Circular Motion Relationships
How Velocity and Radius Drive Centripetal Acceleration
How radius and velocity combine to change centripetal acceleration
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SchuylkillB. Factors Affecting Centripetal Acceleration
1. Velocity and Acceleration?
Direct Square Relationship (Both variables on top, one is squared)
| V | a |
|---|---|
| x 2 | x 4 |
| x 3 | x 9 |
| x 4 | x 16 |
| x 1/2 | x 1/4 |
| x 1/4 | x 1/16 |
2. Acceleration and Radius?
| a | r |
|---|---|
| x 1/2 | x 2 |
| x 1/3 | x 3 |
| x 1/4 | x 4 |
| x 4 | x 1/4 |
| x 2 | x 1/2 |
C. More Word Problems
A 2.0 kg cart travels in a horizontal circle at a constant speed of 6.0 m/s.
If the r of circle is 3.0 m, what is centripetal acceleration?
Challenge
Calculate the speed an earth satellite must have to maintain a circular orbit at an altitude of 2.0 x 105 m (200,000 m) where the acceleration due to gravity is 9.2 m/s² (radius of earth is 6,400,000 m)
Calculate the speed an earth satellite must have to maintain a circular orbit at an altitude of 2.0 x 105 m (200,000 m) where the acceleration due to gravity is 9.2 m/s² (radius of earth is 6,400,000 m)
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Non-uniform Circular Motion
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Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. An object moves in a circle of fixed radius. If its speed doubles, its centripetal acceleration becomes
2. An object keeps the same speed but the radius of its circle is doubled. Its centripetal acceleration becomes
3. A 2.0 kg cart travels in a horizontal circle of radius 3.0 m at 6.0 m/s. What is its centripetal acceleration?
4. A satellite orbits 200,000 m above Earth's surface. Earth's radius is 6,400,000 m. What radius goes into ac = v²/r?
5. If both the speed and the radius are cut in half, the centripetal acceleration becomes