Rotational Inertia of Solid Sphere Suspended from Ceiling

In summary, the rotational inertia of a solid uniform sphere of radius R and mass M about a diameter is (2/5)MR^2. When a light string of length 3R is attached to the surface, the sphere is suspended from the ceiling. To find the rotational inertia about the point of attachment at the ceiling, the parallel axis theorem is used, giving a final result of 47/5mr^2.
  • #1
AlexH
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Homework Statement


A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5)MR^2. A light string of length 3R is attached to the surface and used to suspend the sphere from the ceiling. What is its rotational inertia about the point of attachment at the ceiling?

Homework Equations


mr^2 + md^2

The Attempt at a Solution


I used the parallel axis theorem and got 2/5mr^2 + 9mr^2, which simplifies to 47/5mr^2, but that's not the correct answer.

Thanks for any help!
 
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  • #2
Be sure you know the exact meaning of ##d## in the parallel axis formula.
 

1. What is rotational inertia?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It depends on the object's mass and its distribution around its axis of rotation.

2. How is rotational inertia different from mass?

While mass is a measure of an object's resistance to linear motion, rotational inertia is a measure of its resistance to rotational motion. In other words, it takes into account the object's distribution of mass, rather than just its total mass.

3. How is rotational inertia calculated for a solid sphere suspended from the ceiling?

The rotational inertia of a solid sphere suspended from the ceiling can be calculated using the formula I = (2/5) * m * r^2, where m is the mass of the sphere and r is the radius from its axis of rotation to the outer edge of the sphere.

4. How does the rotational inertia of a solid sphere change if its mass or radius is increased?

If the mass or radius of a solid sphere is increased, its rotational inertia will also increase. This is because the object's distribution of mass around its axis of rotation is changing, resulting in a greater resistance to changes in rotational motion.

5. Why is the concept of rotational inertia important in physics?

The concept of rotational inertia is important in physics because it helps us understand and predict the behavior of rotating objects. It is particularly useful in mechanics, where it is used to analyze the motion of objects such as wheels, gears, and pendulums.

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