Question

44. The diameter of a disc is 1m. It has a mass of
20kg. It is rotating about its axis with a speed
of 120rotations in one minute. Its angular
momentum in kg m/s is​

Answer 1

Answer:

44. The diameter of a disc is 1m. It has a mass of

20kg. It is rotating about its axis with a speed

of 120rotations in one minute. Its angular

momentum in kg m/s is

Answer 2

Given :

• The diameter of a disc = 1m

• Mass=20kg

• It is rotating about its axis with a speed of 120 rotations in one minute.

To Find :

• The value of angular momentum in kgm/s=?

Formula :

• Moment of inertia of flywheel about its axis is :

$\\ \red\bigstar\boxed{\sf{I=\dfrac{1}{2}mr^{2}}}$

• Angular speed :

$\\ \red\bigstar\boxed{\sf{ \omega =\dfrac{ 2 \pi N}{60} }}$

•Angular Momentum :

$\\ \red\bigstar\boxed{\sf{L= I \omega}}$

Solution :

• Moment of inertia of flywheel about its axis is

$\sf{\dfrac{1}{2}m r^{2}}$

Where, r is the radius of flywheel.

$\\ \implies\sf{I=\dfrac{1}{2}m r^{2}}$

$\\ \implies\sf{I=\dfrac{1}{2} \times 20kg \times \bigg(\dfrac{1}{2} m \bigg)^{2}}$

$\\ \implies\sf{I=10 kg \times \dfrac{1}{4}m^{2}}$

$\\ \implies\sf{I=2.5kgm^{2}}$

$\\ \pink\bigstar\boxed{\sf{Moment \: of \: inertia \: about \: its \: axis =2.5 kgm^{2}}}$

•Angular speed is

$\sf{ \omega = \dfrac{2 \pi N}{60}}$

$\\ \implies\sf{ \omega =\dfrac{2 \pi \times 120}{60}}$

$\\ \implies\sf{ \omega= 2 \pi \times 2}$

$\\ \implies\sf{ \omega=4 \pi rad/s}$

Now, Angular momentum is

$\sf{L=I \omega}$

$\\ \implies\sf{L=I \omega }$

$\\ \implies\sf{L=2.5kg m^{2} \times 4 \pi rad/s}$

$\\ \implies\sf{L=10 \pi kgm^{2}/s}$

$\\ \implies\sf{L=10 \times 3.14 kgm^{2}/s}$

$\\ \implies\sf{L=31.4 kgm^{2}/s}$

Hence,The value of angular momentum is 31.4 kgm²/s