Rotational Kinematics: Difference between revisions
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A simple example and application of the concept of rotation is the earth's rotation on it's axis. It rotates once every 24 hours. What is the angular velocity? | A simple example and application of the concept of rotation is the earth's rotation on it's axis. It rotates once every 24 hours. What is the angular velocity? | ||
Angular velocity can also be represented as change in angle (theta) over change in time. In this case, the earth rotates 2pi radians in 24 hours which reduces to pi/12 radians and that becomes | Angular velocity can also be represented as change in angle (theta) over change in time. In this case, the earth rotates 2pi radians in 24 hours which reduces to pi/12 radians and that becomes degrees. | ||
===Middling=== | ===Middling=== | ||
Revision as of 02:27, 4 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.
Examples
Be sure to show all steps in your solution and include diagrams whenever possible
Simple
A simple example and application of the concept of rotation is the earth's rotation on it's axis. It rotates once every 24 hours. What is the angular velocity?
Angular velocity can also be represented as change in angle (theta) over change in time. In this case, the earth rotates 2pi radians in 24 hours which reduces to pi/12 radians and that becomes degrees.
Middling
Difficult
Connectedness
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- How is it connected to your major?
- Is there an interesting industrial application?
History
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See also
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References
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