A man sits on a swivel chair holding two 3 kg weights with his arms outstretched

Question

A man sits on a swivel chair holding two 3 kg weights with his arms outstretched. He is initially rotating at 4 radians/sec in the position shown where L = 1 m. He then draws the weights towards his chest where L = 0.2 m. Assume the man weighs 75 kg and has a radius of gyration about the z-axis of 0.15 m. Neglect the mass of his arms, assume the weights to be perfect spheres with a radius of 0.1 m, and assume there is no friction in the swivel chair. Find the angular velocity after he draws the weights inward toward his chest. (hint: use the conservation momentum) How much work has he done?

Explanation / Answer

a> Angular momentum remains constant. So, initially, I_initial(moment of intertia) = M_1K^2 + 2*M_2(2/5R^2 + D^2)

M_1 = 75, K = 0.15, M_2 = 3, R = 0.1, D = 1m

Final I_final = M_1K^2 + 2*M_2(2/5R^2 + D'^2)

M_1 = 75, K = 0.15, M_2 = 3, R = 0.1, D' = 0.2m

I_initial * w_initial = I_final*w_final => w_final = 30.85/1.95 = 15.82rad/sec

b> work done = 1/2(I_final*w_final^2 - I_initial*w_initial^2) = 182.33J

This is a detailed solution and deserves 5 stars

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