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?

t = 5.77 s

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

the independent variable, or the one that is intentionally manipulated is the speed.

no. dot product   =0 when vecs at right angles