Circular Motion Relationships

 

What's wrong with this picture?



 

 

 



Acceleration Vector
should be directed towards center

 

Kinematics in 2D

 
Penn State  Schuylkill

Go Nittany Lions!!

 

 

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 r of  circle is 3.0 m, what is 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)

 

 

[ Flash ]

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)

 

 

 

 

Non-uniform Circular Motion

Penn State Schuylkill

Go Nittany Lions!!

 

 

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