# 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

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 (2,140 points)