Conceptual Example 14 provides useful background for this problem. A playground carousel is free to rotate about its center on f

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Conceptual Example 14 provides useful background for this problem. A playground carousel is free to rotate about its center on f

rictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 105 kg·m2. When one person is standing at a distance of 1.57 m from the center, the carousel has an angular velocity of 0.512 rad/s. However, as this person moves inward to a point located 0.507 m from the center, the angular velocity increases to 0.795 rad/s. What is the person's mass?

Physics

1 answer:

S_A_V [24] · Answer 1 · 2023-04-30T17:05:05+03:00

For one person standing at a distance of 1.57 m from the center, the carousel has an angular velocity of 0.512 rad/s, the person's mass is mathematically given as

m = 24.2 kg

<h3>What is the person's mass?</h3>

Generally, the equation for the conservation angular momentum is mathematically given as

(I + m * r0^2) * w0 = (I + m * r^2) * w^2

Therefore

(105 + m * 1.78^2) * 0.517 = (105 + m * 0.524^2) * 0.841

m = 24.2 kg

In conclusion, the mass

m = 24.2 kg