A star rotates in a circular orbit about the center of its galaxy. The radius of the orbit is 3.7 x 1020 m, and the angular speed of the star is 9.3 x 10-15 rad/s. How long (in years) does it take for the star to make one revolution around the center?
A star rotates in a circular orbit about the center of its galaxy. The radius of the orbit is 3.7 x 1020 m, and the angular speed of the star is 9.3 x 10-15 rad/s. How long (in years) does it take for the star to make one revolution around the center?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A star rotates in a circular orbit about the center of its galaxy. The radius of the orbit is 3.7 x 1020 m, and the angular speed of the star is 9.3 x 10-15 rad/s. How long (in years) does it take for the star to make one revolution around the center?
Transcribed Image Text:This image illustrates a radial concept often used in physics and engineering related to circular motion. It features a spiral shape to depict rotational movement.
- **Diagram Components:**
- The central point serves as the origin of rotation.
- A line labeled "r" extends from the center to the perimeter, representing the radius of the circle.
- A dashed circular line encircles the spiral, indicating the path of rotational motion.
- A point on this path is marked with a yellow dot, representing an object moving along the circle.
- An arrow labeled "v_T" points tangentially to the circle at the position of the yellow dot, indicating the direction of tangential velocity. This demonstrates the velocity is perpendicular to the radius at any point on the circle.
This diagram provides a visual representation of how tangential velocity is situated in relation to the radius and movement in circular dynamics. It can be used to explain concepts like rotational speed and angular momentum.
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