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 kinetic energy will it have 8.0 s later? A)31 J B)17 J C)11 J D)6.6 J

Question

Quizplus · Accepted Answer

First, we need to find the angular acceleration of the fan:

τ = Iα
0.11 Nm = 0.034 kgm²α
α = 3.24 rad/s²

Using the equation for rotational motion, we can find the angular velocity of the fan after 8.0 seconds:

ω = ω₀ + αt
ω = 0 + 3.24 rad/s²(8.0 s)
ω = 25.92 rad/s

Finally, we can find the kinetic energy of the fan:

K = (1/2)Iω²
K = (1/2)(0.034 kgm²)(25.92 rad/s)²
K = 11.2 J

Rounding to one significant figure, the answer is 11 J, which corresponds to choice C.

A Ventilation Fan with a Moment of Inertia of 0