Circular motion
A-level Physics
Unit G484: The Newtonian World
A-level Physics
Unit G484: The Newtonian World
The mathematical description
of circular motion
The mathematical description
of circular motion
Circular motion
u
v
Questions
1. Comparing situations 1 and 2,- what is the same?- what has changed?
2. explain your second answer [2 marks] .
LO 1: describe motion in a circle in terms of acceleration and force
Uniform motion in a circle LOs
12
Circular motion
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?
LO 1: describe motion in a circle in terms of acceleration and force
Uniform motion in a circle LOs
v1
2
u
Circular motion
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]
LO 1: describe motion in a circle in terms of acceleration and force
Uniform motion in a circle LOs
Circular motion
Learning objectivesAt the end of the lesson you will be able to:
Lesson focus• An introduction to circular motion
• 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
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
To do
A particle is moving at a constant speed in a
circular path.
1. Write down an expression for the
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 .
r
v
LO 2: use the equation for speed
Moving in a circle: speed LOs
Circular motion
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.
LO 3: define the radian
The radian LOs
Circular motion
To answer
The diagram shows a segment of a circle of radius
1.50 m. The angle at the centre is 1.00 rad.
a. What is the length of the arc?
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.
1.00 rad
Now answer Q1 on p 25 of your textbook.
LO 3: define the radian
1.50 m
Using radians LOs
Circular motion
Angular frequency (= angular speed, ω)
angular frequency =
i.e. ω =
For one revolution, ω =
angle through which object moves
time taken
Θt
2πT
LO 2: use the equation for speed
Θ
v
rads
Unit: (rad s-1)
More about the speed of circular motion LOs
Circular motion
Now express linear speed in terms of angular frequency
LO 2: use the equation for speed
Θ
v
v = 2πrT
= 2πrf
ω = 2πT
= 2πf
v = ωr
Angular frequency vs linear speed LOs
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