Torque and the Second Condition of Equilibrium

Torque and the Second Condiction of Equalibrium

Page 1

This text is meant to accompany class discussions. It is not everything there is to know about the basics of torque and the two conditions of equilibrium. It is meant as a prep for class. More detailed notes and examples are given in the class notes, presentations, and demonstrations (click here.)

Click for the questions that go with this reading

This Youtube video is here: www.youtube.com/embed/Mk_WNzVSI00

The diving board rotated off it stand. Watch the video again and notice how it spins of its support. In order to make an object spin faster or slower, a "torque" must be applied. A torque is a force that is applied perpendicular to the distance about a pivot point.

Torque Diagram

The point where the object rotates about is called the "pivot point." This location is also called the "axis of rotation." If the object being rotated is a beam, like the one above, then the pivot point has a more specialized name. It is called a "fulcrum." The distance between the pivot point and the force also has a name, it is called the "moment arm." The force can be in any direction as long as a component of force is perpendicular to the distance that is drawn from the pivot point. Torque has the units of Newton•meters, [Nm], pronounced like it is one word, (audio.) The units of Newton•meters have been used before for energy. The difference is how the Newton•meter was calculated. When force and distance are parellel to each other, energy is aded or removed. When force and distance are perpendicular to each other, a torque is produced. The unit of Joules was created to represent the unit of energy and replaces Newton•meters when talking about energy. But there isn't a special unit for torque. It is just "Newton•meters."

Torques have signs

There are positive and negative torques. Any force that causes a counterclockwise rotation about a pivot point is said to cause a positive torque. Any force that causes a clockwise rotation is said to cause a negative torque.

Troque Signs animation

Visualizing Rotation (Helpful technque) and Making an Extended Free Body Diagram

Video link - http://youtu.be/xVa4vTkQfes

All forces cause a torque about any pivot point unless, either...

the force points away from the pivot point, or,
the force points towards the pivot point.

Calculating a Torque's Magnitude

There are three cases to consider.

1

The force is given to be perpendicular to the moment arm.

Draw a line from the pivot point to the the location where the force acts. If the force and perpendicular to the force's direction, multiply the force's magnitude time the moment arm's length.

The diving board video shown at the top is another example of this.

2

The applied force is at an angle to the moment arm. There two methods for calcualting the torque. It is up to you to choose the method.

Method 1
Method 2

3

There are special cases where a torue is not produced by a force.

Examples

Example
Solution

Calculate the torque about the pivot point, marked with an "X," due only to the hanging mass of 5.00 kg.

Calculate the torque about the pivot point, marked with an "X," due only to the hanging mass of 5.00 kg.

In this case, the force is given as being perpendicular to the distance along the beam. A simple technique for finding the moment arm is to extend the force you are examining, in this case the hanging weight, and draw line from the pivot point to the extened line. Remember the distance and force vectors need to be perpendicular to each other.

Solution

Example 2
Solution

At one point during a trick at a circus, a performer of mass 500 N, is standing on a beam held up only by a rope. Calculate the torque is the axis of rotation is on the beam where the rope attaches.

The weight of the performed is the force. The perpendicular distance betweent where the rope attaches and the weight is 2.5m - 1m = 1.5m.

solution

Example 3
Solution

Calculate the torque generated by the 800.0 N tension at the end of the beam. The pivot point is given to be on the beam next to the wall.

Calculate the torque generated by the 800.0 N tension at the end of the beam. The pivot point is given to be on the beam next to the wall.
solution

Two items to note about this solution:

T_y is used as the force because it is the component perpendicular to the moment arm.
T_y is slid over to where the tension (cable) is applied to the beam. It does not stay as a part of the triangle.

Example 1: Video example of how torque is calculated

This video can be found on YouTube at http://youtu.be/l0Sg29-DF_0

Example 2: Video example of how torque is calculated

This video can be found on YouTube at http://youtu.be/QZ8nuMmXrqQ

by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)

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