Answer: 1.6 m/s
Explanation:
The relationship between linear speed and angular speed for a rotational motion is
[tex]v=\omega r[/tex]
where
v is the linear speed
[tex]\omega[/tex] is the angular speed
r is the distance from the axis of rotation
For the vinyl record here, we have:
[tex]\omega=90 rev/min[/tex]
Keeping in mind that
[tex]1rev = 2\pi rad\\1 min =60 s[/tex]
We can convert it to rad/s:
[tex]\omega = 90 \cdot \frac{2\pi}{60}=9.4 rad/s[/tex]
The diameter of the disk is 34 cm, so the radius is
[tex]r=\frac{34}{2}=17 cm = 0.17 m[/tex]
Therefore, the linear velocity of a point on the circumference is
[tex]v=(9.4)(0.17)=1.6 m/s[/tex]
