A review of the basics of circular motion: The radius of a merry-go-round is 14 meters, and it takes 10 seconds to go around once. We want to calculate the speed of an atom in the outer rim. First, how far does the atom go in 12 s?

a. What is the speed of the atom?
b. What is the direction of the velocity of this atom?

In 12 s, atom goes 17.592 m distance.

(a) Speed of the atom is 8.796 m/s.

(b) The direction of the velocity of this atom is tangent to the circle.

Explanation:

Let r be the radius of the circular path and v be the speed of the atom in the outer rim.

Circumference of the circular path, d = 2πr

Substitute 14 m for r in the above equation.

Circumference of the circular path, d = 2 x π x 14 = 87.96 m

According to the problem, atom completes a revolution in 10 seconds. So, atom covers 87.96 m in 10 seconds.

Distance covered by atom in 1 second = = 8.796 m

Since, atom come back to its initial position after 10 seconds, so displacement of atom is zero. Hence,

Distance covered by atom in 12 seconds = 8.796 x 2 = 17.592 m

(a) Speed of the atom is determine by the relation :

v = =

v = 8.796 m/s

(b) In circular motion, the direction of the velocity of the atom is tangent to the the circle.  

causes

fossil fuels burn

cities become more industrialized

human population grows worldwide