Question

A disc has moment of inertia 0.5 kg-m^2. Find the work done to increase its speed from 3 rps to 8 rps​

Answer 1

Given:

A disc has moment of inertia 0.5 kg-m^2.

To find:

Work done to increase its speed from 3 rps to 8 rps.

Calculation:

According to Work Energy Theorem, the total work done is equal to the change in kinetic energy of the body.

$\therefore \: work = \dfrac{1}{2} I {( \omega2)}^{2} - \dfrac{1}{2} I {( \omega1)}^{2}$

$= > \: work = \dfrac{1}{2} I \bigg \{{( \omega2)}^{2} - {( \omega1)}^{2} \bigg \}$

$= > \: work = \dfrac{1}{2} I \bigg \{{(8 \times 2\pi)}^{2} - {(3 \times 2\pi)}^{2} \bigg \}$

$= > \: work = \dfrac{1}{2} I \bigg \{{(16\pi)}^{2} - {(6\pi)}^{2} \bigg \}$

$= > \: work = \dfrac{1}{2} I \bigg \{256 {\pi}^{2} - 36 {\pi}^{2} \bigg \}$

$= > \: work = \dfrac{1}{2} I \bigg \{220 {\pi}^{2} \bigg \}$

$= > \: work = I \bigg \{110 {\pi}^{2} \bigg \}$

$= > \: work = 0.5 \times \bigg \{110 {\pi}^{2} \bigg \}$

$= > \: work = 55 {\pi}^{2} \: joules$

So, final answer is:

$\boxed{ \bf{\: work = 55 {\pi}^{2} \: joules}}$

Answer 2

Explanation:

see above my friend