173
Circular motion does not persist without a force
I was correct about one thing, however. To make me curve around with
the car, I really did need some force such as a force from my mother,
friction from the seat, or a normal force from the side of the car. (In fact, all
three forces were probably adding together.) One of the reasons why Galileo
failed to refine the principle of inertia into a quantitative statement like
Newton’s first law is that he was not sure whether motion without a force
would naturally be circular or linear. In fact, the most impressive examples
he knew of the persistence of motion were mostly circular: the spinning of a
top or the rotation of the earth, for example. Newton realized that in
examples such as these, there really were forces at work. Atoms on the
surface of the top are prevented from flying off straight by the ordinary
force that keeps atoms stuck together in solid matter. The earth is nearly all
liquid, but gravitational forces pull all its parts inward.
Uniform and nonuniform circular motion
Circular motion always involves a change in the direction of the velocity
vector, but it is also possible for the magnitude of the velocity to change at
the same time. Circular motion is referred to as uniform if |v| is constant,
and nonuniform if it is changing.
Your speedometer tells you the magnitude of your car’s velocity vector,
so when you go around a curve while keeping your speedometer needle
steady, you are executing uniform circular motion. If your speedometer
reading is changing as you turn, your circular motion is nonuniform.
Uniform circular motion is simpler to analyze mathematically, so we will
attack it first and then pass to the nonuniform case.
Self-Check
Which of these are examples of uniform circular motion and which are nonuni-
form.
(a) the clothes in a clothes dryer (assuming they remain against the inside of
the drum, even at the top)
(b) a rock on the end of a string being whirled in a vertical circle
(a) An overhead view of a person
swinging a rock on a rope. A force from
the string is required to make the rock's
velocity vector keep changing direc-
tion.
yes
no
(b) If the string breaks, the rock will
follow Newton's first law and go
straight instead of continuing around
the circle.
(a) Uniform. They have the same motion as the drum itself, which is rotating as one solid piece. No part of the
drum can be rotating at a different speed from any other part. (b) Nonuniform. Gravity speeds it up on the way
down and slows it down on the way up.
Section 9.1Conceptual Framework for Circular Motion