Module 5—Circular Motion

 Lesson Summary

 

This lesson focused on the solution of these questions:

• How do Newton’s first and second laws apply to circular motion?
  
  
• What factors affect acceleration during circular motion?

When an object travels in a circular path, there must be an inward force causing the direction of the motion to change. The inward force can be friction, tension, or gravity, for example. This is a direct application of Newton's first and second laws of motion. It may also be observed, by whirling an object at the end of a string, that there is a relationship between the size of the force and the speed of the object, the mass of the object, and the radius of the arc through which the object moves. Such relationships can be applied to the design and operation of objects that move in horizontal circular paths, such as those commonly experienced in carnival rides.

 

Inward (centripetal) force can be mathematically described by the relationship among velocity, mass, and radius for an object rotating in a horizontal plane. Expressed as an equation,

 

 

Quantity	Symbol	SI Unit
inward (centripetal) force	Fc	N
mass	m	kg
radius of circular path	r	m
speed	v	m/s

 

Applying Newton’s second law to the equation for centripetal force gives the following expression for centripetal acceleration:

 

 

Lesson Glossary

 

centripetal: directed toward the centre of a circle

 

frequency: the number of cycles in a time period (f)

 

horizontal plane: a plane perpendicular to a radius of Earth, usually used to suggest that there is no vertical component to motion or forces

 

period: the time for one complete cycle (T)

 

uniform circular motion: the motion of an object with a constant speed along a circular path