Question

Question 16 (6 points) A 75-N-m torque acts on a wheel with a moment of inertia 275 kg•m². If the wheel starts from rest, how long will it take the wheel to make two (2) revolutions? a) 6.8 s b) 5.8 s c) 7.2 s O d) 9.65 e) 2.4 s

Answer 1

Torque, Ꞇ = 75 Nm

Moment of inertia, I = 275 kgm²

Initial angular speed, ω_{i = 0 rad/s}

Number of revolutions, n = 2

If α is the angular acceleration then

Angular acceleration, α = Ꞇ/I = 75/275 = 0.273 rad/s²

Using the equation, θ = ω_i t + ½ α t²

But, θ = 2πn

2πn = ½ α t²

2 x 3.14 x 2 = ½ x 0.273 x t²

t = 9.6 s

time required to make 2 revolutions is

(d) : 9.6 s