1.
Which weight, if either, do you think would be easier to twirl about its center. Explain why you think so.
Section 13.3 Moment of Inertia
Exercises Warm-up Activities
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.
2.
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.
Definition 13.3.2. Moment of Inertia for Discrete Objects.
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*}
Exercises Activities
1. Bicycle Inertia.
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?
Solution.
Since the radius of the track is much bigger than the size of the bicycle, you can probably treat the bicycle as a single point mass!
2. Weights Inertia.
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?
Solution.
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
\begin{equation*}
\Sigma_i m_i r_i^2 = m_1 r_1^2 + m_2 r_2^2
\end{equation*}
3.
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:- A tennis ball spinning about its center
- A record disc spinning about its center
- A baton spinning about its end
References References
[1]
Inertia Demo: Blue and Red Wands by Physics Demos.
