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A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. the flywheel has mass 40.0 kg and diameter 76.0 cm . the power is off for 35.0 s and during this time the flywheel slows due to friction in its axle bearings. during the time the power is off, the flywheel makes 180 complete revolutions.

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W0lf93
The flywheel is solid cylindrical disc. Moment of inertial = ½ * mass * radius^2 Mass = 40.0 kg Radius = ½ * 76.0 cm = 38 cm = 0.38 meter Moment of inertial = ½ * 41 * 0.36^2 Convert rpm to radians/second The distance of 1 revolution = 1 circumference = 2 * π * r The number of radians/s in 1 revolution = 2 * π 1 minute = 60 seconds 1 revolution per minute = 2 * π radians / 60 seconds = π/30 rad/s Initial angular velocity = 500 * π/30 = 16.667 * π rad/s 170 revolutions = 170 * 2 * π = 340 * π radians The flywheel’s initial angular velocity = 16.667 * π rad/s. It decelerated at the rate of 1.071 rad/s^2 for 48.89 seconds. θ = ωi * t + ½ * α * t^2 θ = 16.667 * π * 48.89 + ½ * -1.071 * 48.89^2 2559.9 - 1280 θ = 1280 radians

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