A high-speed flywheel in a motor is spinning at 500rpm when a power failure sudd

Question

A high-speed flywheel in a motor is spinning at 500rpm when a power failure suddenly occurs. The flywheel has mass 39.0 kg and diameter 72.0 cm . The power is off for 26.0 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 150 complete revolutions.

Part A.) At what rate is the flywheel spinning when the power comes back on? (answer w=?rad/s)

Part B.) How long after the beginning of the power failure would it have taken the flywheel to stop if the power had not come back on? ( answer t=?s)

Part C.) How many revolutions would the wheel have made during this time? (answer N=? rev)

Explanation / Answer

here,

initial angular speed of the flywheel , w0 = 500 rpm

w0 = 52.36 rad/s

mass , m = 39 kg

diameter , d = 72 cm

radius , r = 0.36 m

time for power off , t = 26 s

distance travelled during power off , theta = 942 rad

A)

let the final speed of flywheel be w

theta = w0*t + 0.5 * a*t^2

942 = 52.36 * 26 + 0.5 * a*26^2

a = - 0.62 rad/s^2

w = w0 + a*t

w = 52.36 - 0.62*26

w = 36.24 rad/s

the rate at which the flywheel spinning when the power comes back on is 36.24 rad/s

B)

for final velocity be zero , let the time taken be t'

w = w0 + a*t'

0 = 52.36 - 0.62*t

t = 84.45 s

it takes 84.45 s to stop the flywheel

C)

let the distance travelled be theta'

w^2 - w0^2 = 2 * theta' * a

0 - w0^2 = - 2* theta' * 0.62

theta' = 2210.94 rad

number of revolution are , N = 352

the number of revolution the wheel have made during this time is 352 rev

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