How Is the Angular Momentum of a Clock's Second Hand Calculated?

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SUMMARY

The angular momentum of a clock's second hand is calculated using the formula L = I(omega), where I is the moment of inertia and omega is the angular velocity. For a slender rod, the moment of inertia is given by I = (1/3)ML². In this case, with a length of 0.15m and a mass of 0.006kg, the moment of inertia is 0.000135 kg m². The angular velocity, calculated as 0.10472 rad/s, leads to an angular momentum of approximately 0.0000141372 kg m²/s.

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[SOLVED] Angular Momentum

Homework Statement



Find the magnitude of the angular momentum of the second hand on a clock about an axis through the center of the clock face. The clock hand has a length of 15.0cm and a mass of 6.00g. Take the second hand to be a slender rod rotating with constant angular velocity about one end.


The Attempt at a Solution



Clock hand: 15.0 cm --> .15m
Mass: 6.00 g --> .006kg

L=I(omega)

To get omega:
The second hand does one revolution in 60seconds.

so 1/60 = .01667 rev/s --> .10472 rad/s

To get I:

I = 1/3 ML^2

I = (.006)(.15)^2 = .000135

Now that we got I and omega,

L = (.000135)(.10472)
L = .0000141372

I would have thought that this procedure would have been right, but I got it incorrect.

Final Answer: L= _________ kg m^2/s

Please and thank you. :smile:
 
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Heat said:
To get I:

I = 1/3 ML^2

I = (.006)(.15)^2 = .000135
You forgot to multiply by 1/3.
 
you have good eye. Thank you for your help. :)
 

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