Ahigh-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.

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