The tape in a videotape cassette has a total length 191 m and can play for 1.9 h. as the tape starts to play, the full reel has an outerradius of 35 mm and an inner radius of 11 mm. at some point during the play, both reels will have the same angular speed. what is this common angular speed?

To solve this problem, we will apply the concepts related to the descriptive equations of linear motion that are related to the angular movement. Therefore we will have to:

Once the linear speed is defined as the distance traveled in a period of time (we will convert this period to international units) we will have to:

The average distance of the two turning radii will indicate the moment when the turning speed is the same, therefore

The relationship between the linear velocity and the angular velocity is given by the radius, since this is proportional to the linear velocity when multiplied by the angular velocity.

Therefore the common angular speed is 1.22rad/s