A typical 26-inch bicycle wheel rim has a diameter of 559 mm (22.0") and an outside tire diameter of about 26.2" (665 mm). For our calculation we approximate the radius - r - of the wheel to
r = ((665 mm) + (559 mm) / 2) / 2
= 306 mm
= 0.306 m
The weight of the wheel with the tire is 2.3 kg and the inertial constant is k = 1.
The Moment of Inertia for the wheel can be calculated
I = (1) (2.3 kg) (0.306 m)2
= 0.22 kg m2
The speed of the bicycle is 25 km/h (6.94 m/s). The wheel circular velocity (rps, revolutions/s) - nrps - can be calculated as
nrps = (6.94 m/s) / (2 π (0.665 m) / 2)
= 3.32 revolutions/s
The angular velocity of the wheel can be calculated as
ω = (3.32 revolutions/s) (2 π rad/revolution)
= 20.9 rad/s
The kinetic energy of the rotating bicycle wheel can then be calculated to
Ef = 0.5 (0.22 kg m2) (20.9 rad/s)2
= 47.9 J
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