Question

the hour hand and minute hand for the famous parliament clock tower big ben in london are 2.7 and 4.5 m long and have masses of 60kg and 100 kg. Determine the total rotational kineti cenergy of these hands

Answer 1

Answer:

0.00102 J

Explanation:

h denotes hour hand

m denotes minute hand

Mass of hour hand = 60 kg

Mass of minute hand = 100 kg

Length of hour hand = 2.7 m

Length of minute hand = 4.5 m

Angular velocity is given by

$\omega_h=\dfrac{2\pi}{12\times 60\times 60}$

$\omega_m=\dfrac{2\pi}{60\times 60}$

Moment of inertia is given by

$I_h=\dfrac{mL^2}{3}\\\Rightarrow I_h=\dfrac{60\times 2.7^2}{3}\\\Rightarrow I_h=145.8\ kgm^2$

$I_m=\dfrac{mL^2}{3}\\\Rightarrow I_m=\dfrac{100\times 4.5^2}{3}\\\Rightarrow I_m=675\ kgm^2$

Total kinetic energy is given by

$K=\dfrac{1}{2}(I_h\omega_h^2+I_m\omega_m^2)\\\Rightarrow K=\dfrac{1}{2}(145.8\times (\dfrac{2\pi}{12\times 60\times 60})^2+675(\dfrac{2\pi}{60\times 60})^2)\\\Rightarrow K=0.00102\ J$

The total kinetic energy of the system is 0.00102 J

Answer 2

The total rotational kinetic energy is mathematically given as

K=0.00102 J

What is the total rotational kinetic energy of their hands?

Question Parameters:

the famous parliament clock tower big ben in London are 2.7 and 4.5 m long and have masses of 60kg and 100 kg.

Generally, the equation for the  Moment of inertia is mathematically given

as

$I_h=\dfrac{mL^2}{3}i\\\\I_h=\dfrac{60\times 2.7^2}{3}$

I_h=145.8  kgm^2

Also the minute hand

$I_m=\dfrac{100\times 4.5^2}{3}$

I_m=675 kgm^2

In conclusion, kinetic energy is

$K=\frac{1}{2}(I_h\omega_h^2+I_m\omega_m^2\\\\ K=\frac{1}{2}(145.8\times (\frac{2\pi}{12\times 60\times 60})^2+675(\frac{2\pi}{60\times 60})^2)$

K=0.00102 J

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