Question
During the spin-dry cycle of a washing machine, the motor slows from 90 rad/s to 30 rad/s while the turning the drum
During the spin-dry cycle of a washing machine, the motor slows from 90 rad/s to 30 rad/s while the turning the drum through an angle of 180 radians. What is the magnitude of the angular acceleration of the motor?
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The angular acceleration can be found using the equation of motion for rotational motion:
ωf^2 = ωi^2 + 2αΔθ
where ωf is the final angular velocity, ωi is the initial angular velocity, α is the angular acceleration, and Δθ is the change in angle.
Rearranging for α gives:
α = (ωf^2 - ωi^2) / (2Δθ)
Substituting the given values gives:
α = (30^2 - 90^2) / (2*180)
α = (-8100) / 360
α = -22.5 rad/s^2
The magnitude of the angular acceleration is 22.5 rad/s^2.
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