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Two gerbils run in place with a linear speed of 0.55 m/s on an exercise wheel that is shaped like a hoop. Find the rotational kinetic energy
Question
Two gerbils run in place with a linear speed of 0.55 m/s on an exercise wheel that is shaped like a hoop. Find the rotational kinetic energy of the wheel if the exercise wheel has a radius of 9.5 cm and a mass of 5.0 g. Each gerbil has a mass of 0.02 kg if you think that is important.
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Physics
6 months
2021-07-28T04:36:31+00:00
2021-07-28T04:36:31+00:00 1 Answers
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Answer:
K = 7.56 10⁻⁴ J
Explanation:
The rotational kinetic energy is
K = ½ I w²
They ask us for the kinetic energy of the wheel, which can be approximated as a thin ring, its moment of inertia is
I = M r²
the linear speed of the gerbils is equal to the linear speed of the wheel. The linear and rotational variables are related
v = w r
w = v / r
we substitute
K = ½ (M r²) v² / r²
K = ½ M v²
let’s calculate
K = ½ 5 10⁻³ 0.55²
K = 7.56 10⁻⁴ J