Answer to Question #195978 in Mechanics | Relativity 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

1.

By law of conservation of energy:

$\frac{I\omega^2}{2}=\frac{mv^2}{2}$