Suppose a CAV player makes 48 revolutions per minute. Through how many degrees will a point on the edge of a CD move in 1 minute? In 2 sec?
Each revolution moves through 360 degrees.
So 48 RPM moves through 48*360° in one minute.
In two seconds, the angle is
48*360*(2/60)
=48*12
=576°
To determine the number of degrees through which a point on the edge of a CD moves, we need to know the circumference of the CD.
The circumference (C) of a circle can be calculated using the formula: C = 2πr, where π is a mathematical constant approximately equal to 3.14159 and r is the radius of the circle.
For a CD, the radius can vary but is typically around 6 cm. We will use the value of r = 6 cm for our calculations.
1. Calculating the circumference (C) of the CD:
C = 2πr
C = 2 * 3.14159 * 6 cm
C ≈ 37.7 cm (rounded to one decimal place)
Now that we know the circumference of the CD is approximately 37.7 cm, we can calculate the degrees through which a point on the CD's edge will move.
2. Calculating the degrees moved in 1 minute:
Since the CD player makes 48 revolutions per minute, a point on the edge of the CD will make 48 complete cycles around the circumference in 1 minute. Since one complete revolution is 360 degrees, the degrees moved in 1 minute can be calculated as follows:
Degrees moved in 1 minute = Number of revolutions * Degrees per revolution
Degrees moved in 1 minute = 48 * 360
Degrees moved in 1 minute = 17,280 degrees
Therefore, a point on the edge of the CD will move through 17,280 degrees in 1 minute.
3. Calculating the degrees moved in 2 seconds:
To calculate the degrees moved in 2 seconds, we need to convert the time to minutes first.
2 seconds is equal to 2/60 = 1/30 of a minute.
Degrees moved in 2 seconds = Degrees moved in 1 minute * Fraction of a minute
Degrees moved in 2 seconds = 17,280 degrees * (1/30)
Degrees moved in 2 seconds ≈ 576 degrees
Therefore, a point on the edge of the CD will move through approximately 576 degrees in 2 seconds.