Answer:
α = -0.01625 rad / s²
Step-by-step explanation:
This is an exercise in angular kinematics, we can use the relation
w = w₀ + 2 α θ
linear and angular variables are related
v = w r
w = v / r
Let's reduce the magnitudes to the SI system
v₀ = 91 km / h (1000m / 1km) (1h / 3600s) = 25.278 m / s
v = 48 km / h = 13,333 m / s
θ = 75 rev (2π rad / 1 rev) = 471.24 rad
Let's find the angular velocities
w₀ = v₀ / r
w₀ = 25.278 / 0.78
w₀ = 32,408 rad / s
w = v / r
w = 13.333 / 0.78
w = 17.09 rad / s
we calculate the angular acceleration
α = (w- w₀) / 2θ
α = (17.09 - 32.408) / (2 471.24)
α = -0.01625 rad / s²
the negative sign indicates that the wheel is stopping