How Do You Calculate the Angular Momentum of Big Ben's Clock Hands?

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SUMMARY

The discussion focuses on calculating the angular momentum of the hour and minute hands of Big Ben, which are 2.64 m and 4.5 m long with masses of 69.4 kg and 94 kg, respectively. The moment of inertia for each hand is calculated using the formula I = (1/3)ML². The correct angular velocities are determined as 1.75E-3 rad/s for the minute hand and 1.45E-4 rad/s for the hour hand, leading to the final angular momentum calculations of approximately 1.110375 kg·m²/s for the minute hand and a similar calculation for the hour hand.

PREREQUISITES
  • Understanding of angular momentum and its calculation.
  • Familiarity with the moment of inertia formula for a rod: I = (1/3)ML².
  • Knowledge of angular velocity conversion from revolutions per second to radians per second.
  • Basic physics concepts related to rotational motion.
NEXT STEPS
  • Study the derivation and applications of the moment of inertia for various shapes.
  • Learn about the principles of rotational dynamics in physics.
  • Explore angular momentum conservation in closed systems.
  • Investigate real-world applications of angular momentum in engineering and mechanics.
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Students studying physics, particularly those focusing on rotational dynamics, as well as educators and anyone interested in practical applications of angular momentum calculations.

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Homework Statement



The hour and minute hands of Big Ben in
London are 2.64 m and 4.5 m long and have
masses of 69.4 kg and 94 kg respectively.

1) Calculate the total angular momentum of
the minute hand about the center point.
Treat the hand as long, thin rod. Treat “into
the clock” as the positive direction.
Answer in units of kg · m2/s.

2) Calculate the total angular momentum of the
hour hand about the center point. Treat the
hand as long, thin rod, and “into the clock”
as the positive direction.
Answer in units of kg · m2/s.


Homework Equations



Inertia about center point for rod is:

I= (1/3)ML^2

Lz=Iw

The Attempt at a Solution



For Minute Hand:

I= (1/3) (94kg) (4.5m)^2 = 634.5 kg*m^2

THen
Lz = Iw = (634.5 kg*m^2) (1/60 rev/s) (2pi rad/rev) = 66.44469 kg*m^2/s

For the Hour hand I should do the same.

For both of these, the system says I am wrong, any help?
 
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I have found my mistake...

The Inertia was right but I needed I did second part wrong.

2pi/3600s = 1.75E-3 rad/s for minute hand
2pi/43200s = 1.45E-4 rad/s for hour hand

then

(624.5kg*m^2)( 1.75E-3 rad/s) = 1.110375 for minute hand and repeat for hour hand.
 

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