Kinematics in 2D
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B. Factors Affecting Centripetal Acceleration
1. Velocity and Acceleration?
| ac = | V2 |
| r |
**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 |
x1/4 |
|
x 1/4 |
x1/16 |
2. Acceleration and Radius?
| ac = | V2 |
| r |
Inverse Relationship
| ac = | V2 |
| r |
(One variable on top,
other on bottom)
| a | r |
| x 1/2 | x 2 |
| x 1/3 | x 3 |
x 1/4 |
x 4 |
x 4 |
x1/4 |
x 2 |
x 1/2 |
C. More Word Problems
|
Ex) A 2.0 kg cart travels in a horizontal circle at a constant speed of 6.0 m/s. If the radius of the circle is 3.0 m, what is the centripetal acceleration? |
| ac = | V2 |
| r |
ac = (6.0m/s)2/3.0 m
= 12 m/s2
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)
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)
r = 6400,000 m + 200,000 m
= 6,600,000 m
ac = V2 /r
9.2 m/s2 =V2/(6,600,000m)
9.2 m/s2(6,600,000m) = V2
= 7,792 m/s
or 7800 m/s
(Correct significant Digits)
|
What's wrong with this picture?
|
Non-uniform Circular Motion
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