Question

A bicycle wheel has a radius of 0.33m and rim of 1.2kg . A bicycle has 50 spokes each of 10g. The wheel is moving at 50m/s find the kinetic energy of the wheel

Answer 1

KE = 1/2 w I^2 where w is the angular frequency

V = w R and w = 50 m/s / .33 m = 150 / sec

w = 150 / sec for wheel

Each spoke also has angular velocity of 150 / sec about the center of the wheel since it makes one revolution as the wheel makes one revolution

I1 = 1/3 m L^2 inertia of 1 spoke

i1 = 1/3 * .01 kg * m^2 / 9 = .00037 kg-m^2

I50 = .0185 inertia of 50 spokes about axle

I2 = M R^2 = 1.2 * (1/3)^2 = .1333 kg-m^2

I (wheel) = (.0185 + .1333) = .152 kg-m^2

E = 1/2 * 150 * .152^2 = 11.4 kg-m^2 / sec^2 = 11.4 Joules

1 Joule = M * a * s = kg * m/s^2 * m = kg-m^2 / s^2