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Answer :
The rotational kinetic energy of the wheel represents approximately 14.06% of the total kinetic energy of the unicycle (including the rider).
To find the fraction of the total kinetic energy of the unicycle (including the rider) that is due to the rotational kinetic energy of the wheel, we need to calculate the rotational kinetic energy and the total kinetic energy.
The rotational kinetic energy of the wheel can be calculated using the formula:
Rotational kinetic energy = (1/2) * I * ω^2
where I is the rotational inertia of the wheel and ω is the angular velocity of the wheel.
Given:
Radius of the wheel (r) = 0.80 m
Rotational inertia of the wheel (I) = 0.090 kg m^2
Total mass of the unicycle (m) = 93 kg
The total kinetic energy of the unicycle can be calculated using the formula:
Total kinetic energy = (1/2) * m * v^2
where m is the total mass of the unicycle and v is the constant speed at which it is coasting.
Since the unicycle is coasting at a constant speed, the linear velocity of the wheel is equal to the velocity of the unicycle (v).
To find the fraction of rotational kinetic energy to total kinetic energy, we can divide the rotational kinetic energy by the total kinetic energy and multiply by 100 to express it as a percentage.
Fraction of rotational kinetic energy = (Rotational kinetic energy / Total kinetic energy) * 100
Let's calculate the values:
Rotational kinetic energy = (1/2) * 0.090 kg m^2 * ω^2
To find ω, we can use the relationship between linear velocity (v) and angular velocity (ω) for a wheel:
v = ω * r
Rearranging the equation, we have:
ω = v / r
Substituting the values, we get:
ω = v / 0.80 m
Total kinetic energy = (1/2) * 93 kg * v^2
Now, we can calculate the fraction of rotational kinetic energy to total kinetic energy:
Fraction of rotational kinetic energy = ((1/2) * 0.090 kg m^2 * (v / 0.80 m)^2) / ((1/2) * 93 kg * v^2) * 100
Simplifying the equation, we can cancel out some terms:
Fraction of rotational kinetic energy = (0.090 / 0.80^2) * 100
Calculating the value:
Fraction of rotational kinetic energy ≈ 14.06%
Therefore, the rotational kinetic energy of the wheel represents approximately 14.06% of the total kinetic energy of the unicycle (including the rider).
learn more about rotational kinetic energy from this link.
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