Answer: 895.85 x 10^-6 J or 8.96 x 10^-4 J
Explanation:
Angular kinetic energy E in Joules
E = ½Iw^2
W is angular velocity in radians/sec
1 radian/sec = 9.55 rev/min
I is moment of inertia in kgm^2
I = cMR^2
M is mass (kg), R is radius (meters)
c = 1/3 for a rod around its end, R = length
For minute hand
I = (1/3)(90)(4.44)^2 = 0.33 x 90 x 19.7136 = 585.49
w= 1 rev/hour = 1 rev/3600sec = 2pi/ 3600 = pi/1800 rad/s
KE = 1/2(1/3)(90)(4.44)^2(pi/1800)^2 = 0.5 x 0.33 x 90 x 19.7136 x 3.05 x 10^-6
KE = 0.00089 J
For hour hand
I = (1/3)(58.2)(2.79)^2 = 0.33 x 58.2 x 2.79^2 = 149.5
w = 1 rev/12hour = 1 rev/(12x3600sec) = 2pi/ 12x3600 = pi/21600 rad/s
KE = 1/2(1/3)(90)(4.44)^2(pi/21600)^2 = 0.5 x 0.33 x 90 x 19.7136 x 2.12 x 10^-8
KE = 5.85 x 10^-6 J
Therefore total kinetic energy = 895.85 x 10^-6 J
