Before CDs and cassette tapes, there were vinyl records. The most comon spun with an angular velocity of 33.3 rpm . How many radians does a 33.3 rpm record rotate through in 2.70 seconds?
To find the number of radians a 33.3 rpm record rotates through in 2.70 seconds, we first need to convert the angular velocity from rpm to radians per second.
1 revolution = 2π radians
33.3 rpm = 33.3 revolutions per minute = (33.3 * 2π) radians per minute
To convert from minutes to seconds, we divide by 60:
33.3 * 2π / 60 = 33.3π / 30 radians per second (approx. 3.49 radians per second)
Now we can find the number of radians the record rotates through in 2.70 seconds:
Number of radians = angular velocity * time
= 3.49 radians per second * 2.70 seconds
= 9.423 radians (approximately)