29- Big Ben, the Parliament tower clock in London, has an hour hand 2.70 m long
ID: 2250635 • Letter: 2
Question
29-Big Ben, the Parliament tower clock in London, has an hour hand 2.70 m long with a mass of 300 kg, and a minute hand 4.20 m long with a mass of 100 kg (see figure below). Calculate the total rotational kinetic energy of the two hands about the axis of rotation. (You may model the hands as long, thin rods rotated about one end. Assume the hour and minute hands are rotating at a constant rate of one revolution per 12 hours and 60 minutes, respectively.)
29-Big Ben, the Parliament tower clock in London, has an hour hand 2.70 m long with a mass of 300 kg, and a minute hand 4.20 m long with a mass of 100 kg (see figure below). Calculate the total rotational kinetic energy of the two hands about the axis of rotation. (You may model the hands as long, thin rods rotated about one end. Assume the hour and minute hands are rotating at a constant rate of one revolution per 12 hours and 60 minutes, respectively.)Explanation / Answer
ang. velocity of hour hand = 1 rev/12 hr = [2xPi /12x3600 ] rad/s= 1.454 x 10^(-4) rad/s
ang. velocity of min. hand = 1 rev/ 1hr= [2xPi/3600]rad/s = 1.745 x 10^(-3) rad/s
Kinetic energy
=[0.5x(I of hr. hand) x (ang. velocity^2) ]+[0.5x(I of min. hand) x (ang. velocity^2) ]
I = m(L^2)/3 for both hands.
I of hr. hand = 300 x (2.7^2)/3 = 729 kg m^2
I of min. hand = 100 x (4.2^2)/3= 588 kg m^2
Kinetic Energy = [0.5 x 729 x(1.454^2) x 10^(-8) ]+[0.5 x 588 x(1.745^2) x 10^(-6) ]
=7.7 x 10^(-6) + 895.24 x 10^(-6)
= 902.94 x 10^(-6) J
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