Question 2 1 pts If we cut the annulus in to an infinite number of very thin rings, within each ring every point is the same distance from the axis of rotation (center). Ri Next we need to introduce a variable to identify the location of the slice you have chosen. What variable should you choose to uniquely identify the position of the red ring from all the other rings? Constant Ki which represents the inner radius of the annulus 3 variable r to represent the distance form the axis of rotation (center) to the infinitesimal ring we have chosen to look at C Constant Ro which represents the outer radius of the annulus Question 3 1 pts Next we want to define a mass density function. Is the annulus a 1D. 2D or 3D shape? Do we want to use a 1D. 2D or 3D density? 0 20 O ID O 3D Question 4 1 pts The annulus is a 2D shape so we will us the 2D mass density: o (sigma). The mass density of is to the total mass divided by the total area of the shape. The total mass of the annulus is given as M. What is the total area of our annulus? O XR OF ( R - R; ) O ERQuestion 5 1 pts Knowing the area of the annulus, what is the mass density function & in terms of M. Ro and Ri? Question 6 1 pts Now we want to use the mass density function a to find the mass of a slice (thin ring) that we cut the annulus into. In addition to knowing that our density function a can be written in terms of the total mass and It can also be written in terms of the mass and area of our small slice or ring: From this last equation. we can find the mass of our slice dor will be the density ed [sigma) times the area of our slice d.. IM = edA = - What is the area of one slice (one thin ring) of our annulus? Keep in mind that if we stretch our ring out into a long ribbon. its area will just be its width times length. Your answer should only contain constants and the variable you defined earlier in the questions. OA 2.R (R, R ) Odd didy ONA my Question 7 1 pts So we now know the mass of a thin ring or element of our annulus: HIM = - tardy We will be integrating to find the moment of inertia of our annulus. The integration will be with respect to r. the variable you introduced in an earlier part of the problem. What are the limits of integration for this variable? In other words, what are the smallest and largest possible values for the variable you introduced? The limits of integration for r are ... O fram Ro to Ri O from O to R O fram Ri to Ro O from O to Ri O from O to Ra Question 8 1 pts Now we can plug in to the integral equation for the moment of inertia. Remember that the R in the moment of inertia equation represents the distance from the axis of rotation to the slice you have chasen. Complete this integration, and evaluate for your limits. What do you get? IN: n