies

Apply the parallel axis theorem to find the moment of inertia about any axis parallel to one already known

Calculate the moment of inertia for compound objects

In the preceding section, we defined the moment of inertia but did not show how to calculate it. In this section, we show how to calculate the moment of inertia for several standard types of objects, as well as how to use known moments of inertia to find the moment of inertia for a shifted axis or for a compound object. This section is very useful for seeing how to apply a general equation to complex objects (a skill that is critical for more advanced physics and engineering courses).

Moment of Inertia

We defined the moment of inertia I of an object to be

I

=

∑

i

m

i

r

2

i

for all the point masses that make up the object. Because r is the distance to the axis of rotation from each piece of mass that makes up the object, the moment of inertia for any object depends on the chosen axis. To see this, let’s take a simple example of two masses at the end of a massless (negligibly small mass) rod ((Figure)) and calculate the moment of inertia about two different axes. In this case, the summation over the masses is simple because the two masses at the end of the barbell can be approximated as point masses, and the sum therefore has only two terms.

In the case with the axis in the center of the barbell, each of the two masses m is a distance R away from the axis, giving a moment of inertia of