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Compute the rotor speed of a shredder.

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Compute the rotor speed of a shredder. The shredder's motor inertia is 75,000 lb-ft2, starting time is 30 seconds, and power is 80 kW.

asked Mar 4, 2014 in Others by tracig2401 (240 points)

1 Answer

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We need to look at the total energy exerted by the motor in this time: \( Energy = Power * Time) \)

$$E= P t = 80 kW \cdot 30 sec = 2400 kJ = 2.4 \cdot 10^6 J$$

Angular kinetic energy is  \( E = \frac{1}{2} I \omega^2 \)
with \(\omega\) being the angular velocity in radians per second
and \( I \) being the moment of inertia in \(kg \cdot m^2 \).

We need to convert the given moment of inertia into appropriate units:

$$7.5*10^4 lb \cdot ft^2  \cdot \frac{1 kg}{2.2 lb} \cdot (\frac{0.305 m}{1 ft})^2 = 3170 kg \cdot m^2 $$

Then solve our energy equation for the angular velocity:

$$\omega = \sqrt{\frac{2 E}{I}} =  38.9 \frac{rad}{sec}$$

Converting this to rotations per minute:

$$38.9 \frac{rad}{sec} \cdot \frac{1 rot}{ 2 \pi} \cdot \frac{ 60 sec}{1 min} =372 RPM $$
answered Mar 13, 2014 by jcf1559 (2,140 points)
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