Answer to Question #199683 in Classical Mechanics for Ahmed

Question

Consider a rod of mass 4m and length 2r 

connected to two spheres A and B of identical 

masses m. Balls of mass m fall right above 

sphere A at certain rate that causes the rod 

system to rotate such that, when sphere B 

reaches the position of A it gets hit by a falling 

ball with velocity v. 

 

1 Calculate the angular velocity of the system ωn+1 after it gets hit by ball 

number n in terms of ωn, v and r. 

2 The rotating system reaches ultimately a constant rotational velocity ω0. 

Express ω0 as function of c and r. 

3 How reaching a constant ω0 is still consistent with conservation of energy. 

4 What would be the ultimate rotational velocity ω0 if the rotating system 

includes two roads making a cross shape, and each end is connected to a 

sphere of mass m.

Answer 1

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