Angular Speed | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

Angle turned each second

is the angular displacement divided by the time taken. Its symbol is $\omega$ .
Angular speed tells us how quickly the angle changes. It does not tell us the speed along the circular path.

Definition

2 marks

Model answer: The angular displacement turned per unit time.

\omega=\dfrac{\Delta\theta}{\Delta t}

Symbols

The is the time for one full turn. One full turn is $2\pi$ rad.
The is the number of full turns each second. Its unit is hertz (Hz).
Revolutions per minute means turns per minute. Divide by 60 to get turns per second before using the frequency form below.

\omega=\dfrac{2\pi}{T}

\omega=2\pi f

Worked example

One turn in five seconds

An object makes one full turn in 5.0 s. Find its angular speed.

Write down the period.
$T=5.0\text{ s}$
Substitute the period.
$\omega=\dfrac{2\pi}{T}$
$\omega=\dfrac{2\pi}{5.0}$
$\omega=1.26\text{ rad s}^{-1}$

Answer

\omega=1.26\text{ rad s}^{-1}

Your turnQuick check

A drum turns at 1200 rpm. Find its angular speed.

Show worked answer

First change revolutions per minute into revolutions per second.

f=\dfrac{1200}{60}=20\text{ Hz}

\omega=2\pi f=126\text{ rad s}^{-1}