we are given
A cd has diameter of 120 millimeters
so, d=120mm
so, firstly, we will find radius
[tex]r=\frac{d}{2}[/tex]
we can plug it
[tex]r=\frac{120}{2}mm[/tex]
[tex]r=60mm[/tex]
we know that
1mm=0.001m
so, we get
[tex]r=60*0.001m[/tex]
[tex]r=0.06m[/tex]
the angular speed is about 206 rpm
we know that
1 revolution =2pi radians
so, we get
[tex]w=200*2\pi rad/min[/tex]
now, we can change it into seconds
1 min =60 seconds
so, we get
[tex]w=200*2\pi *\frac{1}{60} rad/sec[/tex]
[tex]w=20.94395 rad/sec[/tex]
now, we can find linear speed(v)
we can use formula
v=w*r
so, we can plug values
and we get
[tex]v=20.94395*0.06 m/sec[/tex]
[tex]v=1.256637 m/sec[/tex]
so, linear speed is 1.257 m/sec............Answer
We will find that the linear speed of the outer rim of the cd is 1.29 m/s.
For the rotation pf an object of radius R that rotates with an angular speed ω the linear speed is:
S = |ω*R|
In this case, we know that:
R = 120mm/2 = 60mm
And the angular speed is 2*pi times the frequency, so we get:
ω = 2*3.14*(206 mîn^-1) = 1,293.68 min^-1
But we want the speed in meters/second, so we need to rewrite both of these quantities.
Knowing that:
R = 60mm = 60*(10^-3 m) = 0.06m
ω = 1,293.68 min^-1 = ( 1,293.68/60) s^-1 = 21.56 s^-1
Then the linear speed is:
S = (0.06 m)*(21.56 s^-1) = 1.29 m/s
If you want to learn more about rotations, you can read:
https://brainly.com/question/9408577
