A ventilation fan with a moment of inertia of 0.034 kg·m² has a net torque of 0.11 N·m applied to it.If it starts from rest,what angular momentum will it have 9.0 s later? A)0.88 kg·m²/s B)0.99 kg·m²/s C)2.0 kg·m²/s D)3.3 kg·m²/s

Question

Quizplus · Accepted Answer

We can use the equation for angular momentum:

L = Iω

where L is angular momentum, I is moment of inertia, and ω is angular velocity.

We need to find ω first, and we can use the equation for torque:

τ = Iα

where τ is torque, I is moment of inertia, and α is angular acceleration.

Rearranging for α:

α = τ/I

Plugging in the numbers:

α = 0.11 N·m / 0.034 kg·m^2
   = 3.24 rad/s^2

Now we can use another kinematic equation to find ω:

ω = αt

Plugging in the numbers:

ω = 3.24 rad/s^2 x 9.0 s
   = 29.16 rad/s

Finally, we can plug ω back into the first equation to find L:

L = Iω
  = (0.034 kg·m^2) x (29.16 rad/s)
  ≈ 0.99 kg·m^2/s

Therefore, the answer is B.

A Ventilation Fan with a Moment of Inertia of 0