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
A person is standing on the edge of a circular platform, which is moving with constant angular speed about an axis passi...A uniform thin rod AB is equipped at both ends with the hooks shown and is supported by a frictionless horizontal table....If a solid sphere of mass m is rolling without slipping, velocity of its centre of mass is vcm then its rotational energ...The rotational kinetic energy of a hollow spherical shell is 2.5 J. If its frequency of rotation is made 10 times, then ...A particle of mass 1 kg is moving along the line y = x + 2 (here x and y are in meter) with speed 2 m/sec. The magnitude...