- Penn State Schuylkill
B. Ways to change centripetal acceleration
1. How does a change in velocity affect 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 |
x 1/16 |
1. How does acceleration change with the radius of the circle?
| ac = | V2 |
| r |
Inverse Relationship (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 kg cart travels in a horizontal circle at a constant speed of 6m/s. If the radius of the circle is 3m, what is the centripetal acceleration?
| ac = | V2 |
| r |
ac = (6m/s)2/3 m
= 12 m/s2
Challenge: Calculate the speed an earth satellite must have to enter a circular orbit at an altitude of 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 enter a circular orbit at an altitude of 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
