Please draw diagram and answer a-c. 9.3 Relating Linear and Angular Kinematics A

Question

Please draw diagram and answer a-c. 9.3 Relating Linear and Angular Kinematics A CD stores movies and much more in a coded pattern of tiny bits 107 m deep. This pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside the player the track is scanned at a constant linear speed of 1.25 m/s. (a) What is the angular speed of the CD when the inner most part of the track is scanned? (b) What is the angular speed of the CD when the outer most part of the track is scanned? (c) The maximum playing time of the CD will be 74 minutes. What would be the length of the track on such a maximum duration if it were stretched to a straight line?

Explanation / Answer

Here ,

v = 1.25 m/s

r1 = 0.025 m

r2 = 0.058m

a) when the inner part is scanned

v = r * w

1.25 = 0.025 * w

w = 50 rad/s

the angular speed is 50 rad/s

b) when the outer part is scanned

v = r * w

1.25 = 0.058 * w

w = 21.6 rad/s

the angular speed is 21.6 rad/s

c) length of the track = speed * time duration

length of the track = 1.25 * 74 * 60 m

length of the track = 5550 m

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