A centrifuge has a rotational inertia of 5.50 × 10−3 kg m2. How much energy must be supplied to bring it from rest to 500 rad/s?
Question
A centrifuge has a rotational inertia of 5.50 × 10−3 kg m². How much energy must be supplied to bring it from rest to 500 rad/s?
Solution
The energy required to bring the centrifuge from rest to a certain speed can be calculated using the formula for rotational kinetic energy:
KE = 0.5 * I * ω^2
where: KE is the kinetic energy, I is the rotational inertia, and ω is the angular velocity.
Given: I = 5.50 × 10−3 kg m^2 ω = 500 rad/s
Substituting these values into the formula gives:
KE = 0.5 * 5.50 × 10−3 kg m^2 * (500 rad/s)^2
Solving this equation will give the energy required in joules.
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