8.0 - Introduction

A child riding on a carousel, you riding on a Ferris wheel: Both are examples of

uniform circular motion. When the carousel or Ferris wheel reaches a constant rate

of rotation, the rider moves in a circle at a constant speed. In physics, this is called

uniform circular motion.

Developing an understanding of uniform circular motion requires you to recall the

distinction between speed and velocity. Speed is the magnitude, or how fast an

object moves, while velocity includes both magnitude and direction. For example,

consider the car in the graphic on the right. Even as it moves around the curve at a

constant speed, its velocity constantly changes as its direction changes. A change

in velocity is called acceleration, and the acceleration of a car due to its change in

direction as it moves around a curve is called centripetal acceleration.

Although the car moves at a constant speed as it moves around the curve, it is

accelerating. This is a case where the everyday use of a word í acceleration í and

its use in physics differ. A non-physicist would likely say: If a car moves around a

curve at a constant speed, it is not accelerating. But a physicist would say: It most

certainly is accelerating because its direction is changing. She could even point out,

as we will discuss later, that a net external force is being applied on the car, so the car must be accelerating.

Uniform circular motion begins the study of rotational motion. As with linear motion, you begin with concepts such as velocity and acceleration

and then move on to topics such as energy and momentum. As you progress, you will discover that much of what you have learned about

these topics in earlier lessons will apply to circular motion.

In the simulation shown to the right, the car moves around the track at a constant speed. The red velocity vector represents the direction and

magnitude of the car’s instantaneous velocity.

The simulation has gauges for the x and y components of the car's velocity. Note how they change as the car travels around the track. These

changes are reflected in the centripetal acceleration of the car. You can also have the car move at different constant speeds, and read the

corresponding centripetal acceleration in the appropriate gauge. Is the centripetal acceleration of the car higher when it is moving faster? Note:

If you go too fast, you can spin off the track. Happy motoring!

8.1 - Uniform circular motion

Uniform circular motion: Movement in a circle

at a constant speed.

The toy train on the right moves on a circular track in uniform circular motion. The

identical lengths of the velocity vectors in the diagram indicate a constant magnitude of

velocityí a constant speed. When an object is moving in uniform circular motion, its

speed is uniform (constant) and its path is circular.

The train does not have constant velocity; in fact, its velocity is constantly changing.

Why? As you can also see in the diagram to the right, the direction of the velocity vector

changes as the train moves around the track. A change in the direction of velocity

means a change in velocity. The velocity vector is tangent to the circle at every instant

because the train’s displacement is tangent to the circle during every small interval of

time.

Uniform circular motion is important in physics. For instance, a satellite in a circular orbit

around the Earth moves in uniform circular motion.

Uniform circular motion

Motion in a circle with constant speed

Instantaneous velocity always tangent

·Velocity changes!

(^166) Copyright 2000-2007 Kinetic Books Co. Chapter 08