14. Torque & Rotational Dynamics

Some trainyards have very large horizontal disks that engines can drive onto, which then rotate to turn the engine around to face the opposite direction. Suppose the train engine is 12 m long and centered at the disk's axis. A 500 N force is applied 5.0 m from the center of the engine, with a rope that makes a $35°$ angle with the side of the engine. What magnitude torque is being applied to the train engine?

Model the propeller of an airplane as a single thin rod, 2.2 m long, with a mass of 80 kg. How much torque is required to bring this propeller from rest to 600 rpm in 2.9 s?

In an introductory torque setup, a rigid lever is pivoted at one end and a force is applied at the handle a distance $r$ from the pivot. If the force makes an angle $\theta$ with the lever arm, what is the magnitude of the torque about the pivot due to the force applied at the handle?