A particle moves with ω =constant and r = r0eβt where r0 and β are constants. For what values of β is the radial force zero?

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A particle moves with ω =constant and r = r0eβt where r0 and β are constants. For what values of β is the radial force zero?

 

The image displays a two-dimensional spiral plotted on a coordinate plane. The spiral starts at the origin, where the x-axis and y-axis intersect, and gradually moves outward while curving around the origin. Here’s a detailed explanation:

1. **Axes**:
   - The horizontal line represents the x-axis.
   - The vertical line represents the y-axis.
   - Both axes have arrows indicating positive directions.

2. **Spiral**:
   - The spiral begins at the origin (0,0) and expands outward in a circular motion.
   - It curves around the origin in a counter-clockwise direction, forming multiple loops as it extends.

This spiral represents a common mathematical shape often used to study properties in polar coordinates, growth patterns, and natural phenomena.
Transcribed Image Text:The image displays a two-dimensional spiral plotted on a coordinate plane. The spiral starts at the origin, where the x-axis and y-axis intersect, and gradually moves outward while curving around the origin. Here’s a detailed explanation: 1. **Axes**: - The horizontal line represents the x-axis. - The vertical line represents the y-axis. - Both axes have arrows indicating positive directions. 2. **Spiral**: - The spiral begins at the origin (0,0) and expands outward in a circular motion. - It curves around the origin in a counter-clockwise direction, forming multiple loops as it extends. This spiral represents a common mathematical shape often used to study properties in polar coordinates, growth patterns, and natural phenomena.
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