A flywheel is a solid disk that rotates about an axis that is perpendicular to the disk at its center. Rotating flywheels provide a means fo

Question

A flywheel is a solid disk that rotates about an axis that is perpendicular to the disk at its center. Rotating flywheels provide a means for storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electric cars. The gasoline burned in a 445-mile trip in a typical midsize car produces about 4.66 x 109 J of energy. How fast would a 19.7-kg flywheel with a radius of 0.351 m have to rotate to store this much energy

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Neala 5 years 2021-08-09T12:47:36+00:00 1 Answers 16 views 0

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  1. thuthao
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    2021-08-09T12:49:00+00:00
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    Answer:

    8.37*10^5 rpm

    Explanation:

    Given that rotational kinetic energy = 4.66*10^9J

    Mass of the fly wheel (m) = 19.7 kg

    Radius of the fly wheel (r) = 0.351 m

    Moment of inertia (I) = \frac{1}{2} mr ^2

    Rotational K.E is illustrated as (K.E)_{rt} = \frac{1}{2} I \omega^2

    \omega = \sqrt{\frac{2(K.E)_{rt}}{I} }

    \omega = \sqrt{\frac{2(KE)_{rt}}{1/2 mr^2} }

    \omega = \sqrt{\frac{4(K.E)_{rt}}{mr^2} }

    \omega = \sqrt{\frac{4*4.66*10^9J}{19.7kg*(0.351)^2} }

    \omega = 87636.04

    \omega = 8.76*10^4 rad/s

    Since 1 rpm = \frac{2 \pi}{60} rad/s

    \omega = 8.76*10^4(\frac{60}{2 \pi})

    \omega = 836518.38

    \omega = 8.37 *10^5 rpm

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