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If the CD rotates clockwise at 500 {\rm rpm} (revolutions per minute) while the last song is playing, and then spins down to zero angular speed in 2.60 {\rms} with constant angular acceleration, what is \text type{\alpha }{alpha}, the magnitude of the angular acceleration of the CD, as it spins to a stop?

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MechEngineer

Answer:

20138 rad/s2

Explanation:

We can convert 500 revolution per minute to radians per second

[tex]\omega = 500rev/min*2\pi rad/rev *\frac{1}{60}min/sec = 52.36 rad/s[/tex]

If the CD is coming to rest at a constant angular acceleration within 2.6 ms (or 0.0026s), this means:

[tex]\alpha = \frac{\delta\omega}{\deltat} = \frac{52.36 - 0}{0.0026} = 20138 rad/s^2[/tex]

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