Rotational Motion Question 216

Question: A horizontal turn table in the form of a disc of radius r carries a gun at G and rotates with angular velocity ω0 about a vertical axis passing through the centre O. The increase in angular velocity of the system if the gun fires a bullet of mass m with a tangential velocity v with respect to the gun is (moment of inertia of gun + table about 0 is I0 )

Options:

A) mvrI0+mr2

B) 2mvrI0

C) v2r

D) mvr2I0

Show Answer

Answer:

Correct Answer: A

Solution:

[a] Given that I0 is the moment of inertia of table and gun and m the mass of bullet.

Initial angular momentum of system about centre

Li(I0+mr2)ω0 - (i) Let w be the nagular velocity of table after the bullet is fired.

Final angular momentum

Lf=(I0ωm(vrω))r. - (ii) Where (vrω) is absolute velocity of bullet to the right.

Equations (i) and (ii);

we get (ωω0)=mvrI0+mr2



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