The tape in a videotape cassette has a total length 266 m and can play for 1.5 h. As the tape starts to play, the full reel has an outer radius of 35 mm and an inner radius of 13 mm. At some point during the play,both reels will have the same angular speed. What is this common angular speed? Answer in units of rad/s Your r

To find the common angular speed at which both reels have the same angular speed, we need to use the relationship between linear speed, angular speed, and radius.<br /><br />Given information:<br />- Total length of the tape: 266 m<br />- Playing time: 1.5 h (5400 s)<br />- Outer radius of the full reel: 35 mm (0.035 m)<br />- Inner radius of the full reel: 13 mm (0.013 m)<br /><br />Step 1: Calculate the linear speed of the tape.<br />Linear speed = Total length of the tape / Playing time<br />Linear speed = 266 m / 5400 s = 0.0493 m/s<br /><br />Step 2: Calculate the angular speed of the full reel.<br />Angular speed = Linear speed / Outer radius<br />Angular speed = 0.0493 m/s / 0.035 m = 1.41 rad/s<br /><br />Step 3: Calculate the angular speed of the inner reel.<br />Angular speed = Linear speed / Inner radius<br />Angular speed = 0.0493 m/s / 0.013 m = 3.78 rad/s<br /><br />Step 4: Find the common angular speed at which both reels have the same angular speed.<br />Since the linear speed is constant, the angular speed will be the same for both reels when the radius is the same.<br />Therefore, the common angular speed is 1./s.