A child is spinning on a bar stool waiting for his brother to get off work. He s

Q: A child is spinning on a bar stool waiting for his brother to get off work. He s

A) L1 = I1*w1 = 3.24*5.87 = 19.02 kg.m^2/s B) I2 = I1 + m*r^2 = 3.24 + 2.27*0.2^2 = 3.331 kg.m^2 C) L1 = L2 I1*w1 = I2*w2 w2 = I1*w1/I2 = 19.02/3.331 = 5.71 rad/s D) Ki = 0.5*I1*w1^2 = 0.5*3.24*5.87^2 = 55.82 J Kf = 0.5*I2*w2^2 = 0.5*3.331*5.71^2 = 54.3 J

ID: 1296818 • Letter: A

Question

A child is spinning on a bar stool waiting for his brother to get off work. He spins with his arms out and his moment (kid and chair) of inertia is 3.24 kg m^2. His initiall angular velocity spinning in the chair is 5.87 rad/s. His brother is ready to leave and tosses the child a 2.27 kg bag of change. the child catches the bag of change while spinning and holds it at a distance of .20m from his axis of rotation. Treat the bag of change as a point particle.

A: What is the initial angular momentum of the system?

B: What is the final moment of Inertia of the system?

C: What is the final angular velocity of the system?

D: Find the initial and final kinetic energies of the system?

Explanation / Answer

A) L1 = I1*w1

= 3.24*5.87

= 19.02 kg.m^2/s

B) I2 = I1 + m*r^2

= 3.24 + 2.27*0.2^2

= 3.331 kg.m^2

C) L1 = L2

I1*w1 = I2*w2

w2 = I1*w1/I2

= 19.02/3.331

= 5.71 rad/s

D) Ki = 0.5*I1*w1^2

= 0.5*3.24*5.87^2

= 55.82 J

Kf = 0.5*I2*w2^2

= 0.5*3.331*5.71^2

= 54.3 J

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