Question

A vinyl record makes 90 rotations in a minute. The diameter of the disk is 34 cm. Find the linear velocity of a point on the circumference of the disk in m/s.

Answer 1

Answer: 1.6 m/s

Step-by-step explanation:

The relationship between linear speed and angular speed for a rotational motion is

`v=\omega r`

where

v is the linear speed

`\omega` is the angular speed

r is the distance from the axis of rotation

For the vinyl record here, we have:

`\omega=90 rev/min`

Keeping in mind that

`1rev = 2\pi rad\\1 min =60 s`

We can convert it to rad/s:

`\omega = 90 \cdot (2\pi)/(60)=9.4 rad/s`

The diameter of the disk is 34 cm, so the radius is

`r=(34)/(2)=17 cm = 0.17 m`

Therefore, the linear velocity of a point on the circumference is

`v=(9.4)(0.17)=1.6 m/s`