A 3-m radius disk is rotating at 6 rad/sec. What is the linear speed of a point that lies on the circumference of the disk?

v = rω = 3*6 = 18 m/s

what about this one:

A cyclist is moving at 6.7 meters/sec, on a bike with 0.25 m radius wheels. What is the angular speed of the wheels, in rad/sec?

The speed of the bike is the same as the speed of a point on the tire, right?

v = rω
6.7 = 0.25ω
so, ω = ___

To find the linear speed of a point on the circumference of the disk, you can use the formula:

Linear Speed = Angular Speed * Radius

In this case, the given angular speed is 6 rad/sec and the radius of the disk is 3 meters.

So, plug in the values into the formula:

Linear Speed = 6 rad/sec * 3 meters

Multiplying the values gives:

Linear Speed = 18 meters/sec

Therefore, the linear speed of a point on the circumference of the disk is 18 meters/sec.