Answer
The linear speed of a point on the edge of the flywheel is 39.6 m/s
Work Step by Step
The flywheel rotates through an angle of $2\pi$ radians 90 times each second. We can find the angular speed of the flywheel:
$\omega = \frac{\theta}{t}$
$\omega = \frac{(2\pi~rad)(90)}{1~s}$
$\omega = (180~\pi)~rad/s$
We can find the linear speed of a point on the edge of the flywheel:
$v = \omega ~r$
$v = (180~\pi~rad/s)(7~cm)$
$v = 3960~cm/s$
$v = 39.6~m/s$
The linear speed of a point on the edge of the flywheel is 39.6 m/s