Question

Physics problem:

A flywheel of mass 35.0kg and diameter of 60.0cm spins at 400rpm when it experiences a sudden power loss. The flywheel slows due to friction in its bearings during the 20.0s the power is off. If the flywheel makes 200 complete revolutions duing the power failure, (a) at what rate is the flywheel spinning when the power comes back on? (b) How long would it have taken for the flywheel to come to a complete stop?

Answer 1

given values:

200 revs = 200*2*pi radian = 1257.14 rad

400rpm = 400*2*pi/60 rad/s = 41.9 rad/s

Now using

θ=θ₀+ω₀*t+0.5*α*t²
θ₀=0
ω₀=41.9
t=20
θ=1257.14

=> 1257.14 = 0+41.9*20+0.5*α*20²

=> 200α = 1257.14 - 838

=> α = 2.0957 rad/s²

now

ω=41.9+2.0957*20 = 83.814 rad/s = 800.04 rpm

If the power had stayed off it will take t sec to a complete stop

=> 0=41.9-2.0957*t

=> t = 41.9/2.0957 = 19.99 sec

=> θ=41.9*19.99-0.5*2.0957*19.99²
=> θ =418.86 rad