Calculating the Moment of Inertia for Alex's Rolling Hoop

What is the moment of inertia of Alex's rolling hoop?

According to the given statement, the moment of inertia of Alex's rolling hoop is 0.0625 kg⋅m².

Understanding Moment of Inertia

Moment of Inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution of the object and how it is rotating around a given axis. In this case, we are calculating the moment of inertia of Alex's rolling hoop.

Calculating the Moment of Inertia

To find the moment of inertia of Alex's rolling hoop, we need to use the formula for the moment of inertia of a hoop, which is:

I = m * r²

Where:

  • I is the moment of inertia
  • m is the mass of the hoop
  • r is the radius of the hoop

Given that the mass of the hoop is 0.250 kg and the radius is 50.0 cm (0.50 m), we can substitute these values into the formula:

I = 0.250 kg * (0.50 m)²

Simplifying the equation, we get:

I = 0.250 kg * 0.25 m²

I = 0.0625 kg⋅m²

Therefore, the moment of inertia of Alex's rolling hoop is 0.0625 kg⋅m².

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