Question

the st joseph river swing bridge in st joseph, michigan has a mass of 300 tons (2.72×10⁵ kg) and is 231 ft (70.4 m) long. if the motor produces 563 knm of torque and takes 10 s to accelerate the bridge to 0.05 rad/s, what is the bridge’s moment of inertia?

Explanation:

Step1: Calculate angular acceleration

Angular acceleration $\alpha = \frac{\Delta \omega}{\Delta t} = \frac{0.05\ \text{rad/s} - 0}{10\ \text{s}} = 0.005\ \text{rad/s}^2$

Step2: Relate torque, inertia, and $\alpha$

Use $\tau = I\alpha$, rearrange to $I = \frac{\tau}{\alpha}$. Convert torque to Nm: $\tau = 563\ \text{kNm} = 563000\ \text{Nm}$

Step3: Compute moment of inertia

$I = \frac{563000\ \text{Nm}}{0.005\ \text{rad/s}^2}$

Answer:

$1.126 \times 10^8\ \text{kg·m}^2$