The picture below shows two weights that have the same mass but that have that mass distributed differently. The upper weight has most of its mass near the center. The lower weight has most of its mass near the edges.
Give a brief description of a situation you have experienced personally where you have noticed something being easier or harder to start or stop rotating than you expected.
Recall the definition of Mass as the capacity of an object to resist changes to its motion. The rotational analogue—the capacity of an object to resist changes to its angular motion—is known as the moment of inertia.
The moment of inertia of a rigid object is its capacity to resist changes to its angular motion. For a set of discrete objects, it can be found as a weighted average of the distance from the axis of rotation squared:
\begin{equation*}
I = \sum_{i} m_ir_i^2
\end{equation*}
You are riding a \(150 \mathrm{~kg}\) bicycle at constant speed along a circular track of radius \(25 \mathrm{~m}\text{.}\) What is the moment of inertia of the bicycle about the center of the track? What assumptions do you need to make in order to use the equation above?
Suppose you want to find the moment of inertia of the lower weight from the Warm-up Activities. What information would you need to know? What assumptions would you want to make? What equations would you decide to use?
There are a couple ways you could do this. You could directly calculate the moment of inertia, if you knew something about what weights were on the barbell and where they were located. Then you could use
It is extremely common to use a reference to find the moments of inertia for common objects. Use this table to determine the moment of inertia for each of the following:
