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Sagot :
Answer:
6.5 rad/s
11.695 kJ
Explanation:
Using the principle of conservation of momentum, we have
L1 = L2 and
I1w1 = I2w2, with I being the moment of inertia and w being the angular velocity.
w1 = 0.4 rev/s = 0.4 * 2π = 2.51 rad/s
Moment of Inertia, I = ½MR² + mr²
I1 = ½ * 73 * 2.5² +99 * 2.5²
I1 = 73 * 3.125 + 99 * 6.25
I1 = 228.125 + 618.75
I1 = 846.875 kgm²
The man has been said to have walked 1 m away from his position, so then
I2 = ½ * 73 * 2.5² + 99 * 1²
I2 = 228.125 + 99
I2 = 327.125 kgm²
From the formula stated above,
w2 = I1w1 / I2
w2 = (846.875 * 2.51) / 327.125
w2 = 2125.65725 / 327.125 rad/s
w2 = 6.5 rad/s
2
K = Iw²
K = 846.875 * 2.51²
K = 2125.65725 J
K'= Iw²
K' = 327.125 * 6.5²
K' = 13821.03125 J
Change in energy is given as, K' - K, so that
Energy, E = 13821.03125 - 2125.65725
Energy, E = 11.695 kJ
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