Question

Calculate the moment of inertia of a skater given the following information. (a) The 60.0-kg skater is approximated as a cylinder that has a 0.110-m radius. (b) The skater with arms extended is approximated by a cylinder that is 52.5 kg, has a 0.110-m radius, and has two 0.900-m-long arms which are 3.75 kg each and extend straight out from the cylinder like rods rotated about their ends.

(a) 3.72 kg⋅m²
(b) 4.25 kg⋅m²
(c) 4.90 kg⋅m²
(d) 5.15 kg⋅m²

Answer 1

To calculate the moment of inertia of a skater, we can use the formula I = (1/2) * m * r^2. For a skater approximated as a cylinder, the moment of inertia is 3.72 kg⋅m². For a skater with extended arms, the moment of inertia is 4.25 kg⋅m².

Step-by-step explanation:

To calculate the moment of inertia of the skater, we can use the formula:

I = (1/2) * m * r^2

For part (a), where the skater is approximated as a cylinder, we plug in the values:

I = (1/2) * 60.0 kg * (0.110 m)^2 = 3.72 kg⋅m²

For part (b), where the skater with arms extended is approximated as a cylinder with extended arms, we add the moments of inertia for the cylinder and the two arms:

I = (1/2) * 52.5 kg * (0.110 m)^2 + 2 * (1/3) * 3.75 kg * (0.900 m)^2 = 4.25 kg⋅m²

Therefore, the correct answer is (b) 4.25 kg⋅m².