Question

A wheel is turning about an axis through its center with constant angular acceleration. Starting from rest, at t = 0, the wheel turns through 8. 20 revolutions in 12. 0 s. At t = 12. 0 s the kinetic energy of the wheel is 36. 0 j. For an axis through its center, what is the moment of inertia of the wheel?

Answer 1

Answer: 0.975 m^2

Step-by-step explanation:

θ = 0.5αt^2

8.20 revolutions = 8.20 x 2π = 51.52 rad

51.52 = 0.5α(12)^2

α = 0.716 rad/s^2

ω = αt = 0.716(12) = 8.592 rad/s

KE = 1/2Iω^2

36 = 0.5I(8.592)^2

I = 0.975 m^2

Therefore, the moment of inertia of the wheel is approximately 0.975m^2