Rotational MotionHard
Question
A circular disk of moment of inertia It is roatating in a horizontal plane, about the symmetry axis, another disc of moment of inertia Ib is dropped coaxially onto the rotatating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed ωf. The energy lost by the initially rotating disc to friction is
Options
A.
B.
C.
D.
Solution
As no external torque is applied to the system, the angular momentum of the system remains conserved.
∴ Lf = Lf
According to given problem,
Itωi = (It + Ib)ωf
or, ωf =
.......(i)
Initial energy, Ei =
Ttωi2 .......(ii)
Final energy, Ef = (It + Ib)ωf2 .......(iii)
Substituting the value of ωf from the equation (i) in equation (iii), we get
Final Energy, Ef = (It + Ib)
.......(iv)
Loss Energy. ᐃE = Ei - Ef
[Using (ii) and (iv)]
∴ Lf = Lf
According to given problem,
Itωi = (It + Ib)ωf
or, ωf =
.......(i)Initial energy, Ei =
Ttωi2 .......(ii)Final energy, Ef =
(It + Ib)ωf2 .......(iii)Substituting the value of ωf from the equation (i) in equation (iii), we get
Final Energy, Ef =
(It + Ib) .......(iv)Loss Energy. ᐃE = Ei - Ef
[Using (ii) and (iv)]Create a free account to view solution
View Solution FreeMore Rotational Motion Questions
When a mass is rotating in a plane about a fixed point, its angular momentum is directed along:...A non uniform rod OA of liner mass density λ = λ0x (λ0 = co nst.) is suspended from ceiling with hinge jo...Two loops P and Q are made from a uniform wire. The radii of P and Q are r1 and r2 respectively, and their moments of in...Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm . Wh...In the above question, the change in angular momentum of disc in first 2 seconds in Nm second will be -...