0.32 Phy1320: angular momentum -- the mathematics of torque  (Page 10/13)

If the door happened to be a really heavy door, you would probably push on the door at a point as close to the outer edge aspossible. This would make it possible for you to cause the door to close with the minimum effort on your part.

The magnitude of the torque

In an attempt to codify your intuition, your instinctive knowledge, or perhaps your acquired knowledge into something more mathematical, we will definethe magnitude of the torque as

torque = r*F

The conventional symbol for torque is the Greek letter tau. However, your Braille display probably won't display that Greek letter, so in this module, Iwill represent torque with the letter T as shown in Figure 6 .

The sign convention for torque

In this module, I will use a sign convention such that a force whose perpendicular component, when acting alone, would cause the object to rotate ina counter clockwise direction as a positive torque.

If that torque is the only torque acting, it would cause a positive angular acceleration.

A definition of torque

You saw a mathematical definition of torque earlier . Figure 6 shows a somewhat less mathematical definition of torque.

The units can be confusing

The units for torque can be confusing because the SI unit for work or energy in joules is also N*m. However, even though torque and energy have the same units, they haveentirely different meanings. Torque is not a form of energy.

A graph board exercise on torque

Imagine a puck sliding in a circular groove that has been cut in the ice at an ice rink. A cross section of the grove is rectangular so that the puck justfits from side to side and sets level on the bottom of the groove. When a puck slides inside the groove, it will move in a large circle.

Apply a force to the puck

If you apply a force to the puck in (almost) any direction, a component of that force will directed toward or away from the center of the circle. For any case wherethe direction of the force doesn't lie on a line from the puck to the center of the circle, there will also be a component of the force that is perpendicular tothat line, which will make it tangential to the circle.

Construct a graph board simulation

Use your graph board and create a Cartesian coordinate system with the origin near the lower-left corner of the graph board. Use pushpins and pipecleaners to draw a quarter of a circle, with the center of the circle at the origin. Make the radius approximately one-half of thesmallest dimension of the graph board. This circle should include the entire upper-right quadrant of your Cartesian coordinate system.

Identify the location of the puck

Now insert a pushpin at a point somewhere on the circle about mid way between the intersection of the circle and the x and y axes of the coordinate system.