Question

21 multiple choice 1 point what is the acceleration of a piece of dust on an old - fashioned record album, 15 cm from the center, if the record is spinning at 33.3 rpm? 1.8 m/s² 1 m/s² 18.5 m/s² 0 m/s²

Explanation:

Step1: Convert angular velocity from rpm to rad/s

The formula to convert revolutions per minute (rpm) to radians per second (rad/s) is \(\omega=\frac{2\pi N}{60}\), where \(N = 33.3\) rpm.
\(\omega=\frac{2\pi\times33.3}{60}\) rad/s \(\approx 3.49\) rad/s.

Step2: Calculate centripetal acceleration

The formula for centripetal acceleration is \(a = r\omega^{2}\). Given \(r=15\space cm=0.15\space m\) and \(\omega\approx3.49\) rad/s.
\(a=(0.15)\times(3.49)^{2}\)
\(a = 0.15\times12.18\)
\(a\approx1.8\space m/s^{2}\)

Answer:

1.8 m/s²