Big Ben, the nickname for the clock in Elizabeth Tower (named after the Queen in

Question

Big Ben, the nickname for the clock in Elizabeth Tower (named after the Queen in 2012) in London, has an hour hand 2.70 m long with a mass of 60.0 kg and a minute hand 4.50 m long with a mass of 100 kg (figure). Calculate the total Rotational kinetic energy of the two hands about the axis of rotation. (You may model the hands as long, thin rods rotates about one end. Assume the hour and minute hands are rotating at a constant rate of one revolution per 12 hours and 60 mmutes. respectively.) Your response differs from the correct answer by more than 100%. J

Explanation / Answer

(Converted) Angular Speed of Clock Hands:

Hour Hand 1.45104 rad/s1.45104 rad/s

Minute Hand 1.75103 rad/s1.75103 rad/s

Rotational Moment of Inertia:

Hour Hand I=1/3(60 kg)(2.70 m)2=145.8 kgm2

Minute Hand I=1/3(100 kg)(4.50 m)2 =675 kgm2

Rotational Kinetic Energy:

Krot=1/2(145.8 kgm2)(1.45104 rad/s)2+1/2(675 kgm2)(1.75103 rad/s)2

=0.0001035J

=1.03x10^-4J

So Rotational kinetic energy is 1.03x10^-4 J Ans

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