Answer :
The rotational kinetic energy (J) of the wheels can be determined using the following formula: K = 1/2(Iω²)where K is the rotational kinetic energy, I is the moment of inertia, and ω is the angular velocity.
To determine the angular velocity, we will first determine the linear velocity of the wheels using the following formula:v = ωr where v is the linear velocity, ω is the angular velocity, and r is the radius of the wheel.
We are given that the radius of the wheel is 14 m, so:v = ωr = 41 m/s.
Since the linear velocity is equal to the circumference of the wheel times the angular velocity, we can also write:v = 2πrω.
Solving for ω:ω = v/2πr = 41/(2π × 14) ≈ 0.465 rad/s.
Now that we have ω, we can calculate the rotational kinetic energy for each wheel separately using the given moment of inertia of 13 kg·m² for each wheel.
The total rotational kinetic energy will be the sum of the kinetic energy of both wheels. K = 1/2(Iω²) = 1/2(13 kg·m²)(0.465 rad/s)²K = 1.01 J (to two decimal places).
Thus, the rotational kinetic energy of each wheel is 1.01 J and the total rotational kinetic energy of both wheels is 2.02 J.
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