Calculating Rotational Inertia of a Disk with Mass M and Radius R

In summary, rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion and depends on the mass distribution and shape of the object. The rotational inertia of a disk can be calculated using the formula I = 1/2 * MR^2, and its unit is kilogram-meter squared (kg-m^2) in the SI system. As the mass or radius of a disk increases, the rotational inertia also increases, meaning that a larger mass or radius results in a greater resistance to changes in rotational motion. The rotational inertia of a disk can be changed by altering its mass, radius, or shape.
  • #1
kolua
69
3
If there is a disk of mass M and radius R that is already rotating, then someone puts a block with mass m on it a meters away from the center of mass.
What is the rotational inertia then?

Is it I=(M+m)R^2?
 
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  • #2
The moment of inertia is additive. The original moment of inertia of the disk should be ##\frac{1}{2}MR^2## and the block's is ##m\cdot (1m)^2## if it's small enough for us to ignore its volume. The answer should be the sum of above.
 

Related to Calculating Rotational Inertia of a Disk with Mass M and Radius R

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 mass distribution and shape of the object.

2. How do you calculate rotational inertia of a disk?

The rotational inertia of a disk can be calculated using the formula I = 1/2 * MR^2, where M is the mass of the disk and R is the radius.

3. What is the unit of rotational inertia?

The unit of rotational inertia is kilogram-meter squared (kg-m^2) in the SI system. In other systems, it can be expressed as slug-foot squared (slug-ft^2) or pound-square foot (lb-ft^2).

4. How does the mass and radius affect rotational inertia of a disk?

As the mass or radius of a disk increases, the rotational inertia also increases. This means that a disk with a larger mass or radius will have a greater resistance to changes in its rotational motion.

5. Can the rotational inertia of a disk be changed?

Yes, the rotational inertia of a disk can be changed by altering its mass or radius. For example, by increasing the mass or radius, the rotational inertia will also increase. Additionally, changing the shape of the object can also affect its rotational inertia.

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