The CD player in your computer rotates a disc at 7200rmp. Determine its velocity in:
a)degrees per second
b)radians per minute
a. multiply by 360deg/rev
b. multiply by 2PI rad/rev
what is rev?
revolutions
is that just the units?
To determine the velocity of the CD player disc in degrees per second, we need to convert the given rotational speed from revolutions per minute (RPM) to degrees per second.
a) Degrees per second:
Since there are 360 degrees in a circle, we can multiply the rotational speed in RPM by 360 to get the angular velocity in degrees per minute. Then, divide by 60 to convert it to degrees per second.
Angular velocity in degrees per minute = RPM * 360
angular velocity in degrees per second = (RPM * 360) / 60
In this case, the rotational speed is given as 7200 RPM:
Angular velocity in degrees per minute = 7200 RPM * 360 = 2,592,000 degrees per minute
Angular velocity in degrees per second = 2,592,000 degrees per minute / 60 = 43,200 degrees per second
Therefore, the velocity of the CD player disc in degrees per second is 43,200 degrees per second.
b) Radians per minute:
To determine the velocity of the CD player disc in radians per minute, we need to convert the given rotational speed from revolutions per minute (RPM) to radians per minute.
In one revolution (360 degrees), there are 2π radians. Therefore, we can multiply the rotational speed in RPM by 2π to get the angular velocity in radians per minute.
Angular velocity in radians per minute = RPM * (2π)
In this case, the rotational speed is given as 7200 RPM:
Angular velocity in radians per minute = 7200 RPM * (2π) = 14,400π radians per minute
Therefore, the velocity of the CD player disc in radians per minute is 14,400π radians per minute.