kinematics
posted by dmkp .
An exercise bicycle's flywheel is 30cm in diameter and 2.5 cm thick and is constructed from steel (density=7850 kg m3) its moment of inertia is 0.156 kg m2 about its axis of rotation
a) calculate the mass of the flywheel
b) calculate the flywheel's radius of gyration
c) whilst exercising a man applies a constant moment of 10.0Nm to the flywheel. Starting from rest the flywheel reaches an angular velocity of 12.0 rad s1 after exactly 1 minute. Calculate the flywheel's angular acceleration, the number of revolutions the flywheel makes and the friction moment applied to the flywheel

m = ρ•V = ρ•π•D²•d/4 =
=7850•3.14•0.09•0.025/4 = 3.12 kg.
R(gyr) =sqrt(I/A) = sqrt(4•I/ π•D²) = =sqrt(4•0.156/3.14•0.09) =1.5 m.
ω= ε•t,
ε = ω/t = 12/60 = 0.2 rad/s².
2•π•N = ε•t²/2,
N = ε•t²/4• π =0.2•3600/4•3.14 =
=57.3 rev.
M  M(fr) =I•ε.
M(fr)= M  I•ε =
=10 – 0.156•0.2 = 9.969 N•m.