A serious audiophile prefers to listen to music on his vinyl record turntable. The 12-inch diameter disk rotates at a constant 33 rpm. How fast is the record passing by the pickup cartridge tip at a radius of 4 inches 1 inch = 2.54 cm)?

Question

Quizplus · Accepted Answer

First, we need to convert the radius from inches to cm:

4 inches x 2.54 cm/inch = 10.16 cm

Next, we can use the formula for linear velocity:

v = ωr

where v is the linear velocity, ω is the angular velocity (in radians/second), and r is the radius. We know that the record rotates at 33 rpm, which is equivalent to 3.47 radians/second (since 1 revolution = 2π radians and there are 60 seconds in a minute):

ω = 33 rpm x 2π/60 = 3.47 rad/s

Plugging in the values, we get:

v = (3.47 rad/s) x (10.16 cm) = 35.3 cm/s

Rounding to the nearest tenth, the answer is 35 cm/s (choice B).

A Serious Audiophile Prefers to Listen to Music on His