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?

 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