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.

Answer 1

K = 7.56 10⁻⁴ J

Step-by-step 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