Moment of inertia for this assembly

In summary, a slender rod with a length of 80.0 cm and a mass of 0.120 kg has two small spheres, one with a mass of 0.0200 kg and the other with a mass of 0.0500 kg, welded to each end. The rod is pivoting about a stationary, frictionless axis at its center and is released from rest while being held horizontal. The linear speed of the 0.0500-kg sphere as it passes through its lowest point can be found by using the parallel axis theorem and considering the spheres as point masses.
  • #1
Elias Waranoi
45
2

Homework Statement


A slender rod is 80.0 cm long and has mass 0.120 kg. A small 0.0200-kg sphere is welded to one end of the rod, and a small 0.0500-kg sphere is welded to the other end. The rod, pivoting about a stationary, frictionless axis at its center, is held horizontal and released from rest. What is the linear speed of the 0.0500-kg sphere as it passes through its lowest point?

Homework Equations


Ip = Icm + Md2
Moment of inertia slender rod Ir = ML2/12
-||- solid sphere Is = 2/5 MR2

The Attempt at a Solution


I'm right around the corner to solve this, I just need to find the sum of the systems moment of inertia. I have the center of mass of the system, I also know that I have to use the parallel axis theorem but I don't have the radius of the small spheres so I don't know how I am supposed to calculate their moment of inertia.

Or should I be able to solve it without knowing the total moment of inertia?
 
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  • #2
You can consider the spheres as point masses on the basis of the term 'small' in the problem statement.
 
  • Like
Likes Elias Waranoi
  • #3
Thanks! That was what I had to do!
 

1. What is moment of inertia and why is it important?

Moment of inertia is a physical property of a rotating object that measures its resistance to changes in its rotational motion. It is important because it helps us understand how an object will behave when subjected to rotational forces, such as when it is spinning or rolling.

2. How is moment of inertia calculated?

Moment of inertia is calculated by summing up the products of the mass of each particle in an object, its distance from the axis of rotation, and its squared distance from the axis. This calculation can be simplified for more complex objects by using calculus or specialized equations.

3. What is the difference between moment of inertia and mass?

Moment of inertia and mass are two different physical properties. Mass is a measure of an object's resistance to changes in linear motion, while moment of inertia is a measure of an object's resistance to changes in rotational motion. In simpler terms, mass determines how an object responds to forces in a straight line, while moment of inertia determines how an object responds to rotational forces.

4. How does the distribution of mass affect the moment of inertia?

The distribution of mass in an object greatly affects its moment of inertia. Objects with the mass concentrated closer to the axis of rotation have a smaller moment of inertia and are easier to rotate, while objects with the mass spread out farther from the axis have a larger moment of inertia and are more difficult to rotate.

5. How can the moment of inertia be used in real-world applications?

The moment of inertia is used in many real-world applications, such as designing machinery, calculating the stability of structures, and predicting the behavior of rotating objects in physics and engineering. It is also used in sports, such as gymnastics and figure skating, to help athletes control their rotational movements and perform more complex maneuvers.

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