Question

a ceiling ceiling ceiling ceiling ceiling fan is turned on and a net torque of 2.4 n·m applied to the blades. the blades have a total moment of inertia of 0.72 kg·m². what is the angular acceleration of the blades?

Explanation:

Step1: Recall the formula for torque

Torque formula is $\tau = I\alpha$, where $\tau$ is torque, $I$ is moment of inertia, and $\alpha$ is angular acceleration.

Step2: Solve for angular acceleration

Rearrange the formula to $\alpha=\frac{\tau}{I}$. Substitute $\tau = 2.4\ N\cdot m$ and $I = 0.72\ kg\cdot m^{2}$. So, $\alpha=\frac{2.4}{0.72}$.

Step3: Calculate the value

$\frac{2.4}{0.72}=\frac{240}{72}=\frac{10}{3}\approx3.33$.

Answer:

Number: $3.33$, Units: $rad/s^{2}$