Question

A 66-N ⋅ m torque acts on a wheel with a moment of inertia 175 kg ⋅ m2. If the wheel starts from rest, how long will it take the wheel to make one revolution?

Answer 1

t = 5.77 s

Step-by-step explanation:

This exercise will use Newton's second law for rotational motion

τ = I α

α = τ / I

α = 66/175

α = 0.3771 rad/s²

now we can use the rotational kinematics relations, remember that all angles must be in radians

θ = 1 rev = 2π radians

θ = w₀ t + ½ α t²

as the wheel starts from rest w₀ = 0

t = √ (2θ/α)

let's calculate

t = √ (2 2π / 0.3771)

t = 5.77 s