Moment of Inertia of an object rotating about its center of mass?

In summary, the moment of inertia of the object formed by attaching a uniform thin rod with mass m=6kg and length L=4m to a uniform sphere with mass M=30kg and radius R=1m about an axis at the center of mass is I=(1/12)mL^2+(2/5)MR^2 = 44.6959. The moment of inertia about an axis at the right edge of the sphere can be calculated using the Parallel Axis Theorem, which states that I=Icm+MD^2, where Icm is the moment of inertia about the center of mass and D is the distance between the two axes.
  • #1
hime
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Moment of Inertia of an object rotating about its center of mass??

Homework Statement


An object is formed by attaching a uniform, thin rod with a mass of m = 6 kg and length L = 4 m to a uniform sphere with mass M = 30 kg and radius R = 1 m.

What is the moment of inertia of the object about an axis at the center of mass of the object and about an axis at the right edge of the sphere?

Homework Equations



Parallel Axis Theorem
I=Icm+MD^2

The Attempt at a Solution



I=Irod+Iball
I=(1/12)mL^2+(2/5)MR^2 =44.6959Please help :)
 
Last edited:
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  • #2


Parallel Axis Theorem
I=Icm+MD^2

If it's a relevant equation, try to use it... :)
 

FAQ: Moment of Inertia of an object rotating about its center of mass?

1. What is the definition of moment of inertia?

The moment of inertia, also known as rotational inertia, is a measure of an object's resistance to changes in its rotational motion. It is dependent on the mass distribution and shape of the object.

2. How is the moment of inertia calculated for a rotating object?

The moment of inertia is calculated by multiplying the mass of each individual particle in the object by its respective distance from the axis of rotation squared, and then summing up all of these values.

3. What is the relationship between moment of inertia and rotational speed?

The moment of inertia is directly proportional to the rotational speed of an object. This means that as the moment of inertia increases, the rotational speed decreases, and vice versa.

4. How does the moment of inertia change when the axis of rotation is changed?

The moment of inertia will change depending on the axis of rotation. For example, if the axis of rotation is moved closer to the center of mass of the object, the moment of inertia will decrease. Conversely, if the axis is moved further away, the moment of inertia will increase.

5. Can the moment of inertia be negative?

No, the moment of inertia cannot be negative. It is always a positive value as it represents the object's resistance to changes in rotational motion.

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