Question

A device consisting of four heavy balls connected by low-mass rods is free to rotate about an axle. It is initially not spinning. A small bullet traveling very fast buries itself in one of the balls. In the diagram, m=0.002 kg, v = 400 m/s, M1 = 1.5 kg, M2 = 0.5 kg, R1 = 0.8 m, and R2 = 0.3 m. The axle of the device is at the origin (0,0,0), and the bullet strikes at location (0.247, 0.761,0) m. 

Just after the impact, what is the angular speed of the device? Note that this is an inelastic collision; the system's temperature increases. angular speed (absolute value of the angular velocity) = _______  radians/s

Answer 1

By angular momentum conservation,

final angula momentum = mvr

[2M1R1^2 +2M2R2^2] = mvr

[2*1.5*0.8^2 +2*0.5*0.3^2]*w = 0.002*400*0.761

w = 0.002*400*0.761/[2*1.5*0.8^2 +2*0.5*0.3^2]

= 0.303 rad/s