Moment of Inertia of spherical masses

In summary, the three small spherical masses have a moment of inertia with respect to an axis perpendicular to the xy plane and passing through x=0 and y=-3. The center of mass is (-0.42, -1.15), while the radius is not found and needs to be determined.
  • #1
gummybeargirl
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Homework Statement


Three small spherical masses are located in a plane at the positions shown below.
The masses are Q=0.700 kg, R=0.400 kg, and S=0.800 kg. Calculate the moment of inertia (of the 3 masses) with respect to an axis perpendicular to the xy plane and passing through x=0 and y=-3. [Since the masses are of small size, you can neglect the contribution due to moments of inertia about their centers of mass.]

Homework Equations


I=∑m*r^2,

The Attempt at a Solution


I tried finding the Center of mass with turned out to be (-0.42, -1.15) and then tried to find the radius to plug into the equation, but that gave me the wrong answer and I am not sure where to even start with this problem.
 

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  • #2
gummybeargirl said:

Homework Statement


Three small spherical masses are located in a plane at the positions shown below.
The masses are Q=0.700 kg, R=0.400 kg, and S=0.800 kg. Calculate the moment of inertia (of the 3 masses) with respect to an axis perpendicular to the xy plane and passing through x=0 and y=-3. [Since the masses are of small size, you can neglect the contribution due to moments of inertia about their centers of mass.]

Homework Equations


I=∑m*r^2,

The Attempt at a Solution


I tried finding the Center of mass with turned out to be (-0.42, -1.15) and then tried to find the radius to plug into the equation, but that gave me the wrong answer and I am not sure where to even start with this problem.

Go back to the definition of 'r' in the equation for calculating moment of inertia. It's nice you found the c.o.m. for the system, but it's irrelevant for solving this problem.
 
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  • #3
Thank you for your help. I got it by using the equation I posted, I was just was confusing r as the radius not as the distance from the axis.
 

What is Moment of Inertia of spherical masses?

Moment of Inertia of spherical masses is a measure of an object's resistance to changes in its rotational motion. It depends on the mass and distribution of the object's mass around its axis of rotation.

How is Moment of Inertia of spherical masses calculated?

Moment of Inertia of spherical masses can be calculated by using the formula I = 2/5 * mr^2, where m is the mass of the object and r is the radius of the sphere.

What factors affect the Moment of Inertia of spherical masses?

The Moment of Inertia of spherical masses is affected by the mass and distribution of mass around the axis of rotation. A larger mass or a greater distance of mass from the axis of rotation will result in a higher Moment of Inertia.

Why is Moment of Inertia important in physics?

Moment of Inertia is important in physics because it helps us understand how an object will behave when subjected to rotation. It is also used in various equations and laws, such as Newton's Second Law of Motion and the Law of Conservation of Angular Momentum.

How does Moment of Inertia of spherical masses relate to real-world applications?

Moment of Inertia of spherical masses is used in many real-world applications, such as in the design of rotating machinery, sports equipment, and vehicles. It is also important in understanding the motion and stability of objects in space, like planets and satellites.

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