Question

Carlos has a collection of old vinyl records. To play some of the records, the turntable rotates through an angle of 3/2pi radians in 1 second. How many revolutions does the record make in one minute?

A. 33 1/3 revolutions per minute
B. 45 revolutions per minute
C. 78 revolutions per minute
D. 16 2/3 revolutions per minute

Answer 1

Explanation:

We know that the turntable rotates through an angle of 3/2pi radians in 1 second.

To find the number of revolutions in one minute, we need to convert the angle to revolutions per minute.

There are 2π radians in one revolution, so we can set up a proportion:

(3/2π radians) / (1 second) = (x revolutions) / (1 minute)

To solve for x, we can cross-multiply and simplify:

(3/2π) * (1 minute) = x * (1 second) * (2π)

x = (3/2π) * (60/1)

x = 45 revolutions per minute

Therefore, the answer is B. 45 revolutions per minute.

I hope it helps!!