Short Answer 
The procedure involves understanding the given data, deriving the effective radius of the tape, calculating the linear speed, and eventually computing the angular speed. The final result indicates that both reels achieve an angular speed of approximately 0.930 rad/s.
Step 1: Understand the Given Data
Start by reviewing the available data to comprehend the scenario fully. Key variables include:
- Total Length of Tape: L = 240 m
- Time Interval: t = 2.1 hours, which equals 7560 seconds
- Outer Radius of Tape: ro = 47 mm
- Inner Radius of Tape: ri = 11 mm
Step 2: Calculate the Effective Radius and Linear Speed
Next, you will calculate the effective radius and linear speed to find the angular speed. The effective radius (r) can be derived using:
- Formula: r = ‚à ö((ro2 + ri2)/2)
- Calculated Effective Radius: r ≈ 0.03413 m
- Linear Speed (v): v = L/t = 240 m / 7560 s = 0.0317 m/s
Step 3: Compute Angular Speed and Conclusion
Finally, you compute the angular speed (ω) using the values found earlier. The relationship between linear speed and angular speed is given by:
- Angular Speed Formula: ω = r × v
- Calculation: Substituting the values gives ω = 0.03413 m × 0.0317 m/s ≈ 0.930 rad/s
- Conclusion: Both reels have the same angular speed of 0.930 rad/s during playback.