Kinematics in 2D

 
Penn State  Schuylkill

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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 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)

 

 

 

 

 

 

 

What's wrong with this picture?



 

 

 



Acceleration Vector should be directed towards center

 

 

 

 

Non-uniform Circular Motion

Penn State Schuylkill

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