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?

One force acting on a machine part is F = (-5.00 N)i + (4.00 N)j. The vector from the origin to the point where the force is applied is r = (-0.450 m)i +(0.150 m)j. (a) In a sketch, show r, F, and the origin.

A machinist is using a wrench to loosen a nut. The wrench is 25.0 cm long, and he exerts a 17.0-N force at the end of the handle at 37° with the handle (Fig. E10.7).

(a) What torque does the machinist exert about the center of the nut?

Calculate the torque (magnitude and direction) about point O due to the force F in each of the cases sketched in Fig. E10.1. In each case, both the force F and the rod lie in the plane of the page, the rod has length 4.00 m, and the force has magnitude F = 10.0 N. (a)

A metal bar is in the xy-plane with one end of the bar at the origin. A force F = 97.00 N)i + (-3.00 N)j is applied to the bar at the point x = 3.00 m, y = 4.00 m. (b) What are the magnitude and direction of the torque with respect to the origin produced by F?