Simple Moment of Inertia question

In summary, the question is asking for the moment of inertia when rotating a massless rod of length R with a mass of 2m attached to one end and a mass of m attached to the other end. The correct method is to treat the masses as separate point particles and calculate their individual moments of inertia, which can then be added together. It is important to note that the term "r" in the equation should refer to the diameter of the masses, not the radius. The book uses "R" to represent the length of the rod.
  • #1
Igottabull
4
0
Rotating a massless rod of length R about the midpoint of the rod with a mass of 2m attached to one end and a mass of m to the other. What is the moment of inertia?

My book is terrible at giving good examples, there's nothing similar to this.

Do I treat them as two separate point particles, take the moment of inertia of each around the axis and add them? (2m*(r/2)^2) + (m*(r/2)^2) I'm assuming I can treat them as points, the drawing has the masses as clearly different sized spheres, but says nothing about their radius or anything of that nature.

Thanks in advance guys.
 
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  • #2
I think I have it right, would still appreciate confirmation though, thanks guys.
 
Last edited:
  • #3
Your concept is correct, but I think you meant diameter instead of radius for the term r used in your equation.
 
  • #4
Actually the book used R as the length of the rod, I probably shouldn't have used lower case there, sorry about the confusion. Thanks again.
 

Related to Simple Moment of Inertia question

1. What is the concept of moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is calculated based on an object's mass and distribution of that mass around an axis of rotation.

2. How is moment of inertia different from mass?

Moment of inertia and mass are different concepts. Mass is a measure of the amount of matter in an object, while moment of inertia is a measure of how that mass is distributed around an axis of rotation.

3. How is moment of inertia calculated?

The moment of inertia of an object can be calculated by summing the products of each particle's mass and its distance from the axis of rotation squared. The exact formula depends on the shape and distribution of the object's mass.

4. What are some real-life examples of moment of inertia?

Moment of inertia can be seen in many everyday objects, such as a spinning top, a pendulum, or a bicycle wheel. It also plays a role in the stability and control of vehicles, such as cars and airplanes, as well as in the design of structures like bridges and buildings.

5. How does moment of inertia affect an object's motion?

Moment of inertia affects an object's motion by determining how much torque is needed to change its rotational speed. Objects with a larger moment of inertia will require more torque to accelerate or decelerate their rotation, while objects with a smaller moment of inertia will rotate more easily.

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