Figure 10-35a shows a disk that can rotate about an axis at a radial distance h from the center of the disk. Figure 10-35b gives the rotational inertia I of the disk about the axis as a function of that distance h, from the center out to the edge of the disk. The scale on the I axis is set by and . What is the mass of the disk?
To determine the mass of the disk, we need to use the formula for rotational inertia, which is given by:
I = m * r^2
where I is the rotational inertia, m is the mass of the object, and r is the radial distance from the axis of rotation.
In this case, Figure 10-35b provides the rotational inertia I as a function of the radial distance h. We can use this information to find the mass of the disk.
To do this, we need to find a point on the graph where we know the rotational inertia and the radial distance. Let's say we choose a point where the radial distance h is known, and the corresponding rotational inertia I is given.
Once we have these values, we can rearrange the formula to solve for the mass m:
m = I / r^2
Given that the scale on the I axis is provided, we can use this information to determine the actual value of I. Similarly, we can use the radial distance h to find the value of r.
By substituting these values into the equation, we can calculate the mass of the disk.