1. A-level Physics
Unit G484:
The Newtonian
World
The mathematical description
of circular motion
Circular motion

2. Uniform motion in a circle LOs
u
1
v
2
Questions
1. Comparing situations 1 and 2,
- what is the same?
- what has changed?
2. explain your second answer [2 marks] .
Circular motion LO 1: describe motion in a circle in terms of acceleration and force

3. Uniform motion in a circle LOs
u
1
v
2
Questions
3. Sketch a vector diagram to show the change in the
velocity (∆v) of the object.
4. In which direction does ∆v point if we make the time
interval between 1 and 2 very small?
Circular motion LO 1: describe motion in a circle in terms of acceleration and force

4. Uniform motion in a circle LOs
u
v
Questions
5. What has happened because the velocity of the object
has changed?
6. What must have made this change happen? [2 marks]
Circular motion LO 1: describe motion in a circle in terms of acceleration and force

5. Lesson focus
• An introduction to circular motion
Learning objectives
At the end of the lesson you will be able to:
• describe motion in a circle in terms of acceleration and force;
• use the equation for speed v = 2πr/T ;
• define the radian;
• convert angles from degrees into radians and vice versa.
Circular motion

6. Learning outcomes
All of you should be able to
• define the radian;
• convert from degrees to radians (and vice versa);
• write an equation to describe the speed of an object moving in a circle.
Most of you should be able to
• write an expression for angular frequency in terms of Θ and t;
• write an expression for angular frequency in terms of Θ and T;
• connect the linear and angular speed of an object travelling in a circle.
Circular motion

7. Moving in a circle: speed LOs
To do
A particle is moving at a constant speed in a  v
circular path.
1. Write down an expression for the r
speed of the particle in terms of v,
r and the time period, T.
2. Do the same in terms of v, r and f .
Circular motion LO 2: use the equation for speed

8. The radian LOs
Definition
The radian is a unit of angular measure.
One radian is the angle subtended at the centre of a circle by an arc equal in
length to the circle’s radius.
Circular motion LO 3: define the radian

9. Using radians LOs
To answer
The diagram shows a segment of a circle of radius
1.50 m. The angle at the centre is 1.00 rad.
1.00
rad
a. What is the length of the arc? 1.50 m
b. If the angle at the centre is increased to
2.00 rad, what is the new length of the arc?
c. Write down an equation relating c, the arc
length, to the radius r and the angle θ
measured in radians.
Now answer Q1 on p 25 of your textbook.
Circular motion LO 3: define the radian

10. More about the speed of circular motion LOs

v
Θ
Angular frequency (= angular speed, ω)
angle through which object moves
angular frequency =
time taken
Θ
i.e. ω =
t
2π rad (rad s-1)
For one revolution, ω = Unit:
T s
Circular motion LO 2: use the equation for speed

11. Angular frequency vs linear speed LOs

v
Θ
Now express linear speed in terms of angular frequency
2πr
v = = 2πrf
T
 v = ωr
2π
ω = = 2πf
T
Circular motion LO 2: use the equation for speed