question archive A wheel is turning about an axis through its center with constant angular acceleration
A wheel is turning about an axis through its center with constant angular acceleration
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A wheel is turning about an axis through its center with constant angular acceleration. Starting from rest, at t=0, the wheel turns through 7.50 revolutions in t= 15.0 s . At 15.0 s the kinetic energy of the wheel is 36.0 J . Part A For an axis through its center, what is the moment of inertia of the wheel? Express your answer with the appropriate units.
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Answer:
θ = 0.5αt^2
7.50 revolutions = 7.50 x 2π = 47.12 rad
47.12 = 0.5α(15)^2
α = 0.418 rad/s^2
ω = αt = 0.418(15) = 6.282 rad/s
KE = 1/2Iω^2
36 = 0.5I(6.282)^2
I = 1.82 kg m^2
