An industrial flywheel (a solid disk) of mass 10.0 kg and radius 17.3 cm is rotating at an angular speed of 22.0 rad/s. Upon being switched to a slower setting, the flywheel uniformly slows down to 13.5 rad/s after rotating through an angle of 13.8 radians. Calculate the angular acceleration of the flywheel in the process of slowing down

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Physics

Dania

18 August, 18:57

An industrial flywheel (a solid disk) of mass 10.0 kg and radius 17.3 cm is rotating at an angular speed of 22.0 rad/s. Upon being switched to a slower setting, the flywheel uniformly slows down to 13.5 rad/s after rotating through an angle of 13.8 radians. Calculate the angular acceleration of the flywheel in the process of slowing down

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Maya Hobbs · Answer 1

During slowing down, initial angular velocity ω₁ = 22 rad / s

final angular velocity ω₂ = 13.5 rad / s

using the law's of motion formula for rotation

ω₂² = ω₁² + 2 αθ, α is angular acceleration and θ is angle in radian rotated during this period

13.5² = 22² - 2xα x 13.8

2xα x 13.8 = 484 - 182.25

α = 10.93 rad / s²