To solve this problem, we need to break it down into two parts:
(a) The total angular displacement of the disc as it plays from the outside at 2.10 cm to the inside at 6.10 cm.
First, let's convert the given values into meters:
- Outside radius (Rout) = 2.10 cm = 0.0210 m
- Inside radius (Rin) = 6.10 cm = 0.0610 m
Next, we can find the circumference of the disc at both the inside and outside:
- Circumference at outside edge = 2Ï€Rout
- Circumference at inside edge = 2Ï€Rin
Then, we can subtract the two circumferences to find the difference:
- Difference in circumference = Circumference at inside edge - Circumference at outside edge
Now, we can divide the difference in circumference by the length of one bit (0.60 mm = 0.0006 m) to find the total number of bits on the track:
- Total number of bits = Difference in circumference / Length of one bit
Finally, we can calculate the angular displacement using the formula:
- Angular displacement = Total number of bits * length of one bit / Circumference at inside edge
(b) The total length of the track.
To find the total length of the track, we can calculate the length between the two circumferences:
- Length between the two circumferences = Difference in circumference
Then, we can calculate the total length of the track (L) by multiplying the length between circumferences with the total number of bits:
- Total length of the track = Length between the two circumferences * Total number of bits
By following these steps, we can find the solutions to both parts of the problem.