Reference Tools & Resources
|
Chapter 11: Rotational Dynamics and Static Equilibrium Reference Tools & Resources |
|
Reference Tools & Resources
I. Key Terms and Phrases
torque: the combination of a force and the distance at which it is applied from an axis that causes angular acceleration.
moment arm: the perpendicular distance from the axis of rotation to the line of force used to calculate torque.
static equilibrium: the state of motion in which an object neither translates nor rotates.
angular momentum: a vector quantity equal to 
that represents a rotational analog of linear momentum.
angular momentum conservation: the principle that the total angular momentum of a system remains constant unless a nonzero external net torque is applied.
right-hand rule: the rules for using your right hand to determine the direction of rotational vector quantities.
II. Other Useful Tips
Sometimes, when performing an analysis of a static equilibrium situation, it is not immediately clear in which direction some of the forces point at the time you draw a free-body diagram. In example 11.4, we didn't determine the direction of the forces exerted by the wall on the beam until the mathematical solution was completed. You can often get around this problem by considering different locations for the axis about which torques are considered. Remember, if there is equilibrium of torques about one axis then there is equilibrium about every axis.
Consider the partial free-body diagram from example 11.4, except this time we place the axis on the right end of the beam instead of on the left end. Now consider the torques about this new axis. Neither T nor Wo will exert a torque about this axis. The force Wb will try to rotate the beam counterclockwise about this axis. Since we know the beam is in equilibrium, the y-component of Fwall must be such as to balance the torque of Wb. Therefore, we can conclude that Fwall,y must point vertically upward. With a little practice you can do this kind of determination in your head fairly quickly. Afterward, you'll have a complete free-body diagram and can solve the numerical problem with the axis placed anywhere you want it.
Another tactic is to put the unknown forces in positive directions and solve the equations as you normally would. If your result comes out positive you guessed correctly; if the result comes out negative then the direction should be reversed.
III. Important Equations
| Name/Topic | Equation | Explanation |
|---|---|---|
| The magnitude of the torque due to a force F. | ||
 |
The rotational forms of Newton's second law. The lower equation is more general. | |
L = rp sinq |
The magnitude for the angular momentum. The lower equation applies to point particles. | |
| Work written in terms of rotational quantities. | ||
| Power written in terms of rotational quantites. |
IV. Know Your Units
| Quantity | Dimension | SI Unit |
|---|---|---|
 |
 |
|
 |
 |
Reference Tools and Resources by David Reid, Eastern Michigan University. ©2002 by Prentice Hall, Inc.
A Pearson Company Distance Learning at Prentice Hall Legal Notice |
