Uniform Circular Motion

 

In order for an object to move at constant speed in a circle, an outside

 

 ______________ must constantly pull the object toward

_____________of circular

 

path.

 

A.     The Equations and Vectors

 

1.    ________________________________ (ac) –

 

 

 

 

Mass moving with circular motion

 

 

 

 

 

 

 

 

 

 

 

 

a)     Equation: _________________ (On reference table)

                

Units 

 

b)     (v) _______________________ velocity - _______________


to circle, in the direction of the motion

 

c)     _____________________ acceleration - directed toward the


____________ of the circle

 

d)     Example problem)

 

Ex) A car moving in a circular path with a radius of 2 m has a velocity of 8 m/s. What is the centripetal acceleration of this car?

 

 

 

 

B.  Different ways we can change centripetal acceleration

 

1. How does acceleration change with velocity?

 

ac = v 2 / r

 

¨       ***Answer - ____________________________ Relationship (Both variables on top, one is squared)

V

ac

X2

X

X3

X

X4

 

1.      How does acceleration change with the radius of the circle?

 

¨       *** Answer - ___________Relationship

 

ac

R

X

X2

X

X3

 

X4

 

C.  More circular Motion Word Problems

 

Example: 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?

 

Equation:

 

 

 

 

 

 

 

 

Challenge Example: Calculate the speed an earth satellite must have to enter a circular orbit at an altitude of 200 km where the acceleration due to gravity at 200,000 m is 9.2 m/s 2 and the radius of earth of earth is 6,400,000 m

 


 

                                                                  

 

 

 

D. Centripetal Force (Fc) - _____________ directed toward


___________________________ which keeps an object moving in a uniform circular path

                            

                             Fc =   mac   =    

                                                      

 

                Force units         (_______________)  or

 

Ex) A 5 kg object moves in a circle at a constant speed of 10 m/s. What is the radius of the object's circular path if the object's centripetal force is 1000 Newtons?

 

E. Changing the Centripetal Force

 

     1.      How does centripetal force change with mass?

 

m

Fc

X2

X

X3

X

 

X4

 

 

 

 

 

 

2.      How does centripetal force change with radius?

 

¨       __________________ Relationship (One variable on top, other on bottom)

 

Fc

R

X

X2

X

X3

 

X4

 

3.      How does centripetal force change with velocity?

 

¨       _____________________ Relationship (Both variables on top, one is squared)

 

v

Fc

X2

X

X3

X

X4