MHB What is the relationship between frequency and angular speed?

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The relationship between frequency and angular speed is defined by the formula ω = 2πf, where ω is the angular speed in radians per minute and f is the frequency in revolutions per minute. For a DVD drive rotating at 4800 rpm, its angular speed can be calculated using this formula. The linear speed at a distance r from the center is determined by the equation v = rω, where v is the linear speed. To find the linear speeds at specific distances (5 cm and 6 cm) from the center, the angular speed must be converted to the appropriate units, such as kilometers per hour. Understanding these calculations is essential for solving the homework problem effectively.
urekmazino
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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!
 
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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?
 
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