a) Angular speed of the innermost part: 50 rad/s, outermost part: 21.6 rad/s
b) The length of the track would be 5,550 m
c) The average angular acceleration is
Explanation:
a)
For an object in uniform circular motion, the relationship between angular speed and linear speed is
where
v is the linear speed
is the angular speed
r is the radius of the circle
Here the linear speed of the track is constant:
v = 1.25 m/s
For the innermost part of the disk,
r = 25.0 mm = 0.025 m
So the angular speed is
For the outermost part,
r = 58.0 mm = 0.058 m
So the angular speed is
b)
The maximum playing time of the disk is
If the track was stretched out in a straight line, the motion of the track would be a uniform motion (since it is moving at constant speed), so we can use the equation
where
v is the linear speed
d is the length coverted in a straight line
t is the time
Substituting v = 1.25 m/s and solving for d,
c)
The angular acceleration is given by
where
is the final angular speed
is the initial angular speed
t is the time
A CD is read from the innermost part to the outermost part, so we have:
(at the innermost part)
(at the outermost part)
t = 74.0 min = 4440 s is the time
Substituting, the average angular acceleration is
where the negative sign means the CD is decelerating.
Learn more about circular motion:
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