(6) Torque and Static Equilibrium

PAGE EDITOR(S): Gabe Nones-Newman, Ben Berman, Kathleen Joyce, Alissa Elan


t = rFsinθ (measured in Nm)
r is the "lever arm" - the distance from the chosen axis of rotation to where the force is being applied to the object. (measured in meters)
F is the force being applied to the object. (measured in Newtons)
θ is the angle between the force vector and the "lever arm."

Torque is a force applied to angular motion instead of linear motion. It leads an object to want to rotate.
Static Equilibrium is when both the forces and the torques are balanced.

Conditions for Static Equilibrium
  1. St = 0
  2. SFx = 0; SFy = 0
  3. v = 0

Question: How do you pull on the wrench in order to make it easiest to turn?
Answer: With a force perpendicular to the wrench. Maximum torque is when the force applied is perpendicular to the lever arm. Since you maximize your torque by exerting a perpendicular force, it is easier to rotate the wrench.

Question: Which wrench do you use in order to make it easier to turn?
Answer: The longer wrench. Because t = rFsinθ and θ 90, the equation becomes t = rF. Since F is the same, the torque is greater when r is greater.

Steps to Solving a Torque Problem:

1. Sketch the situation.
2. Draw a Free Body Diagram - make sure to draw the forces where they are applied on the object.
3. Question: Is the system in static equilibrium? (The answer is yes.)
4. Choose an axis of rotation, preferably one that gets rid of an unknown.
5. Apply the conditions of static equilibrium in order.

Torque is a vector quantity. If the force rotates the object in the counter clockwise direction, the torque is positive. If it rotates in the clockwise direction, the torque is negative.
Why is clockwise the negative torque?
Answer: Think of using a screwdriver: when you tighten a screw, you turn the screwdriver clockwise (righty-tighty). The screw moves away from you, along the negative z axis.

Detailed Diagram of a Fulcrum (rather than a normal level) - Helpful for HW problem #12


( Gives good tips on deciding the direction of the torque)

( A helpful powerpoint on intro to Torque)

( A video proof of torque (starts two minutes in))

(shows how adding weights can affect torque)

Practice Problems:
Here are some multiple choice practice problems (we haven't learned how to do all of them). Click on the side bar that says "practice questions".

Some workout problems:
(Answers: http://physics.unl.edu/~klee/phys151/ClassExercise/Torque2-Class%20Exercise-KEY.pdf)


(Torque-Fulcrum DIagram)

(Picture of the first wrench)
(Picture of the second wrench)
XYZ axis image