Answer
The linear speed of a point on the record $7.4~cm$ from the turntable axis is $~~0.26~m/s$
Work Step by Step
We can express the angular speed in units of $rad/s$:
$\omega = (33\frac{1}{3}~rev/min)(\frac{1~min}{60~s})(\frac{2\pi~rad}{1~rev}) = 3.49~rad/s$
We can find the linear speed of a point on the record $7.4~cm$ from the turntable axis:
$v = \omega~r$
$v = (3.49~rad/s)(0.074~m)$
$v = 0.26~m/s$
The linear speed of a point on the record $7.4~cm$ from the turntable axis is $~~0.26~m/s$
