14. Torque & Rotational Dynamics

Intro to Torque

Multiple Choice
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 $θ$ with the lever arm, what is the magnitude of the torque about the pivot due to the force applied at the handle?
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Multiple Choice
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?
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Multiple Choice
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?
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Multiple Choice
You pull with a 100 N at the edge of a 25 cm long wrench, to tighten a bolt (gold), as shown. The angle shown is 53° . Calculate the torque your force produces on the wrench, about an axis perpendicular to it and through the bolt.
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Textbook Question
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. In a sketch, show r, F, and the origin.
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Textbook Question
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). What torque does the machinist exert about the center of the nut?
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