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?

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

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

gets less

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.