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