A flywheel is a solid disk that rotates about an axis that is perpendicular to t

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 360-mile trip in a typical midsize car produces about 1.90 109 J of energy. How fast would a 11-kg flywheel with a radius of 0.31 m have to rotate to store this much energy? Give your answer in rev/min.

Explanation / Answer

The formula for the rotational kinetic energy is
KEr = 1/2*I^2

where I is the moment of inertia and is the angular speed. We are given KEr, if
we knew I, we could solve for . The moment of inertia depends on the shape of
the object, its distribution of mass, and the axis through which it rotates. Since
this requires some calculus to derive from scratch, we must merely look up the
moment of inertia for our objects. For a solid disk rotating through its center,
the moment of inertia is

I = 1/2MR^2

where M is the mass of the disk and R is its radius. In our case:

I = 1/2(11)(0.31)^2
= 0.52855

Plugging that into the definition above we get:

(1.9 * 10^9) = 1/2(0.52855)^2

= 84790.8 rad/s

But we are asked to quote the answer in rev/min. we need to covert the units as:

= (84790.8 rad/1 s) * (60s/1 min) * (1 rev/2*pi*rad)

= 7.99 *10^6 rev/min

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