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Shkiper50 [21]
3 years ago
14

Two skaters skate toward each other, each moving at 3.3 m/s. Their lines of motion are separated by a perpendicular distance of

1.5 m. Just as they pass each other (still 1.5 m apart), they link hands and spin about their common center of mass. What is the rotational speed of the couple about the center of mass? Treat each skater as a point particle, each with an inertia of 51 kg.
Physics
1 answer:
vredina [299]3 years ago
3 0

Answer:

4.4 rad/s

Explanation:

When the 2 skaters is spinning with a distance of 1.5m, their rotation radius is half of that distance, which is 1.5/2 = 0.75m.

Then their moments of inertia, given that their mass being 51 kg, is (treating them as point mass particle):

I = Mr^2 = 2Mr^2 = 51*0.75^2 = 38.25 kg.m^2

When they change from linear motion to rotational motion, their energy must be conserved:

E_L = E_r

2*(0.5Mv^2) = 2*(0.5I\omega^2)

\omega^2 = \frac{Mv^2}{I}

\omega = v\sqrt{\frac{M}{I}}

\omega = 3.3\sqrt{\frac{51}{38.25}} = 4.4 rad/s

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