What is the relationship between frequency and angular speed?

In summary, the conversation discusses the relationship between angular speed and frequency, as well as the formula for calculating angular speed. It also mentions the formula for calculating linear speed at different distances from the center of rotation. The steps for converting angular speed to linear speed in kilometres per hour are also mentioned.
  • #1
urekmazino
3
0
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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  • #2
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?
 

FAQ: What is the relationship between frequency and angular speed?

What is the difference between frequency and angular speed?

Frequency refers to the number of cycles or revolutions per unit time, while angular speed is the rate at which an object rotates or revolves around a fixed point. Frequency is measured in hertz (Hz) while angular speed is measured in radians per second (rad/s).

How are frequency and angular speed related?

Frequency and angular speed are directly proportional to each other. This means that as the frequency increases, the angular speed also increases. Similarly, as the frequency decreases, the angular speed also decreases.

How is angular speed calculated?

Angular speed is calculated by dividing the angle through which an object rotates by the time taken to complete the rotation. It is represented by the symbol ω (omega) and is measured in radians per second (rad/s).

What is the relationship between linear speed and angular speed?

Linear speed is the distance an object travels per unit time, while angular speed is the rate of rotation per unit time. The linear speed of an object moving in a circular path is directly proportional to its angular speed and the radius of the circle. This relationship is given by the formula v = ωr, where v is the linear speed, ω is the angular speed, and r is the radius of the circle.

How does frequency affect the period of an object?

The period of an object is the time taken to complete one full cycle or revolution. As the frequency increases, the period decreases, and vice versa. This is because a higher frequency means more cycles or revolutions are completed in a given time, resulting in a shorter period.

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