What is the relationship between frequency and angular speed?

[urekmazino]

Hello there, I'm new here and i need some help on my home work.

A DVD drive rotates at an angular frequency of 4800 rpm. a) what is it's angular speed in rpm? b) at 4800 rpm, what is the linear speed (in knm/hr) of (i) the center point and points (ii) 5 cm and (iii) 6 cm from the center?
Thanks!

 

[Olinguito]

Hi urekmazino.

(a) If a device rotates at $f$ revolutions per minute, it will go through $2\pi\times f$ radians in that time. Thus the formula between angular speed $\omega$ and frequency $f$ is
$$\omega\ =\ 2\pi f.$$
Note that whereas frequency (in this problem) is measured in revolutions per minute, angular speed is measured in radians per minute.

(b) The linear (or tangential) speed of a point at distance $r$ from the centre of revolution is $r\omega$, where $\omega$ is the angular speed. In this case, multiplying angular speed in radians per minute by radius in centimetres will give a linear speed in centimetres per minute. Can you convert it to kilometres per hour?