Question

A cd has diameter of 120 millimeters. When playing audio, the angular speed varies to keep the linear speed constant where the disc is being read. When reading along the outer edge of the disc, the angular speed is about 206 rpm (revolutions per minute). Find the linear speed in meters/second. (round your answer to three decimal places.)

Answer 1

we are given

A cd has diameter of 120 millimeters

so, d=120mm

so, firstly, we will find radius

$r=\frac{d}{2}$

we can plug it

$r=\frac{120}{2}mm$

$r=60mm$

we know that

1mm=0.001m

so, we get

$r=60*0.001m$

$r=0.06m$

the angular speed is about 206 rpm

we know that

1 revolution =2pi radians

so, we get

$w=200*2\pi rad/min$

now, we can change it into seconds

1 min =60 seconds

so, we get

$w=200*2\pi *\frac{1}{60} rad/sec$

$w=20.94395 rad/sec$

now, we can find linear speed(v)

we can use formula

v=w*r

so, we can plug values

and we get

$v=20.94395*0.06 m/sec$

$v=1.256637 m/sec$

so, linear speed is 1.257 m/sec............Answer