Question

One way to store energy is in the rotational motion of a flywheel, and some have proposed using such technology to power automobiles. one unit is based on a 6.5-\(\rm kg\) flywheel in the shape of a hoop of radius 0.11 \(\rm m\) that spins as fast as 70000 \(\rm rpm\).

Answer 1

Answer:

The store energy is 2113109.72 J.

Explanation:

Given that,

Radius = 0.11 m

Mass = 6.5 kg

Spins = 70000 rpm

Suppose we need to find how much kinetic energy is stored by the flywheel when it is rotating at its maximum rate

We need to calculate the moment of inertia

Using formula of moment of inertia

$I=mr^2$

Put the value into the formula

$I=6.5\times(0.11)^2$

$I=0.07865\ kg-m^2$

We need to calculate the rotational kinetic energy

Using formula of rotational kinetic energy

$K.E=\dfrac{1}{2}I\omega^2$

Put the value into the formula

$K.E=\dfrac{1}{2}\times0.07865\times(70000\times\dfrac{2\pi}{60})^2$

$K.E=2113109.72\ J$

Hence, The store energy is 2113109.72 J.