Rotational Motion

EXAMPLE PROBLEM ON TORQUE: The Swinging Door

Question
In a hurry to catch a cab, you rush through a frictionless swinging door and onto the sidewalk. The force you extered on the door was 50N, applied perpendicular to the plane of the door. The door is 1.0m wide. Assuming that you pushed the door at its edge, what was the torque on the swinging door (taking the hinge as the pivot point)?

Hints
 
 

  1. Where is the pivot point?
  2. What was the force applied?
  3. How far from the pivot point was the force applied?
  4. What was the angle between the door and the direction of force?
Solution
The pivot point is at the hinges of the door, opposite to where you were pushing the door. The force you used was 50N, at a distance 1.0m from the pivot point. You hit the door perpendicular to its plane, so the angle between the door and the direction of force was 90 degrees. Since 
    = r x F = r F sin(

Figure 1 Diagram of Example Problem 1
then the torque on the door was: Note that this is only the magnitude of the torque; to complete the answer, we need to find the direction of torque. Using the right hand rule, we see that the direction of torque is out of the screen.


Explanation of Torque
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