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

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)

Quizplus · Accepted Answer

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

4 inches x 2.54 cm/inch = 10.16 cm

Next, we can use the formula for linear speed:

v = ωr

where v is the linear speed, ω is the angular speed in radians per second, and r is the radius.

We are given the angular speed in revolutions per minute (rpm), so we need to convert it to radians per second:

ω = (33 1/3 rpm) x (2π radians/revolution) ÷ 60 seconds/minute
ω = 3.49 radians/second

Now we can plug in the values and solve for v:

v = (3.49 radians/second) x (10.16 cm)
v ≈ 35 cm/s

Therefore, the correct answer is choice B: 35 cm/s.

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