Physics, 19.07.2020 14:01 sergiogautosg15

How would a spinning disk's kinetic energy change if its moment of inertia was five times larger but its angular speed was five times smaller

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A spinning disk's kinetic energy will change to one-tenth if its moment of inertia was five times larger but its angular speed was five times smaller.

Relation between Kinetic energy and Moment of Inertia:

Rotational kinetic energy is directly proportional to the rotational inertia and the square of the magnitude of the angular velocity.

Now, let's consider moment of inertia = I and angular speed = ω

It is asked that what would be change in Kinetic energy if

moment of inertia = (five times larger)

angular speed = ω/5 (five times smaller)

The kinetic energy of a spinning body is given as:

$K.E.=\frac{1}{2} I. w^2$

On substituting the values, we will get:

$K.E.= \frac{1}{2} (5I) (\frac{w}{5} )^2 \\\\K.E. =\frac{1}{10} I. w^2$

Kinetic energy will be one-tenth to the kinetic energy before its spinning characteristics were changed.

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Answer from: laura52677

The kinetic energy of a spinning disk will be reduced to a tenth of its initial kinetic energy if its moment of inertia is made five times larger, but its angular speed is made five times smaller.

Explanation:

Let us first consider the initial characteristics of the angular motion of the disk

moment of inertia =

angular speed = ω

For the second case, we consider the characteristics to now be

moment of inertia = (five times larger)

angular speed = ω/5 (five times smaller)

Recall that the kinetic energy of a spinning body is given as

$KE = \frac{1}{2}Iw^{2}$

therefore,

for the first case, the K.E. is given as

$KE = \frac{1}{2}Iw^{2}$

and for the second case, the K.E. is given as

$KE = \frac{1}{2}(5I)(\frac{w}{5} )^{2} = \frac{5}{50}Iw^{2}$

$KE = \frac{1}{10}Iw^{2}$

this is one-tenth the kinetic energy before its spinning characteristics were changed.

This implies that the kinetic energy of the spinning disk will be reduced to a tenth of its initial kinetic energy if its moment of inertia is made five times larger, but its angular speed is made five times smaller.

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