Rotational Kinematics: Difference between revisions
| Line 8: | Line 8: | ||
===A Mathematical Model=== | ===A Mathematical Model=== | ||
Rotation can be characterized by its angular velocity and angular acceleration. The equations | Rotation can be characterized by its angular velocity and angular acceleration. The equations are listed below. | ||
Angular velocity: | |||
:<math>\boldsymbol{{w}} = \frac{\boldsymbol{v}}{\boldsymbol{r}}</math> , | :<math>\boldsymbol{{w}} = \frac{\boldsymbol{v}}{\boldsymbol{r}}</math> , | ||
where <math>{\boldsymbol{v}}</math> is the velocity of the object and <math>{\boldsymbol{r}}</math> is the radius of the circle of motion. | where <math>{\boldsymbol{v}}</math> is the velocity of the object and <math>{\boldsymbol{r}}</math> is the radius of the circle of motion. | ||
Angular acceleration is equal to alpha: | |||
:<math>\boldsymbol{{alpha}} = \frac{\boldsymbol{a_t}}{\boldsymbol{r}}</math> , | |||
where <math>{\boldsymbol{a_t}}</math> is the tangential acceleration of the object and <math>{\boldsymbol{r}}</math> is the radius of the circle of motion. | |||
===A Computational Model=== | ===A Computational Model=== | ||
Revision as of 23:41, 3 December 2015
This page is all about rotation and it's relation to torque. This page is very much a work still in progress by sthevuthasan3.
The Main Idea
Rotational motion is defined as when an object moves about an axis in a circle versus translational motion which involves the object moving in a straight trajectory.
A Mathematical Model
Rotation can be characterized by its angular velocity and angular acceleration. The equations are listed below.
Angular velocity:
- [math]\displaystyle{ \boldsymbol{{w}} = \frac{\boldsymbol{v}}{\boldsymbol{r}} }[/math] ,
where [math]\displaystyle{ {\boldsymbol{v}} }[/math] is the velocity of the object and [math]\displaystyle{ {\boldsymbol{r}} }[/math] is the radius of the circle of motion.
Angular acceleration is equal to alpha:
- [math]\displaystyle{ \boldsymbol{{alpha}} = \frac{\boldsymbol{a_t}}{\boldsymbol{r}} }[/math] ,
where [math]\displaystyle{ {\boldsymbol{a_t}} }[/math] is the tangential acceleration of the object and [math]\displaystyle{ {\boldsymbol{r}} }[/math] is the radius of the circle of motion.
A Computational Model
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