A man drives a go-kart around a circular track with a diameter of 50 m, at a rate of 314 m/minute. What is the frequency at which he circles the track in hertz (Hz)?
- 0.0027 Hz
- 0.03 Hz
- 2 Hz
- 6.25 Hz
B is correct. Hertz (Hz) is a measure of frequency with units of cycles per second, usually written as 1/sec. The number of cycles around the circle can be found by dividing the velocity by the circumference.
The circle circumference is (50 x pi) meters, or approximately 157 meters. The velocity of 314 m/min means that the driver completes 2 laps/min. The frequency in Hz is thus 2 laps/1 min x 1 min/60 sec = 1/30 Hz = 0.03 Hz.
- 0.0027 Hz, incorrect, This answer results from mistaking the formula for the area of a circle (which is pi times the square of the radius) with the formula for circumference (pi times diameter).
- 0.03 Hz, correct.
- 2 Hz, incorrect, This is laps/min rather than laps/second.
- 6.25 Hz, incorrect, This is the area divided by the velocity, with units of 1/min rather than 1/sec.
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