CLOCKS AND WATCHES

Total Rotational Kinetic Energy?

The hour and minute hands of a tower clock like Big Ben in London are 2.74 m and 4.48m long and have masses of 55.7 kg and 90 kg respectively.

Calculate the total rotational kinetic energy of the two hands about the axis of rotation. Model the hands as long thin rods. Answer in units of J.

The moment of inertia of thin rod rotating rotating around an axis at on of its ends is
I = m·l²/3

The rotational kinetic energy is
E = (1/2) · I · ω²

For the short hand
I = 55.7kg · (2.74m)²/3 = 139.39kgm²
ω = 2·π/(12·3600 s) = 1.4544×10^-4 s^-1
=>
E = 1.47×10^-6 J

For the hour hand
I = 55.7kg · (2.74m)²/3 = 50.87kgm²
ω = 2·π/(12·3600 s) = 1.42×10^-4 s^-1
=>
E = 5.38×10^-7 J

For the minute hand
I = 90kg · (4.48m)²/3 = 134.4kgm²
ω = 2·π/3600 s = 1.745×10^-3 s^-1
=>
E = 2.05×10^-4 J

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