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A circular disk of moment of inertia I(t...

A circular disk of moment of inertia `I_(t)` is rotating in a horizontal plane , about its symmetry axis , with a constant angular speed `omega_(i)` . Another disk of moment of inertia `I_(b)` is dropped coaxially onto the rotating disk . Initially the second disk has zero angular speed . eventually both the disks rotate with a constant angular speed `omega_f` . The energy lost by the initially rotating disc to friction is

A

`(1)/(2) (I_(b)^(2))/((I_(t) + I_(b))) omega_(i)^(2)`

B

`(1)/(2) (I_(t)^(2))/((I_(i) + I_(b)))"" omega_(i)^(2)`

C

`(I_(b) - I_(t))/((I_(t) + I_(b))) "" omega_(i)^(2)`

D

`(1)/(2) (I_(b) I_(t))/((I_(t) + I_(b))) "" omega_(i)^(2)`

Text Solution

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A circular disc of moment of inertia I_(t) is rotating in a horizontal plane about its symmetry axis with a constant angular velocity omega_(i) . Another disc of moment of inertia I_(b) is dropped co-axially onto the rotating disc. Initially, the second disc has zero angular speed. Eventually, both the discs rotate with a constant angular speed omega_(f) . Calculate the energy lost by the initially rotating disc due to friction.

A disc of moment of inertia I_(1) is rotating freely with angular speed omega_(1) when another non-rotating disc of moment of inertia I_(2) is dropped on it. The two discs then rotate as one unit. Find the final angular speed.

Knowledge Check

  • A disc of the moment of inertia 'l_(1)' is rotating in horizontal plane about an axis passing through a centre and perpendicular to its plane with constant angular speed 'omega_(1)' . Another disc of moment of inertia 'I_(2)' . having zero angular speed is placed discs are rotating disc. Now, both the discs are rotating with constant angular speed 'omega_(2)' . The energy lost by the initial rotating disc is

    A
    `1/2[(l_(1) + l_(2))/(l_(1)l_(2))]omega_(1)^(2)`
    B
    `1/2[(l_(1) l_(2))/(l_(1)-l_(2))]omega_(1)^(2)`
    C
    `1/2[(l_(1)-l_(2))/(l_(1)l_(2))]omega_1^(2)`
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    `1/2[(l_(2)l_(2))/(l_(1) + l_(2))]omega_(1)^(2)`

  • A disk with moment of inertia I_1 rotates about frictionless, vertical axle with angular speed omega_i A second disk, this one having moment of inertia I_2 and initial not rotating, drops onto the first disk (Fig.) Because of friction between the surfaces, the two eventually reach the same angular speed omega_f . The value of omega_f is. .

    A
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    B
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