Question

A 40 kg flywheel in the form of a uniform circular disc radius 1 m is making 120 revolutions per minute. Calculate the angular momentum

Answer 1

Angular momentum (L) of the disc is 251.42 kg m²/s.

Given:

Mass of the wheel $(m) = 40 kg$

Radius of the disc $(R) = 1 m$

Frequency of the wheel  $(f) = 120 rev/min$

To find:

The angular momentum (L) of the wheel.

Solution:

Step 1

We have been given that the flywheel makes 120 revolutions in 1 minute

Therefore,

No of revolutions made in 1 second  $=\frac{120}{60} = 2rev/sec$  

Hence, the frequency of the wheel is 2

Step 2

Now,

Angular velocity of the wheel ω $=2$πf

Therefore

ω$=2$π($2$)

ω $= 4$π $rad$$/$$s$

Step 3

Now,

We know, Angular momentum of any object is the rotational equivalent of momentum (P) used in linear motion.

Mathematically, it is equal to

$L=R$ × $P$

We know, $P = mv$

$L = mvR$

We know,$v = r$ω

$L = mR^{2}$ω ; or

$L = I$ ω

where, I = moment of inertia

Here, moment of inertia of disc = $\frac{mR^{2} }{2}$

Substituting the given values in the equation, we get

$L =\frac{ 40 (1)^{2}}{2} * 4(\frac{22}{7} )$

$L = 251.42 kg m^{2} /s$

Final answer:

Hence, angular momentum of the disc is $251.42 kg m^{2} /s$.

Answer 2

Answer:

Explanation:

Answer

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Angular momentum (L) of the disc is 251.42 kg m²/s.

Given:

Mass of the wheel  

Radius of the disc  

Frequency of the wheel  

To find:

The angular momentum (L) of the wheel.

Solution:

Step 1

We have been given that the flywheel makes 120 revolutions in 1 minute

Therefore,

No of revolutions made in 1 second    

Hence, the frequency of the wheel is 2

Step 2

Now,

Angular velocity of the wheel ω πf

Therefore

ωπ()

ω π  

Step 3

Now,

We know, Angular momentum of any object is the rotational equivalent of momentum (P) used in linear motion.

Mathematically, it is equal to

×  

We know,  

We know,ω

ω ; or

ω

where, I = moment of inertia

Here, moment of inertia of disc =  

Substituting the given values in the equation, we get

Final answer:

Hence, angular momentum of the disc is .