Angular Speed of Disk with 260 kg Mass and 69 kg Person

[playboy2006]

A flat uniform circular disk (radius = 1.90 m, mass = 260 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a frictionless axis perpendicular to the center of the disk. A 69.0-kg person, standing 1.97 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 3.10 m/s relative to the ground. Find the resulting angular speed (in rad/s) of the disk.

dont understand
please help

 

[Apple123]

Show me some work, and then ill help you. Or atleast convince yourself of the concept. I'd be happy to help, but i don't want to do it for you.

 

[quicknote]

To find the resulting angular speed of the disk, we can use the equation w = v/r, where w is the angular speed, v is the tangential speed, and r is the radius of the circular path. In this case, the radius of the circular path is the distance between the person and the axis, which is 1.97 m. Plugging in the values, we get:

w = (3.10 m/s) / (1.97 m)
= 1.57 rad/s

Therefore, the resulting angular speed of the disk is 1.57 rad/s. This means that the disk is rotating at a rate of 1.57 radians per second.