Question

A high-speed flywheel in a motor is spinning at 450 rpm (revolutions per minute) when a power failure suddenly occurs. The flywheel has mass 45.0 kg and diameter 74.0 cm . The power is off for 25.0 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. A. At what rate is the flywheel spinning when the power comes back on? (rad/s)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? (s)C. How many revolutions would the wheel have made during this time?

Answer 1

a) final angular speed w2 = 414rpm

b) time to stop t = 312.5s

c) angular distance from start to stop s = s = 1171.88 rev

Step-by-step explanation:

Average angular speed wa = (w1+w2)/2 = Angular distance/time = s/t

Given;

w1 = 450 rpm = 450/60 rev/s = 7.5 rev/s

s = 180 rev

t = 25s

a)

s/t = (w1+w2)/2

w2 = 2s/t - w1

Substituting the values;

w2 = 2×180/25 - 7.5 = 6.9 rev/s

w2 = 6.9×60rpm = 414rpm

b)

Angular deceleration a = (w1-w2)/t = (7.5-6.9)/25

a = 0.024 rev/s^2

time t for w2 = 0

t = (w1-w2)/a = (7.5-0)/0.024

t = 312.5 s

c)

Angular distance from start to stop s;

s = w1t - 0.5at^2

s = 7.5×312.5s - 0.5×0.024×312.5^2

s = 1171.88 rev